International Journal of Robust and Nonlinear Control, Jul 16, 2009
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
A Multi-hop Control Network (MCN) consists of a plant where the communication between sensor, act... more A Multi-hop Control Network (MCN) consists of a plant where the communication between sensor, actuator and computational unit is supported by a wireless multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. We address the problem of characterizing controllability and observability of a MCN, by means of necessary and sufficient conditions on the plant dynamics and on the communication scheduling and routing. We provide a methodology to design scheduling and routing, in order to satisfy controllability and observability of a MCN for any fault occurrence in a given set of failures configurations.
Given a wireless network and a graph modelling the node connection topology, we address the probl... more Given a wireless network and a graph modelling the node connection topology, we address the problem of fault diagnosis of nodes. When the external point of access to network information is at a lower layer of the ISO/OSI protocol stack, the problem is trivial. However, as often occurs, a user is able to access the network at the application layer : this implies that the available observation of the network status is considerably restricted, and solving the diagnosis problem is not trivial. In this paper, we state necessary and sufficient conditions for being able to detect which node is faulty, and propose a diagnosis algorithm on the basis of diagnosability definitions and theoretical studies developed for timed and hybrid automata in the computer science community.
The communication protocol IEEE 802.15.4 is becoming pervasive for low power and low data rate wi... more The communication protocol IEEE 802.15.4 is becoming pervasive for low power and low data rate wireless sensor networks (WSNs) applications, including control and automation. Nevertheless, there is not yet any adequate study about control systems networked by this protocol. In this paper, the stability of IEEE 802.15.4 networked control systems (NCSs) is addressed. While in recent works fundamental results are developed for networks that are abstracted only in terms of packet loss and time delays, here the constraints imposed by the protocol to the feedback channel and the network energy consumption are explicitly considered. A general analysis for linear systems with parameter uncertainty and external bounded disturbances with control loops closed over IEEE 802.15.4 networks is proposed. To reduce the number of transmissions and thus save energy, a self-triggered control strategy is used. A sufficient stability condition is given as function of both the protocol and control parameters. A decentralized algorithm to adapt jointly the self-triggered control and the protocol parameters is proposed. It is concluded that stability is not always guaranteed unless protocol parameters are appropriately tuned, and that event-triggered control strategies may be difficult to use with the current version of IEEE 802.15.4.
In the last few years there has been a growing interest in the use of symbolic models for the for... more In the last few years there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems. Symbolic models are abstract descriptions of continuous systems where one symbol corresponds to an "aggregate" of continuous states. In this paper we face the problem of deriving symbolic models for nonlinear control systems affected by disturbances. The main contribution of this paper is in proposing symbolic models that can be effectively constructed and that approximate nonlinear control systems affected by disturbances in the sense of alternating approximate bisimulation.
Secure state estimation is the problem of estimating the state of a dynamical system from a set o... more Secure state estimation is the problem of estimating the state of a dynamical system from a set of noisy and adversarially-corrupted measurements. Intrinsically a combinatorial problem, secure state estimation has been traditionally addressed either by brute force search, suffering from scalability issues, or via convex relaxations, using algorithms that can terminate in polynomial time but are not necessarily sound. In this paper, we present a novel algorithm that uses a satisfiability modulo theory approach to harness the complexity of secure state estimation. We leverage results from formal methods over real numbers to provide guarantees on the soundness and completeness of our algorithm. Moreover, we discuss its scalability properties, by providing upper bounds on the runtime performance. Numerical simulations support our arguments by showing an order of magnitude decrease in execution time with respect to alternative techniques. Finally, the effectiveness of the proposed algorithm is demonstrated by applying it to the problem of controlling an unmanned ground vehicle. Y. Shoukry and P. Tabuada are with the Electrical Engineering Department, UCLA,
Secure state estimation is the problem of estimating the state of a dynamical system from a set o... more Secure state estimation is the problem of estimating the state of a dynamical system from a set of noisy and adversarially-corrupted measurements. Intrinsically a combinatorial problem, secure state estimation has been traditionally addressed either by brute force search, suffering from scalability issues, or via convex relaxations, using algorithms that can terminate in polynomial time but are not necessarily sound. In this paper, we present a novel algorithm that uses a satisfiability modulo theory approach to harness the complexity of secure state estimation. We leverage results from formal methods over real numbers to provide guarantees on the soundness and completeness of our algorithm. Moreover, we discuss its scalability properties, by providing upper bounds on the runtime performance. Numerical simulations support our arguments by showing an order of magnitude decrease in execution time with respect to alternative techniques. Finally, the effectiveness of the proposed algorithm is demonstrated by applying it to the problem of controlling an unmanned ground vehicle.
The paper introduces a new detectability concept for continuous-time Markov jump linear systems w... more The paper introduces a new detectability concept for continuous-time Markov jump linear systems with finite Markov space that generalizes previous concepts found in the literature. The detectability in the weak sense is characterized as mean square detectability of a certain related stochastic system, making both detectability senses directly comparable. The concept can also ensure that the solution of the coupled algebraic Riccati equation associated to the quadratic control problem is unique and stabilizing, making other concepts redundant. The paper also obtains a set of matrices that plays the role of the observability matrix for deterministic linear systems, and it allows geometric and qualitative properties. Tests for weak observability and detectability of a system are provided, the first consisting of a simple rank test, similar to the usual observability test for deterministic linear systems.
This paper addresses the solution of large zero-sum matrix games using randomized methods. We for... more This paper addresses the solution of large zero-sum matrix games using randomized methods. We formalize a procedure, termed as the sampled security policy (SSP) algorithm, by which a player can compute policies that, with a high confidence, are security policies against an adversary using randomized methods to explore the possible outcomes of the game. The SSP algorithm essentially consists of solving a stochastically sampled subgame that is much smaller than the original game. We also propose a randomized algorithm, termed as the sampled security value (SSV) algorithm, which computes a high-confidence security-level (i.e., worst-case outcome) for a given policy, which may or may not have been obtained using the SSP algorithm. For both the SSP and the SSV algorithms we provide results to determine how many samples are needed to guarantee a desired level of confidence. We start by providing results when the two players sample policies with the same distribution and subsequently extend these results to the case of mismatched distributions. We demonstrate the usefulness of these results in a hide-and-seek game that exhibits exponential complexity.
We consider the modeling, stability analysis and controller design problems for discrete-time LTI... more We consider the modeling, stability analysis and controller design problems for discrete-time LTI systems with state feedback, when the actuation signal is subject to switching propagation delays, due to e.g. the routing in a multi-hop communication network. We show how to model these systems as regular switching linear systems and, as a corollary, we provide an (exponential-time) algorithm for robust stability analysis. We also show that the general stability analysis problem is NP-hard in general. Even though the systems studied here are inherently switching systems, we show that their particular structure allows for analytical understanding of the dynamics, and even efficient algorithms for some problems: for instance, we give an algorithm that computes in a finite number of steps the minimal look-ahead knowledge of the delays necessary to achieve controllability. We finally show that when the switching signal cannot be measured it can be necessary to use nonlinear controllers for stabilizing a linear plant.
This work discusses the design of a networked traffic control scheme. We refer to the Grenoble So... more This work discusses the design of a networked traffic control scheme. We refer to the Grenoble South Ring traffic system, as case study, in which the control actions are computed in a control centre far from the traffic system and then sent, through a wireless communication channel, to the actuators placed along the road, i.e. on-ramp traffic lights in the considered case of ramp metering control. The communication channel is affected by delays and packet loss. In order to counteract the effects due to the transmission of the variable over the communication channel, we suggest to adopt a model predictive control (MPC) strategy based on the use of a buffer. Moreover, in order to limit the computational burden and improve the effectiveness of the proposal, the length of the optimization horizon of the predictive control algorithm, and, consequently, the buffer length, is updated relying on a delay estimation. The performances of the proposed approach are assessed in simulation relying on a traffic model the parameters of which are identified using data produced by a commercial microscopic simulator of the Grenoble South Ring traffic system. The capabilities of the considered control scheme when the system parameters vary and the transmitted signals are affected by time delays are highlighted.
Markov jump switched linear systems (MJSLSs) are switched linear systems, where a switching signa... more Markov jump switched linear systems (MJSLSs) are switched linear systems, where a switching signal is governed by a Markov decision process. We consider a polytopic timeinhomogeneous setting, where the transition probabilities (between the operational modes of the system) associated to each discrete action are varying over time, with variations that are arbitrary within a polytopic set. We present and solve for this class of systems the finite horizon optimal control problem.
In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalenc... more In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalence of stochastic external behavior for the class of discrete-time stochastic linear control systems with possibly degenerate normally distributed disturbances. The first notion is inspired by the notion of probabilistic bisimulation for probabilistic chains while the second one by the notion of equivalence of external behavior for (nonstochastic) behavioral systems. Geometric necessary and sufficient conditions for checking these notions are derived. Model reduction via Kalman-like decomposition is also proposed. Connections with stochastic linear realization theory and stochastic reachability are established.
ERC-2014-StG CHAMELEON: A platform for modelling, design, simulation and verifiCation of HierAr... more ERC-2014-StG CHAMELEON: A platform for modelling, design, simulation and verifiCation of HierArchical distributed control systeMs over hEtErogeneous cOmmunication Networks SIR-2014 FLASH: A platform for design of distributed automation systems over heterogeneous networks Group, scientific collaborations and projects Objective: control over wireless networks Controller Challenge: close the loop taking into account the communication protocol Challenge: close the loop taking into account the communication protocol
IEEE Transactions on Intelligent Transportation Systems, 2021
The paper investigates the possibility of using macroscopic information to improve control perfor... more The paper investigates the possibility of using macroscopic information to improve control performance of a vehicular platoon composed of autonomous vehicles. A mesoscopic traffic modeling framework is proposed, and closed loop String Stability is achieved by exploiting Input-to-State Stability (ISS) for the analysis of the platoon. Examples of mesoscopic control laws are illustrated and simulations show the effectiveness of our approach in ensuring String Stability and improving the platoon behavior.
In this paper, we propose a definition of equivalence via stochastic bisimulation for the class o... more In this paper, we propose a definition of equivalence via stochastic bisimulation for the class of discretetime stochastic linear control systems with possibly degenerate normally distributed disturbances. The notion is inspired by the notion of probabilistic bisimulation for probabilistic chains. Geometric necessary and sufficient conditions for checking this notion are derived. Model reduction via Kalman-like decomposition is also proposed. Connections with stochastic reachability are discussed and with finite horizon stochastic safety problems established. A discussion on the use of stochastic bisimulation equivalence for control design is given, and an application to optimal control problems with stochastic reachability specifications is finally presented.
The paradigm of Cyber-Physical Systems of Systems (CPSoS) is becoming rather popular in the contr... more The paradigm of Cyber-Physical Systems of Systems (CPSoS) is becoming rather popular in the control systems research community because of its expressive power able to properly handle many engineered complex systems of interest. Decentralized control techniques offer a promising approach in taming the inherent complexity of CPSoS, also connected with the design of needed communication infrastructures and computing units. In this paper, we propose decentralized control of networks of discrete-time nonlinear control systems, enforcing complex specifications expressed in terms of regular languages, within any desired accuracy. As discussed in the paper, regular languages, while being traditionally studied in the research community of discrete-event systems, also provide a useful mean to model a rather wide variety of complex specifications for control systems. The design of decentralized controllers is based on formal methods and in particular, on the use of discrete abstractions. Efficient synthesis of such controllers is derived by resorting to on-the-fly algorithmic techniques that also allow the use of parallel computing architectures. Advantages and disadvantages of the decentralized approach over a centralized one, also in terms of computational complexity, are discussed. An illustrative example is presented, which shows the applicability and effectiveness of the results proposed.
The transition probabilities of jumps between operational modes of discrete-time Markov(ian) jump... more The transition probabilities of jumps between operational modes of discrete-time Markov(ian) jump linear systems (dtMJLSs) are generally considered to be time-invariant, certain, and often completely known in the majority of dedicated studies. Still, in most real cases the transition probability matrix (TPM) cannot be computed exactly and is time-varying. In this article, we take into account the uncertainty and time-variance of the jump parameters by considering the underlying Markov chain as polytopic and time-inhomogeneous, i.e., its TPM is varying over time with variations that are arbitrary within a polytopic set of stochastic matrices. We show that the conditions used for time-homogeneous dtMJLSs are not enough to ensure the stability of the time-inhomogeneous system, and that perturbations on values of the TPM can make a stable system unstable. We present necessary and sufficient conditions for mean square stability (MSS) of polytopic time-inhomogeneous dtMJLSs, prove that deciding MSS on such systems is NP-hard and that MSS is equivalent to exponential MSS and to stochastic stability. We also derive necessary and sufficient conditions for robust MSS of dtMJLSs affected by polytopic uncertainties on transition probabilities and bounded disturbances.
Context: Cyber-physical systems (CPS) are integrations of computation, networking, and physical p... more Context: Cyber-physical systems (CPS) are integrations of computation, networking, and physical processes. Due to the tight cyberphysical coupling and to the potentially disrupting consequences of failures, security is one of the primary concerns for this type of systems. CPS security is attracting several research efforts from different and independent areas (e.g., secure control, intrusion detection in SCADA systems, etc.), each of them with specific peculiarities, features, and capabilities, resulting in a considerably variegated and complex scientific body of knowledge on the topic. Objective: In this study we aim at identifying, classifying, and analyzing existing research on CPS security in order to better understand how security is actually addressed when dealing with cyber-physical systems. Based on this analysis of the state of the art, we also aim at identifying the implications for future research on CPS security. Method: In order to achieve this, we designed and conducted a systematic mapping study to identify, classify, and compare relevant studies proposing a method or technique for cyber-physical systems security. A comparison framework for classifying methods or techniques for CPS security has been empirically defined; identified relevant studies have been classified on the basis of publication trends, their characteristics and focus, and their validation strategies. Results: We selected a total of 118 primary studies as a result of the systematic mapping process. From the collected data we can observe that (i) even if solutions for CPS security has emerged only recently, in the last years they are gaining a sharply increasing scientific interest across heterogeneous publication venues; (ii) the bulk of the works on security for cyber-physical systems is focused on power grids, and the approaches considering attacks on sensors and their protection completely dominate the scene; regardless of application field and considered system components, all the works on CPS security deal with attacks, in order to either implement or to counteract them, and putting together all this studies gives us the possibility to categorize the existing (cyber-physical) attack models; it comes as surprise that very few papers consider communication aspects or imperfections and attempt to provide non-trivial mathematical models of the communication; (iii) most advanced and realistic validation methods have been exploited in the power networks application domain, but even there a benchmark is still missing. Conclusion: The systematic map of research on CPS security provided here is based on, for instance, application fields, various system components, related algorithms and models, attacks characteristics and defense strategies. This work presents a powerful comparison framework for existing and future research on this hot topic, important for both industry and academia.
In this paper we investigate the exploitation of redundancy when routing actuation data to a disc... more In this paper we investigate the exploitation of redundancy when routing actuation data to a discrete-time LTI system connected to the controller via a wireless network affected by packet drops. We assume that actuation packets can be delivered from the controller to the actuator via multiple paths, each associated with a delay and a packet loss probability. We show that the joint design of controller gain and routing redundancy exploitation can tremendously improve the control performance. To achieve this goal we set up and solve a LQR problem for a class of systems that extends discrete-time Markov Jump Linear Systems, in that both continuous and discrete control signals can be actuated.
International Journal of Robust and Nonlinear Control, Jul 16, 2009
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
A Multi-hop Control Network (MCN) consists of a plant where the communication between sensor, act... more A Multi-hop Control Network (MCN) consists of a plant where the communication between sensor, actuator and computational unit is supported by a wireless multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. We address the problem of characterizing controllability and observability of a MCN, by means of necessary and sufficient conditions on the plant dynamics and on the communication scheduling and routing. We provide a methodology to design scheduling and routing, in order to satisfy controllability and observability of a MCN for any fault occurrence in a given set of failures configurations.
Given a wireless network and a graph modelling the node connection topology, we address the probl... more Given a wireless network and a graph modelling the node connection topology, we address the problem of fault diagnosis of nodes. When the external point of access to network information is at a lower layer of the ISO/OSI protocol stack, the problem is trivial. However, as often occurs, a user is able to access the network at the application layer : this implies that the available observation of the network status is considerably restricted, and solving the diagnosis problem is not trivial. In this paper, we state necessary and sufficient conditions for being able to detect which node is faulty, and propose a diagnosis algorithm on the basis of diagnosability definitions and theoretical studies developed for timed and hybrid automata in the computer science community.
The communication protocol IEEE 802.15.4 is becoming pervasive for low power and low data rate wi... more The communication protocol IEEE 802.15.4 is becoming pervasive for low power and low data rate wireless sensor networks (WSNs) applications, including control and automation. Nevertheless, there is not yet any adequate study about control systems networked by this protocol. In this paper, the stability of IEEE 802.15.4 networked control systems (NCSs) is addressed. While in recent works fundamental results are developed for networks that are abstracted only in terms of packet loss and time delays, here the constraints imposed by the protocol to the feedback channel and the network energy consumption are explicitly considered. A general analysis for linear systems with parameter uncertainty and external bounded disturbances with control loops closed over IEEE 802.15.4 networks is proposed. To reduce the number of transmissions and thus save energy, a self-triggered control strategy is used. A sufficient stability condition is given as function of both the protocol and control parameters. A decentralized algorithm to adapt jointly the self-triggered control and the protocol parameters is proposed. It is concluded that stability is not always guaranteed unless protocol parameters are appropriately tuned, and that event-triggered control strategies may be difficult to use with the current version of IEEE 802.15.4.
In the last few years there has been a growing interest in the use of symbolic models for the for... more In the last few years there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems. Symbolic models are abstract descriptions of continuous systems where one symbol corresponds to an "aggregate" of continuous states. In this paper we face the problem of deriving symbolic models for nonlinear control systems affected by disturbances. The main contribution of this paper is in proposing symbolic models that can be effectively constructed and that approximate nonlinear control systems affected by disturbances in the sense of alternating approximate bisimulation.
Secure state estimation is the problem of estimating the state of a dynamical system from a set o... more Secure state estimation is the problem of estimating the state of a dynamical system from a set of noisy and adversarially-corrupted measurements. Intrinsically a combinatorial problem, secure state estimation has been traditionally addressed either by brute force search, suffering from scalability issues, or via convex relaxations, using algorithms that can terminate in polynomial time but are not necessarily sound. In this paper, we present a novel algorithm that uses a satisfiability modulo theory approach to harness the complexity of secure state estimation. We leverage results from formal methods over real numbers to provide guarantees on the soundness and completeness of our algorithm. Moreover, we discuss its scalability properties, by providing upper bounds on the runtime performance. Numerical simulations support our arguments by showing an order of magnitude decrease in execution time with respect to alternative techniques. Finally, the effectiveness of the proposed algorithm is demonstrated by applying it to the problem of controlling an unmanned ground vehicle. Y. Shoukry and P. Tabuada are with the Electrical Engineering Department, UCLA,
Secure state estimation is the problem of estimating the state of a dynamical system from a set o... more Secure state estimation is the problem of estimating the state of a dynamical system from a set of noisy and adversarially-corrupted measurements. Intrinsically a combinatorial problem, secure state estimation has been traditionally addressed either by brute force search, suffering from scalability issues, or via convex relaxations, using algorithms that can terminate in polynomial time but are not necessarily sound. In this paper, we present a novel algorithm that uses a satisfiability modulo theory approach to harness the complexity of secure state estimation. We leverage results from formal methods over real numbers to provide guarantees on the soundness and completeness of our algorithm. Moreover, we discuss its scalability properties, by providing upper bounds on the runtime performance. Numerical simulations support our arguments by showing an order of magnitude decrease in execution time with respect to alternative techniques. Finally, the effectiveness of the proposed algorithm is demonstrated by applying it to the problem of controlling an unmanned ground vehicle.
The paper introduces a new detectability concept for continuous-time Markov jump linear systems w... more The paper introduces a new detectability concept for continuous-time Markov jump linear systems with finite Markov space that generalizes previous concepts found in the literature. The detectability in the weak sense is characterized as mean square detectability of a certain related stochastic system, making both detectability senses directly comparable. The concept can also ensure that the solution of the coupled algebraic Riccati equation associated to the quadratic control problem is unique and stabilizing, making other concepts redundant. The paper also obtains a set of matrices that plays the role of the observability matrix for deterministic linear systems, and it allows geometric and qualitative properties. Tests for weak observability and detectability of a system are provided, the first consisting of a simple rank test, similar to the usual observability test for deterministic linear systems.
This paper addresses the solution of large zero-sum matrix games using randomized methods. We for... more This paper addresses the solution of large zero-sum matrix games using randomized methods. We formalize a procedure, termed as the sampled security policy (SSP) algorithm, by which a player can compute policies that, with a high confidence, are security policies against an adversary using randomized methods to explore the possible outcomes of the game. The SSP algorithm essentially consists of solving a stochastically sampled subgame that is much smaller than the original game. We also propose a randomized algorithm, termed as the sampled security value (SSV) algorithm, which computes a high-confidence security-level (i.e., worst-case outcome) for a given policy, which may or may not have been obtained using the SSP algorithm. For both the SSP and the SSV algorithms we provide results to determine how many samples are needed to guarantee a desired level of confidence. We start by providing results when the two players sample policies with the same distribution and subsequently extend these results to the case of mismatched distributions. We demonstrate the usefulness of these results in a hide-and-seek game that exhibits exponential complexity.
We consider the modeling, stability analysis and controller design problems for discrete-time LTI... more We consider the modeling, stability analysis and controller design problems for discrete-time LTI systems with state feedback, when the actuation signal is subject to switching propagation delays, due to e.g. the routing in a multi-hop communication network. We show how to model these systems as regular switching linear systems and, as a corollary, we provide an (exponential-time) algorithm for robust stability analysis. We also show that the general stability analysis problem is NP-hard in general. Even though the systems studied here are inherently switching systems, we show that their particular structure allows for analytical understanding of the dynamics, and even efficient algorithms for some problems: for instance, we give an algorithm that computes in a finite number of steps the minimal look-ahead knowledge of the delays necessary to achieve controllability. We finally show that when the switching signal cannot be measured it can be necessary to use nonlinear controllers for stabilizing a linear plant.
This work discusses the design of a networked traffic control scheme. We refer to the Grenoble So... more This work discusses the design of a networked traffic control scheme. We refer to the Grenoble South Ring traffic system, as case study, in which the control actions are computed in a control centre far from the traffic system and then sent, through a wireless communication channel, to the actuators placed along the road, i.e. on-ramp traffic lights in the considered case of ramp metering control. The communication channel is affected by delays and packet loss. In order to counteract the effects due to the transmission of the variable over the communication channel, we suggest to adopt a model predictive control (MPC) strategy based on the use of a buffer. Moreover, in order to limit the computational burden and improve the effectiveness of the proposal, the length of the optimization horizon of the predictive control algorithm, and, consequently, the buffer length, is updated relying on a delay estimation. The performances of the proposed approach are assessed in simulation relying on a traffic model the parameters of which are identified using data produced by a commercial microscopic simulator of the Grenoble South Ring traffic system. The capabilities of the considered control scheme when the system parameters vary and the transmitted signals are affected by time delays are highlighted.
Markov jump switched linear systems (MJSLSs) are switched linear systems, where a switching signa... more Markov jump switched linear systems (MJSLSs) are switched linear systems, where a switching signal is governed by a Markov decision process. We consider a polytopic timeinhomogeneous setting, where the transition probabilities (between the operational modes of the system) associated to each discrete action are varying over time, with variations that are arbitrary within a polytopic set. We present and solve for this class of systems the finite horizon optimal control problem.
In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalenc... more In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalence of stochastic external behavior for the class of discrete-time stochastic linear control systems with possibly degenerate normally distributed disturbances. The first notion is inspired by the notion of probabilistic bisimulation for probabilistic chains while the second one by the notion of equivalence of external behavior for (nonstochastic) behavioral systems. Geometric necessary and sufficient conditions for checking these notions are derived. Model reduction via Kalman-like decomposition is also proposed. Connections with stochastic linear realization theory and stochastic reachability are established.
ERC-2014-StG CHAMELEON: A platform for modelling, design, simulation and verifiCation of HierAr... more ERC-2014-StG CHAMELEON: A platform for modelling, design, simulation and verifiCation of HierArchical distributed control systeMs over hEtErogeneous cOmmunication Networks SIR-2014 FLASH: A platform for design of distributed automation systems over heterogeneous networks Group, scientific collaborations and projects Objective: control over wireless networks Controller Challenge: close the loop taking into account the communication protocol Challenge: close the loop taking into account the communication protocol
IEEE Transactions on Intelligent Transportation Systems, 2021
The paper investigates the possibility of using macroscopic information to improve control perfor... more The paper investigates the possibility of using macroscopic information to improve control performance of a vehicular platoon composed of autonomous vehicles. A mesoscopic traffic modeling framework is proposed, and closed loop String Stability is achieved by exploiting Input-to-State Stability (ISS) for the analysis of the platoon. Examples of mesoscopic control laws are illustrated and simulations show the effectiveness of our approach in ensuring String Stability and improving the platoon behavior.
In this paper, we propose a definition of equivalence via stochastic bisimulation for the class o... more In this paper, we propose a definition of equivalence via stochastic bisimulation for the class of discretetime stochastic linear control systems with possibly degenerate normally distributed disturbances. The notion is inspired by the notion of probabilistic bisimulation for probabilistic chains. Geometric necessary and sufficient conditions for checking this notion are derived. Model reduction via Kalman-like decomposition is also proposed. Connections with stochastic reachability are discussed and with finite horizon stochastic safety problems established. A discussion on the use of stochastic bisimulation equivalence for control design is given, and an application to optimal control problems with stochastic reachability specifications is finally presented.
The paradigm of Cyber-Physical Systems of Systems (CPSoS) is becoming rather popular in the contr... more The paradigm of Cyber-Physical Systems of Systems (CPSoS) is becoming rather popular in the control systems research community because of its expressive power able to properly handle many engineered complex systems of interest. Decentralized control techniques offer a promising approach in taming the inherent complexity of CPSoS, also connected with the design of needed communication infrastructures and computing units. In this paper, we propose decentralized control of networks of discrete-time nonlinear control systems, enforcing complex specifications expressed in terms of regular languages, within any desired accuracy. As discussed in the paper, regular languages, while being traditionally studied in the research community of discrete-event systems, also provide a useful mean to model a rather wide variety of complex specifications for control systems. The design of decentralized controllers is based on formal methods and in particular, on the use of discrete abstractions. Efficient synthesis of such controllers is derived by resorting to on-the-fly algorithmic techniques that also allow the use of parallel computing architectures. Advantages and disadvantages of the decentralized approach over a centralized one, also in terms of computational complexity, are discussed. An illustrative example is presented, which shows the applicability and effectiveness of the results proposed.
The transition probabilities of jumps between operational modes of discrete-time Markov(ian) jump... more The transition probabilities of jumps between operational modes of discrete-time Markov(ian) jump linear systems (dtMJLSs) are generally considered to be time-invariant, certain, and often completely known in the majority of dedicated studies. Still, in most real cases the transition probability matrix (TPM) cannot be computed exactly and is time-varying. In this article, we take into account the uncertainty and time-variance of the jump parameters by considering the underlying Markov chain as polytopic and time-inhomogeneous, i.e., its TPM is varying over time with variations that are arbitrary within a polytopic set of stochastic matrices. We show that the conditions used for time-homogeneous dtMJLSs are not enough to ensure the stability of the time-inhomogeneous system, and that perturbations on values of the TPM can make a stable system unstable. We present necessary and sufficient conditions for mean square stability (MSS) of polytopic time-inhomogeneous dtMJLSs, prove that deciding MSS on such systems is NP-hard and that MSS is equivalent to exponential MSS and to stochastic stability. We also derive necessary and sufficient conditions for robust MSS of dtMJLSs affected by polytopic uncertainties on transition probabilities and bounded disturbances.
Context: Cyber-physical systems (CPS) are integrations of computation, networking, and physical p... more Context: Cyber-physical systems (CPS) are integrations of computation, networking, and physical processes. Due to the tight cyberphysical coupling and to the potentially disrupting consequences of failures, security is one of the primary concerns for this type of systems. CPS security is attracting several research efforts from different and independent areas (e.g., secure control, intrusion detection in SCADA systems, etc.), each of them with specific peculiarities, features, and capabilities, resulting in a considerably variegated and complex scientific body of knowledge on the topic. Objective: In this study we aim at identifying, classifying, and analyzing existing research on CPS security in order to better understand how security is actually addressed when dealing with cyber-physical systems. Based on this analysis of the state of the art, we also aim at identifying the implications for future research on CPS security. Method: In order to achieve this, we designed and conducted a systematic mapping study to identify, classify, and compare relevant studies proposing a method or technique for cyber-physical systems security. A comparison framework for classifying methods or techniques for CPS security has been empirically defined; identified relevant studies have been classified on the basis of publication trends, their characteristics and focus, and their validation strategies. Results: We selected a total of 118 primary studies as a result of the systematic mapping process. From the collected data we can observe that (i) even if solutions for CPS security has emerged only recently, in the last years they are gaining a sharply increasing scientific interest across heterogeneous publication venues; (ii) the bulk of the works on security for cyber-physical systems is focused on power grids, and the approaches considering attacks on sensors and their protection completely dominate the scene; regardless of application field and considered system components, all the works on CPS security deal with attacks, in order to either implement or to counteract them, and putting together all this studies gives us the possibility to categorize the existing (cyber-physical) attack models; it comes as surprise that very few papers consider communication aspects or imperfections and attempt to provide non-trivial mathematical models of the communication; (iii) most advanced and realistic validation methods have been exploited in the power networks application domain, but even there a benchmark is still missing. Conclusion: The systematic map of research on CPS security provided here is based on, for instance, application fields, various system components, related algorithms and models, attacks characteristics and defense strategies. This work presents a powerful comparison framework for existing and future research on this hot topic, important for both industry and academia.
In this paper we investigate the exploitation of redundancy when routing actuation data to a disc... more In this paper we investigate the exploitation of redundancy when routing actuation data to a discrete-time LTI system connected to the controller via a wireless network affected by packet drops. We assume that actuation packets can be delivered from the controller to the actuator via multiple paths, each associated with a delay and a packet loss probability. We show that the joint design of controller gain and routing redundancy exploitation can tremendously improve the control performance. To achieve this goal we set up and solve a LQR problem for a class of systems that extends discrete-time Markov Jump Linear Systems, in that both continuous and discrete control signals can be actuated.
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Papers by Maria Domenica (Marika) Di Benedetto