IEEE Transactions on Automatic Control, Jun 1, 2000
We consider production-distribution systems with buffer and capacity constraints in the presence ... more We consider production-distribution systems with buffer and capacity constraints in the presence of uncertain inputs. We face the problem of finding a control which drives the buffer levels to a prescribed value. We consider a continuous-time model and show that some important properties which fail in general in the discrete-time case. In particular we show that the case in which the controller knows the external input is “equivalent” to the case in which such information is not available. Furthermore, a decentralized strategy can be determined. We also show that in the case of network failures the controller does not need to know the current network configuration in order to guarantee the tracking goal as long as a certain necessary and sufficient condition is satisfied
7.1 Motivations and Preliminaries 7-1 Motivating Example: DC Electric Motor with Uncertain Parame... more 7.1 Motivations and Preliminaries 7-1 Motivating Example: DC Electric Motor with Uncertain Parameters 7.2 Description of the Uncertainty Structures ........7-3 7.3 Uncertainty Structure Preservation with Feedback 7-4 7.4 Overbounding with Affine Uncertainty: The Issue of Conservatism 7-5 7.5 Robustness Analysis for Affine Plants 7-7 Value Set Construction for Affine Plants • The DC-Electric Motor Example Revisited 7.6 Robustness Analysis for Affine Polynomials ..7-10 Value Set Construction for Affine Polynomials • Example of Value Set Generation • Interval Polynomials: Kharitonov’s Theorem and Value Set Geometry • From Robust Stability to Robust Performance • Algebraic Criteria for Robust Stability • Further Extensions: The Spectral Set 7.7 Multiaffine Uncertainty Structures 7-14 7.8 General Uncertainty Structures and Controller Synthesis 7-16 References 7-17 Roberto Tempo IEIIT−CNR Politecnico di Torino
Constraints are encountered practically in every real control problem. It is a tradition (althoug... more Constraints are encountered practically in every real control problem. It is a tradition (although questionable) that in many textbooks constraints are mentioned but, with several exceptions, the design of control systems which take into account constraints is frequently disregarded. In this chapter is is shown how set-theoretic methods are appropriate to control design when constraints are present.
ABSTRACT We consider the problem of stabilizing a dynamic system by means of bounded controls. We... more ABSTRACT We consider the problem of stabilizing a dynamic system by means of bounded controls. We show that the largest domain of attraction can be arbitrarily closely approximated by a “smooth” domain of attraction for which we provide an analytic expression. Such an expression allows for the determination of a (non-linear) control law in explicit form.
Lyapunov functions are crucial in the present book aims, given the strict relation between Lyapun... more Lyapunov functions are crucial in the present book aims, given the strict relation between Lyapunov functions and invariant sets. In this chapter, basic notions of Lyapunov and Lyapunov-like functions will be presented. Before introducing the main concept, a brief presentation of the class of dynamic models will be considered and some preliminary mathematical notions are given.
In this chapter, we survey a few decades of robustness investigation for uncertain systems. We ai... more In this chapter, we survey a few decades of robustness investigation for uncertain systems. We aim at embracing most of the robustness literature, starting from the Lyapunov approach of the ’70s, which involved both quadratic and non-quadratic Lyapunov functions, until recent developments on polynomial techniques for robustness. We consider both time-varying and time-invariant uncertainties, in an inclusive way: important techniques are presented, such as the Lur’e systems framework, qualitative feedback theory, parametric robustness analysis, linear matrix inequalities, parameter-dependent Lyapunov functions, H-infinity, small-gain theorems, non-quadratic Lyapunov functions and Lyapunov–Metzler inequalities. The chapter proposes a critical view on all these techniques, highlighting both advantages and limitations. Illustrative examples and applications are proposed. Technicalities are kept to the least possible level to render the chapter accessible to a broad, possibly interdisciplinary, audience. The chapter is written with a historic view. Nonetheless, future perspectives are emphasized, and several open problems and future research directions are pointed out. The chapter is inspired by the spirit, attitude and fairness of our great friend Roberto Tempo and is written following his invaluable teaching.
IEEE Transactions on Automatic Control, Jun 1, 2000
We consider production-distribution systems with buffer and capacity constraints in the presence ... more We consider production-distribution systems with buffer and capacity constraints in the presence of uncertain inputs. We face the problem of finding a control which drives the buffer levels to a prescribed value. We consider a continuous-time model and show that some important properties which fail in general in the discrete-time case. In particular we show that the case in which the controller knows the external input is “equivalent” to the case in which such information is not available. Furthermore, a decentralized strategy can be determined. We also show that in the case of network failures the controller does not need to know the current network configuration in order to guarantee the tracking goal as long as a certain necessary and sufficient condition is satisfied
7.1 Motivations and Preliminaries 7-1 Motivating Example: DC Electric Motor with Uncertain Parame... more 7.1 Motivations and Preliminaries 7-1 Motivating Example: DC Electric Motor with Uncertain Parameters 7.2 Description of the Uncertainty Structures ........7-3 7.3 Uncertainty Structure Preservation with Feedback 7-4 7.4 Overbounding with Affine Uncertainty: The Issue of Conservatism 7-5 7.5 Robustness Analysis for Affine Plants 7-7 Value Set Construction for Affine Plants • The DC-Electric Motor Example Revisited 7.6 Robustness Analysis for Affine Polynomials ..7-10 Value Set Construction for Affine Polynomials • Example of Value Set Generation • Interval Polynomials: Kharitonov’s Theorem and Value Set Geometry • From Robust Stability to Robust Performance • Algebraic Criteria for Robust Stability • Further Extensions: The Spectral Set 7.7 Multiaffine Uncertainty Structures 7-14 7.8 General Uncertainty Structures and Controller Synthesis 7-16 References 7-17 Roberto Tempo IEIIT−CNR Politecnico di Torino
Constraints are encountered practically in every real control problem. It is a tradition (althoug... more Constraints are encountered practically in every real control problem. It is a tradition (although questionable) that in many textbooks constraints are mentioned but, with several exceptions, the design of control systems which take into account constraints is frequently disregarded. In this chapter is is shown how set-theoretic methods are appropriate to control design when constraints are present.
ABSTRACT We consider the problem of stabilizing a dynamic system by means of bounded controls. We... more ABSTRACT We consider the problem of stabilizing a dynamic system by means of bounded controls. We show that the largest domain of attraction can be arbitrarily closely approximated by a “smooth” domain of attraction for which we provide an analytic expression. Such an expression allows for the determination of a (non-linear) control law in explicit form.
Lyapunov functions are crucial in the present book aims, given the strict relation between Lyapun... more Lyapunov functions are crucial in the present book aims, given the strict relation between Lyapunov functions and invariant sets. In this chapter, basic notions of Lyapunov and Lyapunov-like functions will be presented. Before introducing the main concept, a brief presentation of the class of dynamic models will be considered and some preliminary mathematical notions are given.
In this chapter, we survey a few decades of robustness investigation for uncertain systems. We ai... more In this chapter, we survey a few decades of robustness investigation for uncertain systems. We aim at embracing most of the robustness literature, starting from the Lyapunov approach of the ’70s, which involved both quadratic and non-quadratic Lyapunov functions, until recent developments on polynomial techniques for robustness. We consider both time-varying and time-invariant uncertainties, in an inclusive way: important techniques are presented, such as the Lur’e systems framework, qualitative feedback theory, parametric robustness analysis, linear matrix inequalities, parameter-dependent Lyapunov functions, H-infinity, small-gain theorems, non-quadratic Lyapunov functions and Lyapunov–Metzler inequalities. The chapter proposes a critical view on all these techniques, highlighting both advantages and limitations. Illustrative examples and applications are proposed. Technicalities are kept to the least possible level to render the chapter accessible to a broad, possibly interdisciplinary, audience. The chapter is written with a historic view. Nonetheless, future perspectives are emphasized, and several open problems and future research directions are pointed out. The chapter is inspired by the spirit, attitude and fairness of our great friend Roberto Tempo and is written following his invaluable teaching.
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