lyapunov theory
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Uncertainties and disturbances widely exist in electrohydraulic lifting mechanisms of launcher systems, which may worsen the rapid-erection tracking accuracy and even make the system unstable. To deal with the issue, an asymptotic tracking control framework is developed for electrohydraulic lifting mechanisms of launcher systems. Firstly, the dynamic equations and state-space forms of the electrohydraulic lifting mechanism are modeled. Based on the system model, a nonlinear rapid-erection robust controller is constructed to achieve the improvement of the system control performance, in which a nonlinear feedback term is employed to remove the effects of uncertainties and disturbances on tracking performance. Compared to the existing results, the asymptotic tracking stability of the closed-loop system can be assured based on the Lyapunov theory analysis. In the end, the simulation example of an actual electrohydraulic lifting mechanism of the launcher system is done to validate the effectiveness with the proposed controller.

In this paper, a novel adaptive robust control (ARC) scheme is proposed for electro-hydraulic servo systems (EHSSs) with uncertainties and disturbances. All dynamic functions in system dynamics are effectively approximated by multi-layer radial basis function neural network (RBF NN)-based approximators with online adaptive mechanisms. Moreover, neural network-based disturbance observers (NN-DOBs) are established to actively estimate and efficiently compensate for the effects of not only the matched/mismatched but also the imperfections of RBF NN-based approximators on the control system. Based on that, the nonlinear robust control law which integrates RBF NNs and NN-DOBs is synthesized via the sliding mode control (SMC) approach to guarantee the high-accuracy position tracking performance of the overall control system. Furthermore, the problem of the combination between DOBs and RBF NNs is first introduced in this paper to treat both disturbances and uncertainties in the EHSS. The stability of the recommended control mechanism is proven by using Lyapunov theory. Finally, numerical simulations with several distinct frequency levels of reference trajectory are conducted to convincingly demonstrate the effectiveness of the proposed approach.

Abstract In order to intercept a highly manoeuvering target with an ideal impact angle in the three-dimensional space, this paper promises to probe into the problem of three-dimensional terminal guidance. With the goal of the highly target acceleration and short terminal guidance time, a guidance law, based on the advanced fast non-singular terminal sliding mode theory, is designed to quickly converge the line-of-sight (LOS) angle and the LOS angular rate within a finite time. In the design process, the target acceleration is regarded as an unknown boundary external disturbance of the guidance system, and the RBF neural network is used to estimate it. In order to improve the estimation accuracy of RBF neural network and accelerate its convergence, the parameters of RBF neural network are adjusted online in real time. At the same time, an adaptive law is designed to compensate the estimation error of the RBF neural network, which improves the convergence speed of the guidance system. Theoretical analysis demonstrates that the state and the sliding manifold of the guidance system converge in finite time. According to Lyapunov theory, the stability of the system can be guaranteed by online adjusting the parameters of RBF neural network and adaptive parameters. The numerical simulation results verify the effectiveness and superiority of the proposed guidance law.

Abstract This paper researches two finite-time bounded control methods for Euler-Lagrange systems exposed to external disturbances. A novel full-order terminal sliding mode surface that is convenient for solving the input constraints is designed based on the characters of the hyperbolic tangent function. By using the designed full-order terminal sliding mode surface, the finite-time controller with input constraints can deal with external disturbances with the exactly known upper bound. Further, an adaptive finite-time bounded controller is designed to deal with the external disturbances with the upper bound that cannot be accurately known. Finally, the finite-time stability of the system is proved by using Lyapunov theory and numerical simulations.

This paper proposes an adaptive formation tracking control algorithm optimized by Q-learning scheme for multiple mobile robots. In order to handle the model uncertainties and external disturbances, a desired linear extended state observer is designed to develop an adaptive formation tracking control strategy. Then an adaptive method of sliding mode control parameters optimized by Q-learning scheme is employed, which can avoid the complex parameter tuning process. Furthermore, the stability of the closed-loop control system is rigorously proved by means of matrix properties of graph theory and Lyapunov theory, and the formation tracking errors can be guaranteed to be uniformly ultimately bounded. Finally, simulations are presented to show the proposed algorithm has the advantages of faster convergence rate, higher tracking accuracy, and better steady-state performance.

This investigation attempts to study a possible controller in improving the dynamic stability of capacitive microstructures through mitigating the effects of disturbances and uncertainties in their resultant dynamic behavior. Consequently, a nonsingular terminal sliding mode control strategy is suggested in this regard. The main features of this particular control strategy are its high response speed and its non-reliance on powerful controller forces. The stability of the controller was investigated using Lyapunov theory. For this purpose, a suitable Lyapunov function was introduced to prove the stability of a controller, and the singularity conditions and methods to overcome these conditions are presented. The achieved results proved the high capability of the applied technique in stabilizing of the microstructure as well as mitigating the effects of disturbances and uncertainties.

In public places, it is significant to analyze the stability of the crowd which can support the crowd management and control, and protect the evacuees safely and effectively. The numerical analysis method of system stability based on Lyapunov theory suffers problems that it is difficult to avoid random errors in the initialization of pedestrian density and velocity, as well as cumulative errors due to time increasing, limiting its application. This study adopts a complementary model of theoretical numerical analysis and machine vision with a parallel convolutional neural network (CNN) model. It proposes an approach of stability analysis and closed-loop verification for crowd merging systems. Thereby, this research provides theoretical and methodological support for planning of the functional layout of crowd flow in public crowd-gathering places and the control measures for stable crowd flow.

Singular nonlinear systems have received wide attention in recent years, and can be found in various applications of engineering practice. On the basis of the Takagi-Sugeno (T-S) formalism, which represents a powerful tool allowing the study and the treatment of nonlinear systems, many control and diagnostic problems have been treated in the literature. In this work, we aim to present a new approach making it possible to estimate simultaneously both non-measurable states and unknown faults in the actuators and sensors for a class of continuous-time Takagi-Sugeno singular model (CTSSM). Firstly, the considered class of CTSSM is represented in the case of premise variables which are non-measurable, and is subjected to actuator and sensor faults. Secondly, the suggested observer is synthesized based on the decomposition approach. Next, the observer’s gain matrices are determined using the Lyapunov theory and the constraints are defined as linear matrix inequalities (LMIs). Finally, a numerical simulation on an application example is given to demonstrate the usefulness and the good performance of the proposed dynamic system.

Formations or groups of robots become essential in cases where a single robot is insufficient to satisfy a given task. With an increasingly automated world, studies on various topics related to robotics have been carried out in both the industrial and academic arenas. In this paper, the control of the formation of differential mobile robots based on the leader-follower approach is presented. The leader's movement is based on the least cost path obtained by the A-star algorithm, thus ensuring a safe and shortest possible route for the leader. Follower robots track the leader's position in real time. Based on this information and the desired distance and angle values, the leader robot is followed. To ensure that the followers do not collide with each other and with the obstacles in the environment, a controller based on Artificial Potential Fields is designed. Stability analysis using Lyapunov theory is performed on the linearized model of the system. To verify the implemented technique, a simulator was designed using the MATLAB programming language. Seven experiments are conducted under different conditions to show the performance of the approach. The distance and orientation errors are less than 0.1 meters and 0.1 radians, respectively. Overall, mobile robots are able to reach the goal position, maintaining the desired formation, in finite time.

This study presents LPV H∞ control with an augmented nonlinear observer (ANOB) to improve both the position and yaw tracking errors for Sawyer motors. The proposed control method consists of the forces and torque modulation scheme, an ANOB, and a Lyapunov-based current controller with the LPV H∞ state feedback controller to guarantee the stability of tracking error dynamics. The ANOB is designed to estimate all the state variables including the position, velocity, current, and disturbance using only position feedback. We propose a vertex expansion technique to solve the influence of the convex interpolation parameters in the LPV system on the tracking error performance. To be robust against disturbance, a state feedback controller with the LPV gain scheduling is determined by applying the H∞ control in the linear-matrix-inequality (LMI) technique. The closed-loop stability is proved through the Lyapunov theory. The effectiveness of the proposed control method is evaluated through simulation results and compared with the conventional proportional-integral-derivative (PID) control method to verify both the improved tracking error performance and a suitable disturbance rejection.