Changchun Hua

Robust backstepping control for a class of time delayed systems

In this note, the problem of robust output feedback control for a class of nonlinear time delayed systems is considered. The systems considered are in strict-feedback form. State observer is first designed, then based on the observed states the controller is designed via backstepping method. Both the designed observer and controller are independent of the time delays. Based on Lyapunov stability theory, we prove that the constructed controller can render the closed-loop system asymptotically stable. Simulation results further verify the effectiveness of the proposed approach.

Adaptive Fuzzy Output-Feedback Controller Design for Nonlinear Time-Delay Systems With Unknown Control Direction

In this paper, the robust-control problem is investigated for a class of uncertain nonlinear time-delay systems via dynamic output-feedback approach. The considered system is in the strict-feedback form with unknown control direction. A full-order observer is constructed with the gains computed via linear matrix inequality at first. Then, with the bounds of uncertain functions known, we design the dynamic output-feedback controller such that the closed-loop system is asymptotically stable. Furthermore, when the bound functions of uncertainties are not available, the adaptive fuzzy-logic system is employed to approximate the uncertain function, and the corresponding output-feedback controller is designed. It is shown that the resulting closed-loop system is stable in the sense of semiglobal uniform ultimate boundedness. Finally, simulations are done to verify the feasibility and effectiveness of the obtained theoretical results.

Robust Output Feedback Tracking Control for Time-Delay Nonlinear Systems Using Neural Network

In this paper, the problem of robust output tracking control for a class of time-delay nonlinear systems is considered. The systems are in the form of triangular structure with unmodeled dynamics. First, we construct an observer whose gain matrix is scheduled via linear matrix inequality approach. For the case that the information of uncertainties bounds is not completely available, we design an observer-based neural network (NN) controller by employing the backstepping method. The resulting closed-loop system is ensured to be stable in the sense of semiglobal boundedness with the help of changing supplying function idea. The observer and the controller designed are both independent of the time delays. Finally, numerical simulations are conducted to verify the effectiveness of the main theoretic results obtained

Technical communique: Robust controller design of a class of nonlinear time delay systems via backstepping method

The robust control problem is investigated for nonlinear time delay systems with triangular structure. The uncertain delay disturbances are bounded by nonlinear functions with unknown coefficients. Via the backstepping method, we construct a state feedback controller with the help of Razumikhin lemma. Based on Lyapunov stability theory, we show that the resulting closed-loop system is UUB stable.

Delay-Dependent Stability Criteria of Teleoperation Systems With Asymmetric Time-Varying Delays

This paper addresses the stability-analysis problem for teleoperation systems with time delays. Compared with previous work, communication delays are assumed to be both time-varying and asymmetric, which is the case for network-based teleoperation systems. The stability analysis is performed for two classes of controllers: delayed position-error feedback and delayed torque feedback. By choosing Lyapunov-Krasovskii functional, we show that the master-slave teleoperation system is stable under specific linear-matrix-inequality (LMI) conditions. With the given controller-design parameters, the proposed stability criteria can be used to compute the allowable maximal transmission delay. Finally, both simulations and experiments are performed to show the effectiveness of the proposed method.

Output Feedback Stabilization for Time-Delay Nonlinear Interconnected Systems Using Neural Networks

In this paper, dynamic output feedback control problem is investigated for a class of nonlinear interconnected systems with time delays. Decentralized observer independent of the time delays is first designed. Then, we employ the bounds information of uncertain interconnections to construct the decentralized output feedback controller via backstepping design method. Based on Lyapunov stability theory, we show that the designed controller can render the closed-loop system asymptotically stable with the help of the changing supplying function idea. Furthermore, the corresponding decentralized control problem is considered under the case that the bounds of uncertain interconnections are not precisely known. By employing the neural network approximation theory, we construct the neural network output feedback controller with corresponding adaptive law. The resulting closed-loop system is stable in the sense of semiglobal boundedness. The observers and controllers constructed in this paper are independent of the time delays. Finally, simulations are done to verify the effectiveness of the theoretic results obtained.

Adaptive Tracking Controller Design of Nonlinear Systems With Time Delays and Unknown Dead-Zone Input

This paper focuses on the tracking control problem for a class of nonlinear system with time delays and dead-zone input. The nonsymmetric dead-zone input case is considered without the knowledge of the dead zone parameters. The time delay uncertainties are bounded by a nonlinear function with unknown coefficients. By constructing a novel Lyapunov functional, we design a simple and smooth adaptive state feedback controller. It is shown that the solution of the resulting closed-loop error system converges to an adjustable region exponentially. Finally, numerical examples are included to show the effectiveness of the theoretical results.

Backstepping Control for Nonlinear Systems With Time Delays and Applications to Chemical Reactor Systems

The state feedback control problem is addressed for a class of nonlinear time-delay systems. The time delays appear in all state variables of the nonlinear system, which brings a challenging issue for controller design. With an introduced new Lyapunov-Krasovskii functional, we develop a novel control strategy. With the help of a backstepping method, we design a memoryless state feedback controller, which does not need the precise knowledge of time delays. It is rigorously proved that the closed-loop system is asymptotically stable. Chemical reactor plants are typical nonlinear systems with time delays. We apply the developed method to the control design of a two-stage chemical reactor with delayed recycle streams, and the simulation results verify the effectiveness of the main results.

Decentralized Networked Control System Design Using T–S Fuzzy Approach

The robust control problem is studied for a class of large-scale networked control systems. The subsystems are in the nonlinear form, and they exchange information through the communication networks. The interconnections considered are nonlinear, and not the traditional linear form, which brings a challenging issue for the decentralized control design. We develop a new memoryless control scheme with the use of the decomposition for each subsystem that is based on the input matrix. By Takagi-Sugeno (T-S) fuzzyfication for each subsystem, the interconnected T-S fuzzy subsystems are obtained. When the upper bound functions of uncertain interconnections are known, we design a decentralized memoryless state feedback controller. When the parameters of bound functions are not available, the adaptive method is used, and the decentralized memoryless adaptive controller is developed. By the construction of a new Lyapunov-Krasovskii functional, we prove the stability of the resultant closed-loop system for the both cases. Finally, we apply the theoretic results to the decentralized controller design of networked interconnected chemical reactor systems. The simulations are performed, and the effectiveness of the proposed method is demonstrated.

New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay Using Delay-Decomposition Approach

This brief is concerned with the problem of asymptotic stability of neural networks with time-varying delays. The activation functions are monotone nondecreasing with known lower and upper bounds. Novel stability criteria are derived by employing new Lyapunov-Krasovskii functional and the integral inequality. The developed stability criteria have delay dependencies and the results are characterized by linear matrix inequalities. New and less conservative solutions to the global stability problem are provided in terms of feasibility testing. Numerical examples are finally given to demonstrate the effectiveness of the proposed method.