In this paper, the problem of robust fault tolerant control for a class of singular systems subject to both time-varying state-dependent nonlinear perturbation and actuator saturation is investigated. A sufficient condition for the existence of a fixed-gain controller is first proposed which guarantees the regularity, impulse-free and stability of the closed-loop system under all possible faults. An optimization problem with LMI constraints is formulated to determine the largest contractively invariant ellipsoid. An adaptive fault tolerant controller is then developed to compensate for the failure effects on the system by estimating the fault and updating the design parameter matrices online. Both of these two controllers are in the form of a saturation avoidance feedback with the advantage of relatively small actuator capacities compared with the high gain counterpart. An example is included to illustrate the proposed procedures and their effectiveness.

Fault tolerant control for singular systems with actuator saturation and nonlinear perturbationFault tolerant control for singular systems with actuator saturation and nonlinear perturbation.

In this paper, a novel iterative two-stage dual heuristic programming (DHP) is proposed to solve the optimal control problems for a class of discrete-time switched nonlinear systems subject to actuators saturation. First, a novel nonquadratic performance functional is introduced to confront control constraints of the saturating actuator. Then, the iterative two-stage DHP algorithm is developed to solve the Hamilton-Jacobi-Bellman (HJB) equation of the switched system with the saturating actuator. Moreover, the convergence and optimality of the two-stage DHP algorithm are strictly proven. To implement this algorithm efficiently, there are two neural networks used as parametric structure to approximate the costate function and the corresponding control law, respectively. Finally, simulation results are given to verify the effectiveness of the proposed algorithm.

Neural-Network-Based Constrained Optimal Control Scheme for Discrete-Time Switched Nonlinear System Using Dual Heuristic Programming

In this technical note, the asymptotic stability analysis and state-feedback control design are investigated for a class of discrete-time switched nonlinear systems via the smooth approximation technique. The modal dwell-time switching property is considered to constrain switchings between nonlinear subsystems. A kind of autonomous switchings, i.e., state-partition-dependent switching, is introduced within each approximated piecewise-affine (PWA) subsystem. Combining with the state partition information, the novel asymptotic stability conditions with less conservatism are derived for the induced switched PWA systems with dual switching mechanism based on the approach of multiple Lyapunov functions in piecewise quadratic form. Then, the design of PWA state-feedback controllers is implemented. The effectiveness of the obtained theoretical results is demonstrated by a numerical example.

Multiple Lyapunov Functions Analysis Approach for Discrete-Time-Switched Piecewise-Affine Systems Under Dwell-Time Constraints

In this paper, we investigate the problem of exponential stability and asynchronous stabilization for a class of switched nonlinear systems. The Takagi and Sugeno (T-S) fuzzy model is employed to approximate the subnonlinear dynamic systems. With two-level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce continuous-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. By the use of delicately constructed piecewise Lyapunov-like functions (PLFs) and minimum dwell time method, we obtain the exponential stability of the switched fuzzy systems, which allows us to have stable and unstable nonlinear subsystems. In practice, for the control problem, it inevitably takes some time to identify the system modes and apply the matched controller, the asynchronous phenomena between the system modes switching and the controllers switching generally exists. Based on the result of stability, the fuzzy state feedback controller under asynchronous switching is proposed for switched fuzzy systems. In addition, the lower bound of minimum dwell time can be obtained using convex optimization such that the switched fuzzy system can be exponentially stabilized if its minimum dwell time is larger than the bound. The stability results and control laws of the switched fuzzy systems are formulated in the form of linear matrix inequalities that are numerically feasible. Finally, two illustrated numerical examples are presented to show the effectiveness of the obtained theoretical results.

The Exponential Stability and Asynchronous Stabilization of a Class of Switched Nonlinear System Via the T–S Fuzzy Model

A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays

This paper considers the stabilization problem of impulsive switched linear systems with saturated control input, in which the impulses are viewed as control or disturbances. Under arbitrary switching rule and dwell time switching rule, the local stabilization conditions are obtained in terms of LMIs, respectively. The corresponding optimization problems are formulated to obtain a bigger attractive region. Our results show that impulsive control can recover part of attractive region, or allow a wide range of switching signals. If the impulses occur as disturbances, we have to increase the dwell time of switching signals to offset the effects of disturbances. Numerical examples are given to show the effectiveness of the results proposed.

Stabilization of impulsive switched linear systems with saturated control input

Control of switched linear systems with actuator saturation and its applications

This paper investigates the control synthesis problem for discrete-time switched linear systems with input saturation. Based on minimal dwell time approach, state feedback controller and dynamic output feedback controller are respectively designed in terms of LMIs. The corresponding optimization problems are formulated to obtain a bigger attractive region. Compared with previous results, our proposed results can recover part of attractive region. Finally, numerical example is presented to illustrate the effectiveness and value of our obtained results.

Control Synthesis of Discrete-Time Switched Linear Systems with Input Saturation Based on Minimum Dwell Time Approach

In this paper, we consider an optimal control problem of switched systems with a continuous-time inequality constraint. Because of the complexity of this constraint, it is difficult to solve this problem by standard optimization techniques. To overcome this difficulty, the problem is divided into a bi-level optimization problem involving a combination of a continuous-time optimal control problem and a discrete optimization problem. Then, a modified Broyden-Fletcher-Goldfarb-Shanno algorithm and a discrete filled function method is first proposed to solve this bi-level optimization problem. Finally, a numerical example is presented to illustrate the efficiency of our method.

Constrained optimal control of switched systems based on modified BFGS algorithm and filled function method

This paper considers the asymptotic stability problem for a class of neural networks with discrete and distributed delays. Based on a new augmented Lyapunov functional and integral inequalities, the new asymptotic stability condition is established in terms of linear matrix inequality. Meanwhile, the importance of some augmented terms in the Lyapunov functional are discussed. Compared with previous methods to deal with the distributed delay, our method is less conservative due to the use of the new Lyapunov functional. Finally, numerical examples illustrate the relaxation of obtained results and our claims.

Kanjian Zhang

Papers

Stabilization of impulsive switched linear systems with saturated control input

Control of switched linear systems with actuator saturation and its applications

Control Synthesis of Discrete-Time Switched Linear Systems with Input Saturation Based on Minimum Dwell Time Approach

Constrained optimal control of switched systems based on modified BFGS algorithm and filled function method

Improved asymptotic stability conditions for neural networks with discrete and distributed delays