Xiushan Cai

Control design for one-sided Lipschitz nonlinear differential inclusions.

This paper considers stabilization and signal tracking control for one-sided Lipschitz nonlinear differential inclusions (NDIs). Sufficient conditions for exponential stabilization for the closed-loop system are given based on linear matrix inequality theory. Further, the design method is extended to signal tracking control for one-sided Lipschitz NDIs. A control law is designed such that the state of the closed-loop system asymptotically tracks the reference signal. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design technique.

Globally uniformly asymptotical stabilisation of time-delay nonlinear systems

Globally uniformly asymptotical stabilisation of nonlinear systems in feedback form with a delay arbitrarily large in the input is dealt with based on the backstepping approach in this article. The design strategy depends on the construction of a Lyapunov–Krasovskii functional. A continuously differentiable control law is obtained to globally uniformly asymptotically stabilise the closed-loop system. The simulation shows the effectiveness of the method.

Robust Stabilization of Linear Differential Inclusions with Affine Uncertainty

The linear differential inclusion subjected to disturbance with affine uncertainty is considered. Nonlinear feedback laws are constructed by the convex hull Lyapunov functions. Design objectives including stabilization, disturbance rejection with bounded reachable set and bounded L2 gain are achieved. Simulation results are given to verify the effectiveness of the presented design.

Output tracking and disturbance rejection of linear differential inclusion systems

The globally tracking problem of linear differential inclusion systems with disturbances is studied in this article. By using the Hamilton–Caylay Theorem, an operator is constructed such that tracking problem is converted into a standard stabilisation problem. A control law is designed such that the output signal of the closed-loop system tracks some reference signal and rejects the disturbances. A second-order LDI system is used to illustrate the effectiveness of the proposed design technique.

Robust model predictive control with ℓ1-gain performance for positive systems

Abstract This paper is concerned with robust model predictive control for positive systems. The technique of model predictive control is extended to the context of positive systems. By using the linear copositive Lyapunov function approach, a robust model predictive controller for positive systems is first constructed. Being unlike the classic robust control with l 2 -gain performance, the robustness of the underlying systems is guaranteed by means of l 1 -gain performance. In order to increase the feasibility of the present conditions, a multi-step control strategy is then utilized. Accordingly, a cone invariant set is addressed to satisfy the recursive feasibility of the present design. All present conditions can be described by linear programming. Meanwhile, the main computation of these conditions is completely off-line, by which the computational burden is reduced. Finally, an illustrative example is given to show the effectiveness of the design.

Uniformly ultimately bounded tracking control of linear differential inclusions with stochastic disturbance

Abstract: The tracking control of linear differential inclusions with stochastic disturbance is considered. The feedback law is constructed by the convex hull Lyapunov function. The design objective is to make the error system uniformly ultimately bounded in mean square. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.

Asymptotic tracking control for a class of reference signals for linear differential inclusions

Tracking control for linear differential inclusions with disturbances is investigated in this paper. Based on the convex hull Lyapunov function, a feedback control law is designed such that the output of the closed-loop system without disturbances globally asymptotically tracks the desired reference signal. Under the bounded disturbances, the tracking error is bounded. An example is given to illustrate how to make the output of the closed-loop system track a sinusoidal signal, a cosine signal and a circular signal. The simulation shows the effectiveness of the proposed method.

A Control Lyapunov Function Approach to Stabilization of Affine Nonlinear Systems with Bounded Uncertain Parameters

This paper considers the robust stabilization problem of a class of affine nonlinear systems with bounded uncertain time-invariant parameters. A robust control Lyapunov function (RCLF) is introduced for the considered system. Based on the RCLF, a globally asymptotically stabilizing controller is then designed. The proposed controller is robust under the variant of system parameters. As the applications of the proposed scheme, the stabilization of uncertain feedback linearizable systems and the unified chaotic system are investigated, respectively. A numerical example on the unified chaotic system is also provided to illustrate the effectiveness of the presented method.

Predictor-based stabilisation for discrete nonlinear systems with state-dependent input delays

ABSTRACT We consider predictor-based stabilisation for discrete nonlinear systems with state-dependent input delays. The key design is how to determine the prediction horizon and the predictor state. Sufficient conditions for stabilisation of the closed-loop system are obtained. An explicit feedback law is presented for compensating state-dependent input delay. Since input delay is dependent on state, a region of attraction is estimated for the closed-loop system. The proposed predictor-based design can be applied in controlling the yaw angular displacement of a four-rotor mini-helicopter.

Observer design for a class of nonlinear system in cascade with counter-convecting transport dynamics

Observer design for ODE-PDE cascades is studied where the finite-dimension ODE is a globally Lipschitz nonlinear system, while the PDE part is a pair of counter-convecting transport dynamics. One major difficulty is that the state observation only rely on the PDE state at the terminal boundary, the connection point between the ODE and the PDE blocs is not accessible to measure. Combining the backstepping infinite-dimensional transformation with the high gain observer technology, the state of the ODE subsystem and the state of the pair of counter-convecting transport dynamics are estimated. It is shown that the observer error is asymptotically stable. A numerical example is given to illustrate the effectiveness of the proposed method.