Robust Model Predictive Control For Uncertain Time-delay Systems

It is well known that the time-delay can be found in the most of industrial processes owing to the actions from transmission, measure and so on, and often results in the in stability and poor performance.Meanwhile, the model, which is used to describe the dynamics of controlled system, always has some uncertainty due to the complexity of practical systems. Therefore, more values can be obtained from the research into the delay systems with uncertainties.Based on the existing theoretical results on predictive control, this paper is devoted to the study of robust predictive control for uncertain time-delay systems. To achieve this goal, the relevant theory and approaches, such as linear matrix inequalities (LMI) and Lyapunov stability theory are employed in the research work. The design method of state feedback or output feedback robust predictive controller is presented for uncertain time-delay systems with norm-bounded or polytopic parameter uncertainties. In addition, the robust stability and feasibility of the closed-loop systems are analyzed and a delay-independent or delay-dependent condition is obtained. We investigate initially the robust predictive control of uncertain time-delay systems as follows:1. The problem of robust state feedback predictive control is presented for multi-input delay uncertain systems in terms of LMI methods. By minimizing the worst-case linear quadratic objective function, the state feedback predictive controller is designed and a piecewise constant control sequence is obtained. The robust stability and feasibility of the closed-loop systems are guaranteed by the proposed design method.2. The problem of robust output feedback predictive control is studied for delay systems with norm-bounded uncertainty in terms of LMI methods. Then the robust output feedback controller is designed for a class of systems with immesurable state and time-varying parameter uncertainties. Based on the principle of moving horizon optimization, a picewise of continuous output feedback control sequence is obtained. It is shown that the resulting closed-loop is feasible and asymptotically stable.3. A linear state transformation is proposed to continuous-time polytopic uncertain time-delay systems. Based on LMI methods, the problem of parameter uncertainty and time-delay is investigated. An upper bound on the robust performance index is presented based on the Lyapunov-Krasovskii function. Then a picewise of continuous state feedback control sequence is obtained by solving a convex optimization problem subject to a number of LMI feasibility constraints. Feasible solutions of optimization problem guarantees closed-loop stability.4. A robust guaranteed cost predictive controller is designed for a class of systems with norm-bounded uncertainties and time-varying delay. Based on LMI methods, the min-max optimization problem of infinite horizon is formulated the linear programming problem. This leads to a notable reduction in the complexity of online computation. Closed-loop stability is guaranteed depending on the feasible solutions at the initial time.