Robustness issues in predictive control and systems including time delays

Methods for the design of predictive controllers for uncertain linear systems with guaranteed closed-loop stability are developed as well as conditions for robust stability and stabilization of bilinear and time-delay systems are also derived. Specifically, a systematic technique to design robust predictive controllers for unconstrained linear systems is proposed first. The robustified controller retains the servo performance of a nominal predictive controller designed using conventional methods. In addition, a robust predictive regulator may be designed to guarantee perfect steady-state rejection of asymptotically constant disturbances. The robust predictive methodology is developed for systems affected by unstructured uncertainty, and is based on solving a discrete-time model-matching problem. It is shown that the robustified controller can be classified as a predictive controller because it minimizes the same performance functional as its nominal counterpart. The design of robust predictive controllers for a second order unstable plant illustrates the proposed method.;For systems that are subject to time-domain constraints, a new technique for the design of robust predictive regulators is proposed based on mixed ;Finally, the asymptotic stability and stabilization in the face of uncertainty is examined for bilinear and time-delayed plant models. A variety of robust stability conditions is derived for those plants in the last several chapters. The obtained sufficient conditions guarantee the stability of the systems under state-feedback control in the presence of a norm-bounded, nonlinear, and possibly time-varying uncertainty. The effects of saturation and other input nonlinearities are examined, and finally incorporated in the continuous-time robust stability conditions. The method makes use of the matrix measure and integrodifferential inequalities to derive the robustness conditions as a function of the known uncertainty bounds. A characterization of the domain of attraction is given in the case of uncertain bilinear systems.;Suggestions for further work include the following: investigate other recently proposed mixed optimization approaches to predictive regulator design, explore further the robust stabilization of uncertain bilinear systems with time delays using linear or nonlinear feedback and sliding-mode control, and finally, formulate and solve the problem of designing stabilizing predictive controllers for bilinear constrained process models.