Study On Robust Optimal Control For Uncertain Time-delay Systems

The problem of robust optimal control for uncertain time-delay systems is one of the important research subjects. Time-delay systems exist in many systems such as industry. The environments and parameters of systems change all the time. So there are uncertainties in them. Moreover, there are double complexities in nonlinear time-delay systems. Therefore, the analysis of control for systems with time-delay is significant both in theory and in practice.Firstly, the relative studies on the robust optimal control for time-delay systems up to now are given in detail. Then, this dissertation considers the guaranteed cost control problems for a class of uncertain time-delay systems whose controller uncertainties are concerned. The existences of the guaranteed cost control law and design method of the controller are derived in terms of linear matrix inequation (LMI).At last, based on the maximum principle, this dissertation considers the optimal output tracking (OOT) problem for a class of time-delay systems whose reference input to be tracked is produced by a general exosystem. The existence and uniqueness of the OOT control law are studied and an approximate design procedure of the law is given. The physical realization problem of the feedforward control is discussed. The main contents are given as follows.1. Some problems relative to the robust optimal control for uncertain time-delay systems are presented with their main research methods at first. Then, a detail expression of studies is introduced on the robust control problems, guaranteed cost control problems and OOT problems for the time-delay in the state. The objective and contents of this dissertation are given finally.2. Some theories relative to the robust optimal control problems are introduced. Also theories of robust control, guaranteed cost control, LMI and optimal output tracking control are given. Then some lemmas are introduced.3. The reliable guaranteed cost control for a class of time-delay uncertain linear systems with norm-bounded uncertainties and actuator failure is considered. The existences of the guaranteed cost control law, design method of the controller and a minimal value of cost function are derived in terms of LMI.4. The guaranteed cost control problem for the uncertain nonlinear systems with time-delay is investigated. Using the Lyapunov functional method combined with LMI technique, some conditions for the existence of such controller are derived. By solving the specified LMIs, the design method for the guaranteed cost controller is given. The solutions of the optimal problem give the minimal upper bound on the cost function.5. The problem of the optimal output tracking (OOT) control for linear time-delay systems with sinusoidal disturbances is considered, where the reference input is generated by an exosystem. The sequence of linear nonhomogeneous two-point boundary value (TPBV) problem is constructed by using the successive approximation approach (SAA). The adjoint vector utilized to compensate for the time-delay can be obtained by solving this problem sequence. The feedforward control action is introduced by using the state of the exosystem, disturbance information and its derivative. The control law consists of an accurate linear feedback term, feedforward terms and the time-delay compensation which is the limit of the sequence of the adjoint vector. A reduced-order reference input observer is constructed to make the feedforward control law physically realizable.6. The OOT problem for a class of nonlinear time-delay systems with persistent disturbances is considered where the reference input and the external disturbance are described by the exosystems. This problem is transformed into a sequence of nonhomogeneous linear TPBV problems without time-delay and time-advance terms using the SAA. An approximate procedure is presented to obtain the adjoint vector sequence by iteratively solving the sequence of TPBV problems. The OOT control law obtained consists of an accurate linear feedback term, feedforward terms, and a nonlinear time-delay compensation term which is the limit of the adjoint vector sequence. By using the finite-step iteration of the adjoint vector sequence, we can obtain a suboptimal output tracking control law. A reduced-order disturbance observer and a reference input observer are constructed to make the feedforward control law physically realizable. Simulation results demonstrate the validity of this design algorithm.7. Finally, the main work in this dissertation is summarized and a proposition is indicated on the research work in the future.