Study On Sensitivity Approach Of Optimal Output Tracking Control For Time-Delay Systems

Strictly speaking, time-delay exists in the most practical control systems, which mainly results from the time taken in the online data acquisition from the sensors, the time taken in the processing of the sensory data and the time taken by the actuator to produce the required control force. Time-delay may result in degradation in the control efficiency and instability of the control systems. So the research on the control theory of time-delay systems has attracted much attention of the scholars. The optimal output tracking control (OOTC) theory is one of the important research fields of the optimal control theory. In recent years, modern industries and national defenses have made a development, which result in more and more applications of the OOTC theory in various fields such as ocean information detection technique, space technique, economic system, intelligent robot and chemical industry. However, up to now, there are few results on the OOTC problem for time-delay systems. So the research on the problem is important in both theory and application fields.Firstly, the history of the development in the OOTC theory of time-delay systems is reviewed in detail. Then, the dissertation considers the OOTC problems for linear time-delay systems, linear time-delay systems with external disturbances, linear interconnected large-scale time-delay systems and linear interconnected large-scale time-delay systems with external disturbances, respectively. The existence and uniqueness of the OOTC laws are studied and the design methods of the OOTC laws are given. The physical realization problems of the control laws are also discussed. The main contents are shown as follows.1. The relative contents of the optimal control theory and the OOTC theory are briefly described. And the latest research tendencies of the OOTC problems for time-delay systems and large-scale systems are discussed respectively. 2. The OOTC problem for linear time-delay systems with the finite horizon and infinite horizon quadratic performance indexes is studied. First by introducing a sensitivity parameterεand extending the variables of the system to the Maclaurin series atε= 0, the original OOTC problem is reformulated into a sequence of inhomogeneous linear two-point boundary value (TPBV) problems without time-advance or time-delay terms. Then by using the iterative process, the OOTC laws can be obtained, which consist of the linear analytic terms and the compensation term. The linear analytic terms can be obtained by solving the matrix differential or algebraic equations. The compensation term can be obtained from a recursion formula of the adjoint vectors. In the control laws, the state of the reference input exosystem is used to construct the feedforward control action, which improves the tracking precision. Finally, a reduced order reference input observer is constructed such that the control laws are physically realizable.3. The OOTC problem for linear time-delay systems with sinusoidal disturbances is discussed. By using the sensitivity approach, the finite horizon and infinite horizon OOTC laws are obtained. A reduced order reference input observer is constructed such that the control laws are physically realizable.4. The external disturbance model is extended from the sinusoidal disturbance model to more general deterministic disturbance model that described by a linear exosystem. The OOTC problem for linear time-delay systems with persistent deterministic disturbances is considered. By using the sensitivity approach, the finite horizon and infinite horizon OOTC laws are obtained. In the control laws, the state of the disturbance exosystem and the state of the reference input exosystem are used to construct the feedforward control action, which reduces the effect of the external disturbance on the system performance and improves the tracking precision. Finally, by constructing a reduced order disturbance observer and a reduced order reference input observer, the physical realization problem of the control laws is solved.5. The OOTC problem for linear interconnected large-scale time-delay systems with the finite horizon and infinite horizon quadratic performance indexes is studied. The large-scale time-delay system consists of N subsystems. By using the sensitivity approach, the original OOTC problem is reformulated into a sequence of inhomogeneous linear decoupling TPBV problems without time-advance or time-delay terms. Then by using the iterative process, the OOTC laws can be obtained, which consist of the linear analytic terms and the compensation term. Finally, by designing the reduced order reference input observers to reconstruct the states of the reference input exosystems, the physical realization problem of the control laws is solved.6. The OOTC problem for linear interconnected large-scale time-delay systems with sinusoidal disturbances is discussed. By using the sensitivity approach, the finite horizon and infinite horizon OOTC laws are obtained. The reduced order reference input observers are constructed such that the control laws are physically realizable.7. The OOTC problem for linear interconnected large-scale time-delay systems with persistent disturbances is considered. By using the sensitivity approach, the finite horizon and infinite horizon OOTC laws are obtained. Finally, the reduced order disturbance observers and the reduced order reference input observers are designed to reconstruct the states of the disturbance exosystems and the states of the reference input exosystems, respectively. And the physical realization problem of the control laws is solved.8. The conclusions are given finally. And the directions for the future research work are indicated.