Preview Control For Serveral Classes Of Linear Stochastic Systems

Preview control theory is a kind of control theory and technology. It can improve the operation efficiency of the dynamic systems. Since it was proposed, the researches of preview control theory and the applications have never been interrupted. Since stochastic phenomena widely exist in the reality, the study of stochastic system is always the hot issue. Based on the idea of preview control theory, preview control theory and the stochastic system is combined to study the preview control problem for several classes of linear stochastic systems.At first, as the theoretical basis, the preview controller for a class of linear continuous stochastic systems in finite horizon is designed. Then, the conclusion is extended to the infinite horizon. Meanwhile, the stability problem of the closed-loop system is discussed and the corresponding state observer is designed. Furthermore, for the linear continuous stochastic system with time-delay, the optimal controller based on the preview control idea is obtained. Then, the method is applied to singular system. The preview controller for a class of pulse free linear continuous singular stochastic system is gained. At last, the preview controller based on the linear stochastic differential system is studied. The detailed research work is as following:1. The design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon is proposed, using the method of augmented error system. First of all, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of being unable to differentiate the state equation like in deterministic systems, the integrator is introduced. Thus, the stochastic augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the stochastic augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the stochastic augmented error system being equal to the controller of the original system is obtained. Finally, the conclusion is extended to the infinite-horizon by the redesigning of the performance index,and the state observer is also obtained.2. For a class of linear continuous-time stochastic systems with time-delay, the time-delay terms are formally eliminated by a non-singular transformation and the systems is translated into a linear stochastic system without time-delay. Then, the optimal controller for the time-delay stochastic system is obtained based on the preview control method. For a class of inpulse free linear continuous-time singular stochastic system, a restricted equivalent linear transformation is induced to translate the singular system into a normal linear stochastic system and an algebra system. Then, the optimal preview controller for the linear singular stochastic system is gained by the method for solving the normal linear stochastic system.3. For a class of linear continuous time stochastic systems based on stochastic differential equation, a compensation input is induced to translate the system to the stochastic system with a form of normal stochastic differential equation. Then, an assistant system is introduced for state shifting and an integrator is introduced to construct the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal preview controller of the original system is obtained. Finally, the stability of the stochastic augmented error system is discussed.For all the conclusions in this paper, strict mathematic derivations and proofs have been given and the effectiveness has been shown by the simulation.