Multi-Objective Optimal Control For Discrete Bilinear System With Disturbances

The bilinear system could be used to describe many different objects, and with the existence of the bilinear term, its accuracy is obvious better than the traditional linear model, so it has been widely applied in the control engineering. In the actual project, the existing of the disturbances seriously affected the performance of the system, so the disturbance rejections become part of the issues that can not be ignored in the system research. Meanwhile, in many practical problems, the performance index of the system is many-sided; the controller based on one performance index is hard to satisfy the anticipant requirements. At present, the achievement considered comprehensively the aspects talked above are very little.This thesis first reviews the multi-objective optimal control algorithm for linear discrete-time system by dynamic programming. Then based on the algorithm of linear system, the multi-objective optimal control problem for discrete bilinear system with disturbance is studied. The main research can be summarized as follows:Firstly, give a brief overview of the paper; introduce the research situation and development prospects of the bilinear system. Introduce the type of the optimal control methods and the optimal control performances. Emphasized the theoretical basis of the thesis that was used solving the multi-objective problem, which is "Dynamic Programming".Secondly, for discrete linear system, an approximate optimal algorithm for multi-objective system is proposed. Introduced a multi-stage decision problem to preliminary described the ideas and methods of dynamic programming. Then detailed introduced the foundation that was used to solving discrete linear system and quadratic performance index problem and give the specific algorithm that was solved the optimal control law. The design process aimed at the two cases that the objective function in multi-objective discrete linear system is respectively linear and nonlinear is given. At last, a detailed analysis of the calculation with examples is given.Then, for discrete bilinear system, on the basis of the multi-objective optimal control algorithm of discrete linear system, multi-objective optimal control problem for discrete bilinear system is studied. Firstly the mathematical model of discrete bilinear system with multi-objective problems is given, by analyzing and simplifying, approximately transformed it into a linear system model, then give the specific algorithm that was solved the optimal control law. The design process aimed at the two cases that the objective function in multi-objective discrete bilinear system is respectively linear and nonlinear is given. The simulation result demonstrates the effect of the proposed method.Finally, the multi-objective optimal control problem for discrete bilinear system with disturbance is studied. On the basis of the discrete bilinear system, dynamic programming and multi-objective optimal control theory, an approximate optimum algorithm for multi-objective discrete bilinear system with disturbance is proposed. In view the disturbance phenomenon exists in the actual; the disturbance model analysis is given. Summarized the general disturbance and the sinusoidal perturbation mathematical model, and then proposed an optimal control design method for the control system with general disturbance and the sinusoidal disturbance. At last, the simulation result demonstrates the effect of the proposed method.