Optimal Guaranteed Cost Control Of Uncertain Singular Systems Via Sliding Mode Control

In view of the widespread applications of singular systems in various fields in recent years,it has prompted scholars to conduct an in-depth and systematic study on them.With the development of modern control theory,the control problems of the singular systems are no longer limited to that the closed-loop systems are stable,regular and impulse free.At the same time,the closed-loop systems are also required to meet the optimal performance.In this thesis,the sliding mode control of uncertain singular systems is studied first.Then considering the sliding mode control and the optimal guaranteed cost control can work together in the systems,the control problems of the singular systems with time-delay are studied.The main work includes the following aspects:First of all,for the existence of uncertainties in singular systems,consider the introduction of sliding mode control.Among the design methods related to stability problems,sliding mode control has the special advantage that the sliding mode dynamics are completely robust and the physical implementation is simple,considering the parameter changes and external disturbances that meet the matching conditions.Then,after selecting the appropriate integral sliding mode surface,the ideal sliding mode dynamics of the corresponding singular systems are obtained by sliding mode surface s(t)=0 and s(t)=0 according to the arrival condition.In this thesis,the linear matrix inequality(LMI)condition is given to ensure the dynamic of sliding mode is admissible,and the design algorithm of integral sliding mode surface gain K is obtained.Finally,the state trajectory of singular systems can reach the sliding mode surface and stay on the sliding mode surface,completing the suppression of the uncertainty.Then,considering the mathematical model of the systems,designing the linear sliding surface and the dynamic sliding mode controller,the closed-loop form of the singular systems with uncertain time-delay is obtained.The systems are proved to reach the sliding surface within a finite time by the Lyapunov function.When analyzing the sliding mode dynamics of the closed-loop singular systems with uncertain time-delay,a sufficient condition for the nominal systems is given.Basis on this,a criterion that allows the singular systems with uncertain time-delay to be admissible when the uncertain parameters are bounded norm is given,and the suppression of uncertainties is completed.Then in the case of giving a quadratic index,a sufficient condition is given for the singular systems with time-delay to ensure that there exists a state feedback guaranteed cost controller.Then,the LMI is used to give the related controller design algorithms and to establish the convex optimization problem.Convex optimization algorithms can be used to test whether LMI can solve and generate a specific solution.Finally,the main work of the full text is summarized,and the future research on guaranteed cost related to singular systems is prospected.