Disturbance-observer-based Sliding Mode Control For Delayed Systems

Sliding mode control is essentially a kind of variable structure control.The main idea of sliding mode control is to drive the states of systems at any initial position into the predesigned sliding surface in finite time and then slide to an equilibrium point asymptotically.Compared with traditional control methods,the main advantages of sliding mode control are that it has appealing abilities of good transient performance,fast response,and especially complete robustness against matched disturbances and uncertainties.Therefore,it has been extensively applied in mobile machine control,ship control,satellite attitude control,spacecraft control,manipulator control,and so on.However,in some practical systems,the sliding mode control may not be designed and applied when the external disturbances are hard to or can not directly be measured.Therefore,it is important to find an effectively method to obtain the information of unknown disturbances.On the other hand,considering the influence of time delay on stability performance of systems,the study of dynamic behavior of delayed systems has very important significance in sense of theory and practice.Based on the above analysis,this thesis introduces the disturbance observer into the design of sliding mode control and focuses on the sliding mode control strategies for delayed systems with unknown disturbances by using LyapunovKrasovskii method and linear matrix inequality(LMI)technique.It mainly includes:In Chapter 1,the research background and practical significance of this topic are firstly introduced.Then,the basic features and a brief history of sliding mode control are emphasized.Finally,we provide the structure of this thesis.In Chapter 2,the synchronization of nonidentical networks with unknown disturbances is analyzed and studied.On the one hand,we consider the synchronization for nonidentical chaotic neural networks by designing the observerbased sliding mode control strategy.Firstly,the information of unknown disturbances can be estimated by the designed disturbance observer and then is passed to the sliding mode controller.Then,we design the observer-based sliding mode controller such that the error systems can be driven into the sliding surface and have the sliding mode dynamic in the surface.By constructing the sliding surface function dependent on the structure of the systems,it can effectively deal with synchronization problem even with complex structure.After that,some sufficient conditions are derived to guarantee the synchronization of chaotic neural networks by constructing Lyapunov-Krasovskii functional and using the LMI technique.On the other hand,under the same research idea,we also study the globally asymptotical synchronization of nonidentical complex dynamic networks with delays and unknown disturbances.The designed sliding mode controller not only ensures the accessibility of integral sliding surface,but also overcomes the influence of disturbances in the control channel.We finally present two simulation examples to illustrate the effectiveness of the results.In Chapter 3,the stabilization problem of delayed systems with mismatched disturbances is analyzed and studied.Firstly,a nonlinear disturbance observer is constructed to compensate the mismatched disturbances,where the disturbances are harmonic disturbances represented by a linear system.A sliding mode controller based on disturbance observer is designed to ensure that the nonlinear sliding surface is finite-time reachable.Then,we consider the coupling system comprised by delayed system and disturbance error dynamic.By constructing Lyapunov-Krasovskii functional and using LMI technique,the trajectories of the systems converge to a disturbance-dependent state asymptotically.The theoretical results are applied to the study of product concentration in a continuous stirred tank reactor,and the effectiveness of our results is demonstrated by numerical simulations.In particular,when there is no time delay in the systems,the unknown disturbances are assumed to tend to a constant steady state in infinite time.Moveover,the proposed sliding mode controller is dependent on the boundary of disturbance error,which can not only guarantee that the trajectories of the systems reach the sliding surface in finite time,but also reduce chattering effectively.By constructing a suitable Lyapunov function,some sufficient conditions are given to show that the systems tend to a disturbance-dependent state asymptotically.Finally,an example with numerical simulations is given to illustrate the rationality of the method.In Chapter 4,the practical stability for nonlinear delayed systems with unknown disturbances is analyzed and studied.Although the information of external disturbances is hard to or can not directly be measured,the derivative of the disturbances is bounded.By using LMI technique and Young’s inequality,we firstly present an important lemma to show that the delayed systems are locally bounded.In addition,the information of unknown disturbances can be estimated by the designed nonlinear disturbance observer and then is passed to the sliding mode controller.Then,the observer-based event-triggered sliding mode control strategy is designed to ensure the existence of practical sliding mode and realize robust practical stability of the systems.The research results not only save the control cost,but also reduce the chattering frequency through the design of trigger rules.Finally,the effectiveness of the proposed results is verified by two simulation examples.