| In the real world,most systems are nonlinear.Therefore,the research on nonlinear systems has always been a hot topic in academic community.Many scholars have done large numbers of works on Lipschitz systems and one-sided Lipschitz systems,and achieved rich results.However,the derived conditions may be some conservative if the nonlinear function is described by Lipschitz or one-sided Lipschitz constraints.For example,when the scope of nonlinear function is expanded,the sufficient conditions for the stability of desired systems obtained by Lipschitz constraint or one-sided Lipschitz constraint are not solvable.Hence,nonlinear systems satisfying incremental quadratic constraint attract attention gradually in the field of control.The essence of Lipschitz constraint and one-sided Lipschitz constraint is to describe the nonlinear function in the form of inequality through a parameter,while the incremental quadratic constraint describes the nonlinear function through a set of parameterized matrices.On the other hand,due to the physical restriction of actuator,actuator saturation is a common problem existing in control systems.If the actuator saturation is ignored in the design of control system,the control efficiency may be reduced,and even the system may be unstable,resulting in disastrous consequences.This paper considers the nonlinear systems satisfying incremental quadratic constraint.Firstly,the design method of state observer is given for this kind of nonlinear systems.Then,a controller is designed for incremental quadratic constrained nonlinear systems subject to actuator saturation.In addition,in view of the expansibility of system,the distributed control protocol is designed for nonlinear multi-agent systems with actuator saturation.The contents of this paper are mainly summarized as follows:1.Observer design for a class of uncertain nonlinear systems satisfying incremental quadratic constraint.The uncertainties existing in systems are described by a monotonic set-valued function,and a novel extended-type framework observer is proposed for the systems.The extended-type observer contains three correction terms,namely linear correction term,nonlinear correction term and set-valued correction term,which can increase the freedom of designed observer and lead to less conservative results.Simulation experiments are carried out using mechanical rotor system and vertical takeoff UAV system.The results demonstrate the validity of designed observer.2.Control design for incremental quadratic constrained nonlinear systems with actuator saturation.In this thesis,the saturated nonlinear input is transformed into a series of convex combination forms of linear feedback by the linear convex hull method,and the Sprocedure is employed to deal with the incremental quadratic constrained nonlinearity.In order to obtain a lager domain of attraction,the composite Lyapunov function is constructed to ensure sufficient conditions for the stability of closed systems,and the estimate problem of maximizing domain of attraction is transformed into a convex optimization problem of maximizing a parameter.A numerical simulation case of chemical stirring reaction system illustrates the validity of the proposed approaches.3.Consensus design for nonlinear multi-agent systems with actuator saturation.A novel nonlinear multiple convex hull representation is presented for multiagent systems with actuator saturation.By using this method,each control gain matrix and auxiliary gain matrix are further decomposed into the form of convex combination of multiple matrices.Based on multiple convex hull representation,the consensus control protocols for leaderless multi-agent systems and leader-following multi-agent systems are designed respectively.In order to determine a lager domain of consensus,the composite Lyapunov function is extended to the distributed composite Laplacian function,and sufficient conditions for the consensus of multi-agent systems are given.Simulation experiments are carried out for a leaderless multi-agent system and a leader-following multi-agent system.The results show that the presented protocol is effective and the proposed method leads to a larger domain of consensus than the traditional linear convex hull method.This paper designs the observer,saturation controller and distributed control protocol for nonlinear systems satisfying incremental quadratic constraint,which makes up for shortcomings of current research on nonlinear systems with incremental quadratic constraint,and has important theoretical significance.Meanwhile,the design methods of observer,controller and distributed control protocol proposed in this paper are expected to be applied to practical engineering fields such as driverless car,autonomous underwater vehicle and multi-unmanned aerial vehicle formation flight control. |
