On Finite-time Control Of Several Classes Of Switched Nonlinear Systems

Switched nonlinear systems have attracted great interest due to their great significance of theoretical study and many applications in engineering.Stability and convergence are two important factors in control systems.Finite-time stability means that the system state is convergent to the origin in finite time and has faster convergence.Thus the study of finite-time control is significant both in theory and practice.Although some important results on finite-time control of switched nonlinear systems have been obtained in the literature,the corresponding results for switched nonlinear systems with mixed power orders or state constraints have not been reported to date.This paper studies finite-time control for sereral important classes of switched nonlinear systems by using finite-time control theory,Lyapunov function method and recursive design approach.Some novel finite-time stability conditions are established,and several efficient control schemes are proposed.The main contributions of this paper are as follows:1)The adaptive finite-time stabilization for a class of switched nonlinear systems in strict-feedback form is studied,where nonlinear functions are unknown and only required to be continuous.A recursive design approach is used to construct a controller and adaptive laws.In the design procedure,neural networks are used to appropriate the unknown continuous functions.It is shown that the state of the closed-loop system can converge to a small neighborhood of the origin in finite time for any switching signals.2)The adaptive finite-time stabilization for a class of switched nonlinear systems in p-normal form is discussed,where the power orders of the system are ratios of odd integers and not less than one,and the nonlinear functions contain unkown parameters.A state feedback controller and adaptive laws are constructively designed by using the adding one power integrator technique.It is proved that the state of the closed-loop system can converge to the origin in finite time under arbitrary switching.3)The finite-time stabilization for a class of switched nonlinear systems in p-normal form with mixed power orders is addressed.Compared with the exsisting results,the restrictions on power orders of the system are relaxed,and some power orders are allowed to be ratios of positive even integers over odd integers,and nonlinear functions are not required to satisfy the non-triangular form.In order to overcome the obstacle that the existing finite-time control design approaches cannot be directly applied to the addressed systems,a finite-time stability criterion for switched nonlinear systems with state-dependent switching is proposed.With the proposed criterion,state feedback controllers of individual subsystems and a state-dependent switching law are constructively designed by using the convex combination method and the adding a power integrator technique,and it is proved that the state of the closed-loop system can converge to the origin in finite time.4)The finite-time stabilization for a class of switched nonlinear systems in p-normal form with mixed power orders and state constraints is considered.State constraints mean that some or full states are required to remain in a given bounded region.A barrier Lyapunov function is constructed to overcome the effect of state constraints.Using the adding a power integrator technique,state feedback controllers of individual subsystems and a state-dependent switching law are constructively designed.It is proved that the state constraint of the closed-loop system is not violated at any time,and the state can converge to the origin in finite time.5)The finite-time output tracking for a class of switched nonlinear systems in p-normal form with mixed power orders is investigated.The considered system is a highly nonlinear system whose Jacobian linearization may have uncontrollable modes,and sometimes it is difficult to find a control law to achieve accurate tracking.To obtain the results of controller design,a finite-time boundedness criterion for switched nonlinear systems with state-dependent switching is proposed.With the proposed criterion,state feedback controllers of individual subsystems and a state-dependent switching law are constructed by using the convex combination method and the adding a power integrator technique.It is shown that the tracking error can converge to a small neighborhood of zero in finite time.