Research On Control Of Switched Nonlinear Systems With Different Powers

As an important class of hybrid systems,switched nonlinear systems are of great significance both in theory and practical applications.Since uncertain parameters,unknown control directions,random disturbances,quantized input and unmeasurable states are usually exists in the actual systems,which may degrade system performance and even lead to system instability.On the other hand,due to the interaction between continuous variables dynamic and discrete event dynamic,The dynamic behavior of system becomes more complicated.Thus many problems of controller design and stability analysis need to be solved.In recent years,researchers have achieved fruitful results in the field of feedback control of switched nonlinear systems,but there are relatively few results under the situation of different powers.Based on adding a power integrator technique,dynamic gain approach,Nussbaum-type gain method,unbounded time-varying scaling method,and Lyapunov stability theory,this paper aims to solve the problems of state feedback stabilization and tracking,quantized control,finite-time adaptive control and output feedback stabilization for several classes of switched nonlinear systems with different powers.The main contents are summarized as follows:(1)The problem of practical output tracking control is studied for a class of switched nonlinear systems with different powers.The dynamic gain technique can reduce the conservativeness of the control strategy and simplify the form of the controller.Based on the convex combination method,the original system is converted into a non-switched system.Combined with adding a power integrator technique,a dynamic state feedback controller and a proper switching law are designed.According to the Lyapunov stability theorem,it is proved that all signals of the closed-loop system are globally bounded and the error of the output and reference signal converges to any small neighborhood containing zero.Finally,a mechanical system of two inverted pendulums connected by a spring and a numerical example are given to illustrate the effectiveness of the proposed control algorithm,respectively.(2)The problem of adaptive quantized control is considered for a class of switched nonlinear systems with different powers.The system power is any odd positive number while the control directions are unknown.Hysteretic quantizer is introduced to avoid actuator chattering.Incorporating Nussbaum-type gain method into adding a power integrator technique,a new adaptive feedback controller is designed.Finally,by Lyapunov stability theory and Barbalat's lemma,it is shown that all signals of the closed-loop system are bounded and the system state asymptotically converges to the equilibrium point.(3)The problem of global state feedback stabilization is investigated for a class of switched stochastic nonlinear systems with different powers.Based on the unbounded time-varying scaling method,the original system becomes a new system by coordinate transformation of states.By backstepping technique and stochastic Lyapunov stability theorem,a state feedback controller is designed to ensure that the closed-loop system is globally asymptotically stable in probability.Finally,the continuous stirred tank reactor with a two-mode feed stream and a third-order numerical example are used to demonstrate the effectiveness of the proposed control strategy,respectively.(4)The problem of finite-time adaptive control is considered for a class of switched stochastic nonlinear systems with different powers.The system powers can be taken the ratio of any odd positive integer and odd positive integer.Uncertain parameters appear in the system drift and diffusion terms.By delicate coordinate transformations,the common Lyapunov function is constructed.Based on adding a power integrator technique,an adaptive feedback controller is designed to guarantee that the system state is regulated to the origin almost surely while maintaining the boundedness in probability of all signals of the closed-loop system.(5)Output feedback stabilization problem is studied for a class of stochastic nonlinear systems with different powers.Both the drift terms and the diffusion terms satisfy the lower-triangular homogeneous growth condition.First,a finite-time homogeneous output feedback controller is designed for the nominal system.By homogeneous domination idea,we introduce new scaling gain transformations,and construct a homogeneous observer and an output feedback controller.By selecting appropriate scaling gains,the finite-time stability in probability of the closed-loop system is achieved.Moreover,the obtained control method can be extended to a class of switched stochastic nonlinear systems with nonlinearities satisfying the upper-triangular homogeneous growth condition.