Parameterized Controller Design For The Switched Hamiltonian Systems

In this paper,we concentrate mainly on the parameterization of controller method and its application in stabilization control,adaptive control,robust control and optimization control for switched polynomial systems.The main work is summarized as follows:1.The adaptive passivityH₂/H_?control for switched polynomial systems is studied.A parameterized adaptive controller with the function of nonlinear compensation and performance regulation is designed.Then,with the designed parameterized controller,the nonlinear term of the system is compensated and the system is transformed into switched dissipative Hamiltonian system.A parameter solution algorithm is proposed.The obtained interval value can be used to achieve the H₂ optimization performance for the system.2.The H_?robust control of switched polynomial systems with passive and non-passive subsystems is studied.A dissipative Hamiltonian realization method for polynomial systems is studied.Utilizing this method,one or several polynomial subsystem can be feedback equivalent to passive subsystem under certain conditions.For the sake of rendering the Lyapunov function possess required decay rate along the corresponding passive subsystem,and then exponentially stabilize the switched polynomial system,a parameterized controller is designed.By selecting the storage function of the passive subsystem as its Lyapunov function,a polynomial matrix inequality condition containing parameters is obtained.Afterwards,the polynomial matrix inequality solution problem is transformed into the parameter space division problem.Thus,the interval value of the parameters can be obtained and the controller meeting the requirements can be achieved.In addition,we generalize the above results to solve theC^r-parameterized feedback exponential passivity problem for switched polynomial systems.Then,theC^r-parameterized feedback exponential passivity property of the switched polynomial system is utilized to solve the robust stabilization problem when uncertain terms and disturbance are emerged in the system.3.A parameterized Lyapunov function method is proposed to solve the feedback passification problem and robust exponentially stabilization problem for switched polynomial system with input control constraints.The parameterized controller is designed respectively and the interval value of the parameter is solved out.Then,the maximum domain of attraction of the system is estimated and the corresponding controller is designed.In addition,the global asymptotic stabilization andL₂disturbance attenuation problem of switched polynomial Hamiltonian system subject to actuator saturation is studied by using parameterization of controller method.4.The adaptive H_?control under arbitrary switching law and adaptive passification under state dependent switching law for switched polynomial time-delay systems are studied by using the parameterization of controller method.Under above two circumstances,the parameterized controllers are designed and the polynomial function inequality constraint conditions are obtained respectively.Then,by solving the polynomial function inequality constraint condition with the symbolic computation based parameter solution algorithm,the interval value of the parameter is obtained.With the obtained interval value,the parameter of the parameterized controller can be adjusted for the purpose of improving the system performance.