Stability Analysis And Optimal Control Of A Class Of Parameter Varying Systems

In this paper,we discuss the optimal control problem of a class of linear parameter varying systems(LPV).This system originates from the control problem of aero-engine and has strong practical significance.First,we describe the model of the LPV system,and use the existence and uniqueness theorem of solutions in the theory of differential equations and the continuous dependence theorem of parameters to give the qualitative analysis of this kind of LPV system,and prove the existence of the local solution first,and then use the extension theorem of ordinary differential equation to paste the extension of the local solution,so as to obtain the overall existence of the solution.Considering the initial value as a parameter,we discuss the continuous dependence of the solution on the initial value and the parameter.Second,we present the LPV system optimal control problem,and we approximate control function by piecewise constant function,so as to convert the original optimal control problem into optimal parameter selection problem of a finite number of decision variables using the control parameterization method(CP),then we derive the gradient formula of the control parameters of the objective function corresponding to the variational method and the costate method.Finally,based on the framework of the CP method,we obtain the gradient information by the previous method based on the costate method and the variational method,and the traditional nonlinear optimization algorithm is combined to design a concrete algorithm for solving the problem.The validity of the algorithm is verified by solving several numerical examples,and the results are compared and illustrated.