Guaranteed Cost Intermittent Control For A Class Of Nonlinear Systems

Due to the wide existence of nonlinear systems in practical applications,the dynamic behavior of nonlinear systems has been studied.In this thesis,the nonlinear system and its linearized system are studied respectively,and these results are applied to the heavy haul train system and spacecraft system.The theories and analysis methods suitable for the stability research of nonlinear systems are established,which better reveals the dynamic evolution mechanism and working principle of nonlinear system control.The specific research contents are as follows:The guaranteed cost intermittent control problem of nonlinear systems with parameter uncertainty is studied,for the convenience of control design,the linearization of the system is considered.The guaranteed cost intermittent control method is proposed to realize the asymptotic stability of the linearized system,and the stability criterion of the guaranteed cost intermittent controller is given.Since the upper bound of the guaranteed cost function is a nonlinear function,in order to facilitate the optimal control design of the linearized system,the auxiliary variable transformation method is introduced to transform the nonlinear optimization problem into a convex optimization problem.The effectiveness of the proposed control method is verified by numerical simulation,and compared with the previous guaranteed cost control method and periodic intermittent control method.It shows that the proposed optimal guaranteed cost intermittent control method shows superior performance in energy efficiency.The finite-time guaranteed cost intermittent control problem for nonlinear systems with parameter uncertainty is discussed.Based on the finite time stability technique and Lyapunov stability theory,the finite time stability criterion of nonlinear control systems is derived.According to the Carathéodory condition and a new comparison lemma,the finite-time stability criteria of the nonlinear piecewise continuous systems are derived.The designed Lyapunov function ensures the existence of the system satisfying the sufficient condition of finite time stability by using Hamilton-Jacobi-Bellman theory.Finally,the uncertain nonlinear model is given to illustrate the performance of the proposed control method.