Finite-time Stabilization And Synchronization For A Class Of Nonlinear Systems Via Optimal Control

In general,any system can be stabilized by finite-time stabilization technique if control cost is not considered.However,control cost is an important factor in control field.In this thesis,we apply optimal control method to finite-time stabilization problem of a class of nonlinear systems such that its control cost is reduced.After that,finite-time synchronization via optimal control is considered.By introducing the finite-time stabilization concept,designing an appropriate control,and constructing the Lyapunov function,we obtain a sufficient condition to achieve the finite-time stabilization.we formulate a controlled system based on Lyapunov function.Then,by introducing the control cost functional,the finite stabilization problem is formulated into an optimal control problem,that is,the control function is optimized such that the system achieve the finite-time the stabilization with minimum control cost.By utilizing control parameterization method and control parameter enhancing technique,this optimal control problem is well solved.At the same time,considering external perturbations are inevitably exist,finite-time stabilization the nonlinear system with stochastic vibration is also considered.Numerical simulations demonstrate the effectiveness of the theoretical analysis.Finally,the finite-time mixed outer synchronization of neural networks is studied.By using strict mathematical proof and designing suitable feedback controllers,sufficient conditions are given to ensure the finite-time outer synchronization of the neural network.Moreover,optimal control method is utilized to guarantee that the finite-time outer synchronization is achieved with minimum control cost.The theoretical results are verified by numerical simulations.