Finite-time Control Based on Linear Quadratic Performance Index

The finite-time feedback control problem based on quadratic performance index is studied for a class of linear continuous systems. Combining the finite-time Lyapunov stability theorem with the Hamilton-Jacobi-Bellman equation in dynamic programming, the nonlinear finite-time optimal feedback control law with the derivative of finite-time V-function is designed for the linear quadratic performance index function. This control law ensures the finite-time stability of the systems and minimizes the performance index function. Then the specific finite-time V-function is constructed to verified that the control law containing this function can guarantee the finite-time stability and optimality of the given systems, and numerical simulations show the effectiveness of the control law.