Successive Approximation Optimal Control for A Class of Chaotic Systems

In this paper, successive approximation approach for optimal control of the equilibrium states of the Lorenz system is presented. We first formulate the equations of perturbed state of Lorenz equilibrium states problem and a sequence of linear two-point boundary value problem. A suboptimal control law is obtained by using iteration of the nonlinear compensation sequence of perturbed equation. The suboptimal control functions can successfully suppress arbitrary initial states to equilibrium states and achieve the stability. Finally, computational simulations of optimal control for equilibrium stabilization of Lorenz system are provided to illustrate the results.