Stabilizing constrained chaotic system using a symplectic psuedospectral method

Abstract

The problem of controlling chaotic systems has drawn much attention in the last two decades. However, the controlled system may be subjected to complicated constraints and few researches on controlling chaos take constraints into consideration. Therefore, the stabilization of constrained chaotic system is solved under the frame of nonlinear optimal control in this paper. A symplectic pseudospectral method based on qusilinearizaiton techniques and the parametric variational principle is developed to solve constrained nonlinear optimal control problems with arbitrary Lagrange-type cost functional. At the beginning of the proposed method, the original nonlinear optimal control problem is converted into a series of linear-quadratic constrained optimal control problems. Then each of the converted linear quadratic problems is transformed into a standard linear complementarity problem. The proposed method is successfully applied to stabilizing constrained chaotic systems around an unstable equilibrium point or an unstable periodic orbit. Numerical simulations demonstrate that the developed method is effective and efficient, and constraints are strictly satisfied.