Legendre Polynomials Iterative Technique for Solving a Class of Nonlinear Optimal Control Problems

A computational algorithm is proposed to solve a class of nonlinear optimal control problems. The proposed algorithm is based on replacing the original nonlinear optimal control problem by a sequence of time-varying linear quadratic optimal control problems. This is accomplished by employing an iterative technique developed by Banks [1-5] which is based on replacing the original nonlinear system by a sequence of linear time-varying systems. Then each of the time-varying linear quadratic optimal control problems is transformed into a standard quadratic programming problem by parameterizing the state variables by a finite length Legendre polynomials with unknown parameters. The solution of a standard nonlinear optimal control problem is presented, to show the effectiveness of the proposed method.