A Hybrid Numerical Approach for Solving Nonlinear Optimal Control Problems

This paper presents an iterative computational method for addressing constrained nonlinear optimal control problems‎, ‎specifically those involving terminal state‎, ‎state saturation‎, ‎and control saturation constraints‎. ‎The proposed approach reformulates the original problem into a sequence of constrained linear time-varying quadratic optimal control problems‎. ‎This is achieved by iteratively approximating the nonlinear dynamic system using constrained linear time-varying models‎. ‎Each reformulated problem is then converted into a standard quadratic programming problem by applying Chelyshkov polynomials in conjunction with a collocation method‎. ‎Finally‎, ‎the resulting problems are solved to obtain optimal control solutions