Solving Constrained Optimal Control Problems Using State-Dependent Factorization and Chebyshev Polynomials

The present work introduces a method to solve constrained nonlinear optimal control problems using state-dependent coefficient factorization and Chebyshev polynomials. A recursive approximation technique known as approximating sequence of Riccati equations is used to replace the nonlinear problem by a sequence of linear-quadratic and time-varying approximating problems. The state variables are approximated and expanded in Chebyshev polynomials. Then, the control variables are written as a function of state variables and their derivatives. The constrained nonlinear optimal control problem is then converted to quadratic programming problem, and a constrained optimization problem is solved. Different final state conditions (unspecified, partly specified, and fully specified) are handled, and the effectiveness of the proposed method is demonstrated by solving sample problems.