Linear Pseudospectral Method with Chebyshev Collocation for Optimal Control Problems with Unspecified Terminal Time

In this paper, a linear Chebyshev pseudospectral method (LCPM) is proposed to solve the nonlinear optimal control problems (OCPs) with hard terminal constraints and unspecified final time, which uses collocation scheme quasi-linearization. First, Taylor expansion around differential equations of system used obtain set perturbation equations. Second, first-order necessary conditions for OCPs these time are derived, provide successive correction formulas time. Traditionally, varying cannot be solved in an analytical manner. Third, Lagrange interpolation, whose supporting points orthogonal Chebyshev–Gauss–Lobatto (CGL), employed discretize resulting problem. Therefore, series successfully derived approximating polynomial space. It should noted that approximation close best approximation, CGL can closed form. Finally, LCPM applied air-to-ground missile guidance The simulation results show it has high computational efficiency convergence rate. A comparison other typical OCP solvers provided verify optimality algorithm. addition, Monte Carlo simulations presented, algorithm strong robustness stability. potential onboard application.