Nonlinear Optimal Midcourse Guidance Using Sequential Pseudospectral Model Predictive Control

A sequential pseudospectral model predictive control (SPMPC) method is proposed for nonlinear optimal midcourse guidance with a general performance index. First, the optimal midcourse guidance problem is formulated as a standard Bolza optimal control problem. Then, integral prediction and Taylor expansion are employed to convert it into a sequence of quadratic optimal control subproblems. Differing from previous work, the proposed method makes full use of the predicted nominal trajectory to sequentially approximate the nonlinear performance index as a quadratic function of deviations. The coefficients in this function are composed of the partial derivatives of the Lagrange term in the performance index, and need to be updated at each iteration. Next, the calculus of variations and Gauss pseudospectral collocation are utilized to successfully derive an approximate analytical optimal solution to the subproblem in the orthogonal polynomial space. Although the analytical solution is mathematically complex, it provides an effective correction to the current control, facilitating its convergence to the desired optimal solution. The SPMPC method is evaluated in a midcourse guidance scenario with the objective of maximizing terminal velocity. Numerical results demonstrate that this method can efficiently produce the optimal command, which significantly increases the terminal velocity of the missile in comparison with traditional midcourse guidance methods. Monte Carlo simulation results further validate its strong stability and robustness.