Gradient Method for Solving Multisystem Integrated Optimal Control Problem With Undetermined Terminal Time

This article aims at proposing a multisystem gradient method (MSGM) for solving the integrated nonlinear optimal control problem with multiple systems and unspecified terminal time. This method is based on the influence functions, which are used to predict changes in performance indices and terminal conditions caused by changes in control and terminal time, so as to update the improvements of control and terminal time. To improve the computational efficiency, the linear Gauss pseudospectral technology is employed, which successfully transfers the nonlinear differential equations into a set of linear algebraic equations. In addition, all systems are discreted in the orthogonal points, which leads to the fact that the coupling degree among the systems is very low. In most calculations, each system is independent of the other, and only the multiplier associated with terminal time needs to be solved simultaneously. In other words, the computational complexity will be significantly reduced, which is suitable for online applications. Finally, MSGM is applied to the multimissile cooperative guidance with the same attack time. The simulation results show that the algorithm has high computational efficiency and fast convergence rate. In addition, the stability and robustness of the algorithm are also excellent.