终端受限的线性-非二次最优控制问题

Linear-Nonquadratic Optimal Control Problem with Terminal Constraints

该文研究一类(输出)终端受限的线性 非二次最优控制问题,在系统输出能控、目标泛函(是依赖于控制函数与相应的输出函数的泛函且)在一定程度上可以不定等条件下用一列终端不受限(因而易于求解)的线性 非二次最优控制问题作为原终端受限问题的近似,建立起很强的收敛性结果———近似问题的最优控制(函数)列与最优值数列分别一致收敛与收敛到原问题的最优控制(函数)与最优值.

This paper studies a linearnonquadratic optimal control problem with terminal constraints. Under the conditions that the system is output controllable,the objective functional is allowed to be indefinite to a certain extent,etc.,the authors approximate the above terminal constrained problem by a series of linearnonquadratic optimal control problems without terminal constraints and establish a rather strong convergence result--the optimal control functions of the approximate problems uniformly converge to the optimal control function of the original terminal constrained problem and the optimal values of the approximate problems (also) converge to the optimal value of the original problem.