This paper presents a novel sequential inverse optimal control (SIOC) method for discrete-time systems, which calculates the unknown weight vectors of the cost function in real time using the input and output of an optimally controlled discrete-time system. The proposed method overcomes the limitations of previous approaches by eliminating the need for the invertible Jacobian assumption. It calculates the possible-solution spaces and their intersections sequentially until the dimension of the intersection space decreases to one. The remaining one-dimensional vector of the possible-solution space's intersection represents the SIOC solution. The paper presents clear conditions for convergence and addresses the issue of noisy data by clarifying the conditions for the singular values of the matrices that relate to the possible-solution space. The effectiveness of the proposed method is demonstrated through simulation results.

中文翻译：

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离散时间系统的顺序逆最优控制

本文提出了一种新颖的离散时间系统顺序逆最优控制（SIOC）方法，该方法利用最优控制离散时间系统的输入和输出实时计算成本函数的未知权重向量。所提出的方法通过消除对可逆雅可比假设的需要，克服了先前方法的局限性。它依次计算可能解空间及其交集，直到交集空间的维数减小到一。可能解空间交集的剩余一维向量表示 SIOC 解。该论文提出了明确的收敛条件，并通过阐明与可能解空间相关的矩阵奇异值的条件来解决噪声数据的问题。通过仿真结果证明了该方法的有效性。