Sequential Inverse Optimal Control of Discrete-Time Systems

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.