Modified -Policy Iteration Based Adaptive Dynamic Programming for Unknown Discrete-Time Linear Systems

this article, the 1-policy iteration (1-PI) method for the optimal control problem of discrete-time linear systems is reconsidered and restated from a novel aspect. First, the traditional 1-PI method is recalled, and some new properties of the traditional 1-PI are proposed. Based on these new properties, a modified 1-PI algorithm is introduced with its convergence proven. Compared with the existing results, the initial con-dition is further relaxed. The data-driven implementation is then constructed with a new matrix rank condition for veri-fying the feasibility of the proposed data-driven implementation. A simulation example verifies the effectiveness of the proposed method.