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

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