Adaptive Optimal Control for Discrete-Time Linear Systems via Hybrid Iteration

In this paper, a novel dynamic programming (DP) and adaptive dynamic programming (ADP) algorithms are proposed, namely hybrid iteration (HI), for discrete-time linear systems. The proposed HI approach fill up the performance gap of two well- known DP algorithms, i.e., policy iteration (PI) and value iteration (VI). In particular, HI drops the need of the prior knowledge of an initial stabilizing control policy required in PI, and at the same time it maintains a fast quadratic convergence rate compared with VI. A data-driven adaptive optimal controller design is also proposed based on the proposed HI algorithm. Simulation results for randomly generated discrete-time linear systems with different system orders demonstrate that the proposed HI approach can significantly save CPU time and reduce the number of learning iterations to converge to the optimal solution comparing with the VI approach. The data-driven HI method is implemented to an application of turbocharged diesel engine with exhaust gas recirculation, and the simulation results illustrate the efficacy of the proposed HI method.