Online Learning Algorithm Design for Adaptive Output Regulation With Initial Excitation

This paper investigates the adaptive optimal output regulation of completely unknown linear time-invariant systems. First, a dynamic state feedback control policy with assured convergence rate requirement is developed such that the output regulation problem is transformed into a tractable optimization problem by incorporating the internal model. Then, an online-verifiable initial excitation-based dual-integrator-based learning algorithm is first proposed for establishing data-driven learning algorithm. The optimal data-driven control policy is learned by solving the linear regression equation (LRE) based on online system data, where the uniqueness of the LRE solution is established by verifying an invertible matrix under an online-verifiable initial excitation condition, rather than requiring the full-rank condition. Compared with existing iterative learning algorithms, our proposed algorithm relaxes those limitations, including the persistent exciting condition, the computation of memory-expensive delayed-window integral, the full-rank condition, an intelligent data-storage, and an initial stabilizing control policy. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed algorithms, and detailed comparisons with existing algorithms are provided.