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Toward the aim of zero tracking error and user-specified convergence rate, a data-driven output tracking design for unknown linear discrete-time systems is investigated in this work. For policy learning, we customize a virtual auxiliary system, based on which an enhanced Bellman equation with the user-specified convergence rate is derived. This allows us not to explicitly measure the time for the system evolution, while only the input–output data are sufficient in our design. By utilizing the robust output regulation technique, we can learn an optimal tracker for such an auxiliary system via policy iteration and value iteration. It is proved that the output tracking error of the original discrete-time system converges to zero at the specified convergence rate. The effectiveness of the proposed algorithms is illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven model-free inverse reinforcement learning (RL) algorithm to reconstruct the unknown cost function of the demonstrated discrete-time (DT) dynamical systems with antagonistic disturbances. We propose an inverse RL policy iteration scheme that uses system dynamics and the input policies, for deriving our main result of a data-driven off-policy inverse Q-learning algorithm using only demonstrated trajectories of the antagonistic system without knowing system dynamics and the control policy gain. This data-driven algorithm consists of Q -function evaluation, state-penalty weight improvement, and action policies update. We guarantee unbiased estimates in the data-driven algorithm when exploration noises exist for the persistence of the excitation. An example verifies the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, to eliminate the tracking error by using adaptive dynamic programming (ADP) algorithms, a novel formulation of the value function is presented for the optimal tracking problem (TP) of nonlinear discrete-time systems. Unlike existing ADP methods, this formulation introduces the control input into the tracking error, and ignores the quadratic form of the control input directly, which makes the boundedness and convergence of the value function independent of the discount factor. Based on the proposed value function, the optimal control policy can be deduced without considering the reference control input. Value iteration (VI) and policy iteration (PI) methods are applied to prove the optimality of the obtained control policy, and derived the monotonicity property and convergence of the iterative value function. Simulation examples realized with neural networks and the actor–critic structure are provided to verify the effectiveness of the proposed ADP algorithm. [ABSTRACT FROM AUTHOR]