Model predictive control (MPC) has been widely employed as an effective
method for model-based constrained control. For systems with unknown dynamics,
reinforcement learning (RL) and adaptive dynamic programming (ADP) have
received notable attention to solve the adaptive optimal control problems.
Recently, works on the use of RL in the framework of MPC have emerged, which
can enhance the ability of MPC for data-driven control. However, the safety
under state constraints and the closed-loop robustness are difficult to be
verified due to approximation errors of RL with function approximation
structures. Aiming at the above problem, we propose a data-driven robust MPC
solution based on incremental RL, called data-driven robust learning-based
predictive control (dr-LPC), for perturbed unknown nonlinear systems subject to
safety constraints. A data-driven robust MPC (dr-MPC) is firstly formulated
with a learned predictor. The incremental Dual Heuristic Programming (DHP)
algorithm using an actor-critic architecture is then utilized to solve the
online optimization problem of dr-MPC. In each prediction horizon, the actor
and critic learn time-varying laws for approximating the optimal control policy
and costate respectively, which is different from classical MPCs. The state and
control constraints are enforced in the learning process via building a
Hamilton-Jacobi-Bellman (HJB) equation and a regularized actor-critic learning
structure using logarithmic barrier functions. The closed-loop robustness and
safety of the dr-LPC are proven under function approximation errors. Simulation
results on two control examples have been reported, which show that the dr-LPC
can outperform the DHP and dr-MPC in terms of state regulation, and its average
computational time is much smaller than that with the dr-MPC in both examples.Comment: The paper has been submitted at a IEEE Journal for possible
publicatio