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Data-Driven Control of Unknown Systems: A Linear Programming Approach
We consider the problem of discounted optimal state-feedback regulation for
general unknown deterministic discrete-time systems. It is well known that
open-loop instability of systems, non-quadratic cost functions and complex
nonlinear dynamics, as well as the on-policy behavior of many reinforcement
learning (RL) algorithms, make the design of model-free optimal adaptive
controllers a challenging task. We depart from commonly used least-squares and
neural network approximation methods in conventional model-free control theory,
and propose a novel family of data-driven optimization algorithms based on
linear programming, off-policy Q-learning and randomized experience replay. We
develop both policy iteration (PI) and value iteration (VI) methods to compute
an approximate optimal feedback controller with high precision and without the
knowledge of a system model and stage cost function. Simulation studies confirm
the effectiveness of the proposed methods
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