Title: Simple Policy Evaluation for Data-Rich Iterative Tasks,
Abstract: A data-based policy for iterative control task is presented. The proposed
strategy is model-free and can be applied whenever safe input and state
trajectories of a system performing an iterative task are available. These
trajectories, together with a user-defined cost function, are exploited to
construct a piecewise affine approximation to the value function. Approximated
value functions are then used to evaluate the control policy by solving a
linear program. We show that for linear system subject to convex cost and
constraints, the proposed strategy guarantees closed-loop constraint
satisfaction and performance bounds on the closed-loop trajectory. We evaluate
the proposed strategy in simulations and experiments, the latter carried out on
the Berkeley Autonomous Race Car (BARC) platform. We show that the proposed
strategy is able to reduce the computation time by one order of magnitude while
achieving the same performance as our model-based control algorithm.