Learning Model Predictive Control: Theory and Applications

In control design, the goal is to synthesize policies which map observations to control/nactions. Two key elements characterize today's modern design problems: an abundance/nof historical data and tasks which are in full or in part repetitive. The requirements are/nstate and input constraint satisfaction, and performance is assessed by evaluating the cost/nassociated with the closed-loop trajectories./nIn iterative control design, the policy is updated using historical data from past executions/nof the control task. The policy update strategy should guarantee/n(a) recursive constrain satisfaction,/n(b) iterative performance improvement with respect to previous executions, and/n(c) locally optimal behavior at convergence./nAt present few methodologies are available to iteratively design predictive control policies,/nwhich satisfy the above requirements. The most common approaches resorts to update/nthe policy after performing system identification. Guarantees are provided for constraint/nsatisfaction, but not for iterative performance improvements and/or optimality./nThis thesis introduces an iterative control design methodology for constrained linear/nand nonlinear systems performing iterative tasks. It leads to algorithms which iteratively/nsynthesize predictive control policies for classes of systems, where there are few, or no tools,/ncurrently available./nWe will focus on three classes of discrete time dynamical systems: (i) constrained linear/nsystems, (ii) constrained nonlinear systems, and (iii) constrained uncertain linear systems./nFor these three classes of systems we study iterative optimal control problems and we exploit/nknowledge of the system dynamics and historical closed-loop data in the synthesis process./nAfter each iteration of the control task, we construct a policy which uses forecast to compute/nsafe control actions, and it is guaranteed to improve the closed-loop performance associated/nwith stored historical data./nWe call this approach the Learning Model Predictive Control (LMPC) framework. For/nthe above systems, we introduce the policy design which exploits historical data to compute/n(i) a control invariant set that represents a safe set of states from which the control task/ncan be completed and (ii) a control Lyapunov function which for each state of the safe set/napproximates the closed-loop cost of completing the task. By using the propose syntheses,/nwe prove that properties (a),(b) and (c) can be guaranteed for the three classes of discrete/ntime dynamical systems under consideration./nWe start by presenting the LMPC design for linear and nonlinear system subject to convex/nand nonconvex constraints. Then, we focus on minimum time optimal control problems/nfor linear and nonlinear systems. Afterwards, we solve the robust case for linear systems/nsubject to bounded additive uncertainty. Finally, we present a data based policy to reduce/nthe computational burden of the LMPC at convergence./nIn the concluding part of the thesis, we present a system identification strategy tailored/nto iterative tasks and we demonstrate the applicability of the proposed approach through/nautonomous racing experiments on the Berkeley Autonomous Race Car (BARC) platform./nExperimental results show that the LMPC safely learns to race a vehicle at the limits of/nhandling.

Advisor: Borrelli, Francesco