Learning Model Predictive Control: Theory and Applications

In control design, the goal is to synthesize policies which map observations to controlactions. Two key elements characterize today's modern design problems: an abundanceof historical data and tasks which are in full or in part repetitive. The requirements arestate and input constraint satisfaction, and performance is assessed by evaluating the costassociated with the closed-loop trajectories.In iterative control design, the policy is updated using historical data from past executionsof the control task. The policy update strategy should guarantee (a) recursive constrain satisfaction, (b) iterative performance improvement with respect to previous executions, and (c) locally optimal behavior at convergence.At present few methodologies are available to iteratively design predictive control policies,which satisfy the above requirements. The most common approaches resorts to updatethe policy after performing system identification. Guarantees are provided for constraintsatisfaction, but not for iterative performance improvements and/or optimality.This thesis introduces an iterative control design methodology for constrained linearand nonlinear systems performing iterative tasks. It leads to algorithms which iterativelysynthesize predictive control policies for classes of systems, where there are few, or no tools,currently available.We will focus on three classes of discrete time dynamical systems: (i) constrained linearsystems, (ii) constrained nonlinear systems, and (iii) constrained uncertain linear systems.For these three classes of systems we study iterative optimal control problems and we exploitknowledge of the system dynamics and historical closed-loop data in the synthesis process.After each iteration of the control task, we construct a policy which uses forecast to computesafe control actions, and it is guaranteed to improve the closed-loop performance associatedwith stored historical data.We call this approach the Learning Model Predictive Control (LMPC) framework. Forthe above systems, we introduce the policy design which exploits historical data to compute(i) a control invariant set that represents a safe set of states from which the control taskcan be completed and (ii) a control Lyapunov function which for each state of the safe setapproximates the closed-loop cost of completing the task. By using the propose syntheses,we prove that properties (a),(b) and (c) can be guaranteed for the three classes of discretetime dynamical systems under consideration.We start by presenting the LMPC design for linear and nonlinear system subject to convexand nonconvex constraints. Then, we focus on minimum time optimal control problemsfor linear and nonlinear systems. Afterwards, we solve the robust case for linear systemssubject to bounded additive uncertainty. Finally, we present a data based policy to reducethe computational burden of the LMPC at convergence.In the concluding part of the thesis, we present a system identification strategy tailoredto iterative tasks and we demonstrate the applicability of the proposed approach throughautonomous racing experiments on the Berkeley Autonomous Race Car (BARC) platform.Experimental results show that the LMPC safely learns to race a vehicle at the limits ofhandling