A Learning Model Predictive Controller (LMPC) for iterative tasks is presented. The controller is referencefree and is able to improve its performance by learning from previous iterations. A safe set and a terminal cost function are used in order to guarantee recursive feasibility and nondecreasing performance at each iteration. The paper presents the control design approach, and shows how to recursively construct terminal set and terminal cost from state and input trajectories of previous iterations. Simulation results show the effectiveness of the proposed control logic.

In this paper we present a Learning Model Predictive Control (LMPC) strategy for linear and nonlinear time optimal control problems. Our work builds on existing LMPC methodologies and it guarantees finite time convergence properties for the closed-loop system. We show how to construct a time varying safe set and terminal cost function using historical data. The resulting LMPC policy is time varying and it guarantees recursive constraint satisfaction and performance improvement. Computational efficiency is obtained by convexifing the safe set and terminal cost function. We demonstrate that, for a class of nonlinear system and convex constraints, the convex LMPC formulation guarantees recursive constraint satisfaction and performance improvement. Finally, we illustrate the effectiveness of the proposed strategies on minimum time obstacle avoidance and racing examples. arXiv:1911.09239v1 [eess.SY]

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In this paper we present a Learning Model Predictive Controller (LMPC) for autonomous racing. We model the autonomous racing problem as a minimum time iterative control task, where an iteration corresponds to a lap. The system trajectory and input sequence of each lap are stored and used to systematically update the controller for the next lap. In the proposed approach the race time does not increase at each iteration. The first contribution of the paper is to propose a local LMPC which reduces the computational burden associated with existing LMPC strategies. In particular, we show how to construct a local safe set and approximation to the value function, using a subset of the stored data. The second contribution is to present a system identification strategy for the autonomous racing iterative control task. We use data from previous iterations and the vehicle's kinematic equations of motion to build an affine time-varying prediction model. The effectiveness of the proposed strategy is demonstrated by experimental results on the Berkeley Autonomous Race Car (BARC) platform.