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In this paper we present a Learning Model Predictive Control (LMPC) strategyfor linear and nonlinear time optimal control problems. Our work builds onexisting LMPC methodologies and it guarantees finite time convergenceproperties for the closed-loop system. We show how to construct a time varyingsafe set and terminal cost function using closed-loop data. The resulting LMPCpolicy is time varying and it guarantees recursive constraint satisfaction andnon-decreasing performance. Computational efficiency is obtained by convexifingthe safe set and terminal cost function. We demonstrate that, for a class ofnonlinear system and convex constraints, the convex LMPC formulation guaranteesrecursive constraint satisfaction and non-decreasing performance. Finally, weillustrate the effectiveness of the proposed strategies on minimum timeobstacle avoidance and racing examples.

Minimum Time Learning Model Predictive Control