Optimal Control with Weighted Average Costs and Temporal Logic Specifications

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Eric M. Wolff, Ufuk Topcu and Richard M. Murray
2012 Robotics: Systems and Science (RSS) Conference

We consider optimal control for a system subject to temporal logic constraints. We minimize a weighted average cost function that generalizes the commonly used average cost function from discrete-time optimal control. Dynamic programming algorithms are used to construct an optimal trajectory for the system that minimizes the cost function while satisfying a temporal logic specification. Constructing an optimal trajectory takes only polynomially more time than constructing a feasible trajectory. We demonstrate our methods on simulations of autonomous driving and robotic surveillance tasks.