Approximate optimal hybrid control synthesis by classification-based derivative-free optimization

Hybrid systems are widely used in safety-critical areas. Hybrid optimal control synthesis, which aims to generate an optimal sequence of control inputs for a given task, is one of the most important problems in the field. The classical Gradient-based methods are efficient but they require the system under control should be differentiable. Sampling-based methods have no such limitations, but the ability of existing ones to solve complex control missions is restricted. In this paper, we propose a practical and efficient method to solve a general class of hybrid optimal control problems. Basically, we transform the control synthesis problem into a derivative-free optimization (DFO) problem. Then, we adapt a start-of-art classification-based DFO method to solve the optimization problems based on sampled variables efficiently. Furthermore, for complex state space, which is difficult to solve, we present a piecewise control synthesis method to make a tradeoff between optimality and efficiency by generating feasible and piecewise optimal control inputs instead. The empirical results on two complex real-world hybrid systems: a vehicle and a quadcopter drone system, demonstrate that our method outperforms existing methods significantly.