Parameter Tuning for Optimal Control of Switched Systems With Applications in Hypersonic Vehicles

Optimal control of switched systems (OCSS) is of great importance since they have significant practical implementation. This letter aims to tackle the problem of adapting OCSS to additional objective functions. We propose an algorithm to enable a tunable OCSS to adjust its parameters dynamically with respect to an additional loss function in a bi-level framework. At the higher level, the algorithm utilizes gradient descent to minimize this additional objective function while simultaneously addressing an optimal control problem at the lower level. By differentiating the maximum principle for the optimal control of switched systems, gradient computation is achieved by solving an auxiliary initial value problem. Besides theoretical analysis, the algorithm’s effectiveness is also numerically demonstrated by optimal control problems of a hypersonic vehicle with a combined-power engine.