A Continuous Optimization Approach to Drift Counteraction Optimal Control

Drift counteraction optimal control (DCOC) aims at optimizing control to maximize the time (or a yield) until the system trajectory exits a prescribed set, which may represent safety constraints, operating limits, and/or efficiency requirements. To DCOC problems formulated in discrete time, conventional approaches were based on dynamic programming (DP) or mixed-integer programming (MIP), which could become computationally prohibitive for higher-order systems. In this paper, we propose a novel approach to discrete-time DCOC problems based on a nonlinear programming formulation with purely continuous variables. We show that this new continuous optimization-based approach leads to the same exit time as the conventional MIP-based approach, while being computationally more efficient than the latter. This is also illustrated by numerical examples representing the drift counteraction control for an indoor airship.