Robust Discrete-Time Pontryagin Maximum Principle on Matrix Lie Groups

• 成果类型: Article
• 署名作者: Joshi, Anant A.; Chatterjee, Debasish; Banavar, Ravi N.
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Bombay
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3100553
• 发表日期: 2022
• 页码: 3545-3552
• 关键词: Optimal control; MANIFOLDS; Aerospace electronics; uncertainty; games; STANDARDS; Numerical simulation; geometric control; optimal control; Pontryagin maximum principle (PMP); Robust control; saddle point

摘要

This article considers a discrete-time robust optimal control problem on matrix Lie groups. The underlying system is assumed to be perturbed by exogenous unmeasured bounded disturbances, and the control problem is posed as a min-max optimal control wherein the disturbance is the adversary and tries to maximize a cost that the control tries to minimize. Assuming the existence of a saddle point in the problem, we present a version of the Pontryagin maximum principle (PMP) that encapsulates first-order necessary conditions that the optimal control and disturbance trajectories must satisfy. This PMP features a saddle point condition on the Hamiltonian and a set of backward difference equations for the adjoint dynamics. We also present a special case of our result on Euclidean spaces. We conclude with applying the PMP to robust version of single axis rotation of a rigid body.