Robust Discrete-Time Pontryagin Maximum Principle on Matrix Lie Groups

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Abstract

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.

Citation

@ARTICLE{9497722,
  author={Joshi, Anant A. and Chatterjee, Debasish and Banavar, Ravi N.},
  journal={IEEE Transactions on Automatic Control}, 
  title={Robust Discrete-Time Pontryagin Maximum Principle on Matrix Lie Groups}, 
  year={2022},
  volume={67},
  number={7},
  pages={3545-3552},
  doi={10.1109/TAC.2021.3100553}}