Robust Discrete-Time Pontryagin Maximum Principle on Matrix Lie Groups
- 27 July 2021
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 67 (7), 3545-3552
- https://doi.org/10.1109/tac.2021.3100553
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 maximise a cost that the control tries to minimise. 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.Keywords
Funding Information
- Indian Space Research Organization (18ISROC001)
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