{
  "id": "2007.13459",
  "version": "v1",
  "published": "2020-07-27T12:02:55.000Z",
  "updated": "2020-07-27T12:02:55.000Z",
  "title": "Robust Discrete-Time Pontryagin Maximum Principle on Matrix Lie Groups",
  "authors": [
    "Anant A. Joshi",
    "Debasish Chatterjee",
    "Ravi N. Banavar"
  ],
  "categories": [
    "math.OC"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-27T12:02:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "robust discrete-time pontryagin maximum principle",
      "matrix lie groups",
      "robust optimal control problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}