{
  "id": "1307.7395",
  "version": "v1",
  "published": "2013-07-28T19:49:32.000Z",
  "updated": "2013-07-28T19:49:32.000Z",
  "title": "A soothing invisible hand: moderation potentials in optimal control",
  "authors": [
    "Debra Lewis"
  ],
  "comment": "26 pages, 6 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "A moderation incentive is a continuously differentiable control-dependent cost term that is identically zero on the boundary of the admissible control region, and is subtracted from the `do or die' cost function to reward sub-maximal control utilization in optimal control systems. A moderation potential is a function on the cotangent bundle of the state space such that the solutions of Hamilton's equations satisfying appropriate boundary conditions are solutions of the synthesis problem - the control-parametrized Hamiltonian system central to Pontryagin's Maximum Principle. A multi-parameter family of moderation incentives for affinely controlled systems with quadratic control constraints possesses simple, readily calculated moderation potentials. One member of this family is a shifted version of the kinetic energy-style control cost term frequently used in geometric optimal control. The controls determined by this family approach those determined by a logarithmic penalty function as one of the parameters approaches zero, while the cost term itself is bounded.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-28T19:49:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J15",
      "37N35"
    ],
    "keywords": [
      "optimal control",
      "moderation potential",
      "soothing invisible hand",
      "energy-style control cost term",
      "control constraints possesses simple"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7395L"
    }
  }
}