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Optimal Control and Mechanics

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Encyclopedia of Systems and Control

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Introduction

There are very natural close connections between mechanics and optimal control as both involve variational problems. This is a huge subject and we just touch on some interesting connections here. A survey and history may be found in Sussman and Willems (1997). Other aspects may be found in Bloch (2003).

Variational Nonholonomic Systems and Optimal Control

Variational nonholonomic problems (i.e., constrained variational problems) are equivalent to optimal control problems under certain regularity conditions. This issue was investigated in Bloch and Crouch (1994), employing the classical results of Rund (1966) and Bliss (1930), which relate classical constrained variational problems to Hamiltonian flows, although not optimal control problems. We outline the simplest relationship and refer to Bloch (2003) for more details.

Let Q be a smooth manifold and TQ its tangent bundle with coordinates \((q^{i},\dot{q}^{i})\). Let \(L : TQ \rightarrow\mathbb{R}\)be a given smooth...

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Authors and Affiliations

  1. Department of Mathematics, The University of Michigan, Ann Arbor, MI, USA

    Anthony Bloch

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  1. Anthony Bloch
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Correspondence to Anthony Bloch .

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Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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Bloch, A. (2014). Optimal Control and Mechanics. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_46-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_46-1

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