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Encyclopedia of Systems and Control pp 1–8Cite as

Optimal Control and the Dynamic Programming Principle

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Abstract

This entry illustrates the application of Bellman’s Dynamic Programming Principle within the context of optimal control problems for continuous-time dynamical systems. The approach leads to a characterization of the optimal value of the cost functional, over all possible trajectories given the initial conditions, in terms of a partial differential equation called the Hamilton–Jacobi–Bellman equation. Importantly, this can be used to synthesize the corresponding optimal control input as a state-feedback law.

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Bibliography

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, SAPIENZA – Università di Roma, Rome, Italy

    Maurizio Falcone

Authors
  1. Maurizio Falcone
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Correspondence to Maurizio Falcone .

Editor information

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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© 2014 Springer-Verlag London

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Falcone, M. (2014). Optimal Control and the Dynamic Programming Principle. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_209-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_209-1

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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