A numerical method for hybrid optimal control based on dynamic programming

This contribution extends a numerical method for solving optimal control problems by dynamic programming to a class of hybrid dynamic systems with autonomous as well as controlled switching. The value function of the hybrid control system is calculated based on a full discretization of the state and...

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Veröffentlicht in:Nonlinear analysis. Hybrid systems Jg. 5; H. 2; S. 254 - 274
Hauptverfasser: Rungger, Matthias, Stursberg, Olaf
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.05.2011
Schlagworte:
Approximation
Discretization
Dynamic programming
Dynamical systems
Dynamics
Errors
Hybrid systems
Mathematical analysis
Mathematical models
Nonlinear dynamics
Numerical analysis
Optimal control
Value function
Hybrid systems
Value function
Approximation
Dynamic programming
Optimal control
ISSN:1751-570X
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Beschreibung
Zusammenfassung:This contribution extends a numerical method for solving optimal control problems by dynamic programming to a class of hybrid dynamic systems with autonomous as well as controlled switching. The value function of the hybrid control system is calculated based on a full discretization of the state and input spaces. A bound for the error due to discretization is obtained from modeling the error as perturbation of the continuous dynamics and the cost terms. It is shown that the bound approaches zero and that the value function of the discretized variant converges to the value function of the original problem if the discretization parameters go to zero. The performance of a numerical scheme exploiting the discretized system is illustrated for two different examples treated previously in literature.
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ISSN:1751-570X
DOI:10.1016/j.nahs.2010.09.002