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Zbl 1197.49038
Attia, Sid Ahmed; Azhmyakov, Vadim; Raisch, Joerg
On an optimization problem for a class of impulsive hybrid systems. (English)
[J] Discrete Event Dyn. Syst. 20, No. 2, 215-231 (2010). ISSN 0924-6703; ISSN 1573-7594/e

Summary: This contribution addresses the problem of optimal control for a class of hybrid systems, where discrete transitions are accompanied by instantaneous changes in the continuous state variables, and where these changes can be considered as control variables. Based on a variational approach, necessary conditions of optimality are first established. The problem is then cast as a parametric optimization problem for which gradient information is derived. Finally, we discuss assumptions that guarantee convergence of a conceptual algorithm to a stationary solution. A brief discussion on the main implementation issues is also included.

MSC 2000:: *49N25 Impulsive optimal control problems
49K20 Optimal control problems with PDE (nec./ suff.)

Keywords: hybrid systems; optimization; gradient methods; state jump; switching; parameter optimization

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