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Hybrid Control Systems and Viscosity Solutions

Dharmatti, Sheetal and Ramaswamy, Mythily (2005) Hybrid Control Systems and Viscosity Solutions. In: SIAM Journal on Control and Optimization, 44 (4). pp. 1259-1288.

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We investigate a model of hybrid control system in which both discrete and continuous controls are involved. In this general model, discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set A or a controlled jump set C where the controller can choose to jump or not. At each jump, the trajectory can move to a different Euclidean space. We prove the continuity of the associated value function V with respect to the initial point. Using the dynamic programming principle satisfied by V , we derive a uasi-variational inequality satisfied by V in the viscosity sense. We characterize the value function V as the unique viscosity solution of the quasi-variational inequality by the comparison principle method.

Item Type: Journal Article
Publication: SIAM Journal on Control and Optimization
Publisher: Society for Industrial and Applied Mathematics
Additional Information: Copyright for this article belongs to Society for Industrial and Applied Mathematics.
Keywords: dynamic programming principle;viscosity solution;quasi-variational inequality;hybrid control
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 27 Dec 2005
Last Modified: 19 Sep 2010 04:22
URI: http://eprints.iisc.ac.in/id/eprint/4790

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