Hybrid control systems and viscosity solutions

Dharmatti, Sheetal ; Ramaswamy, Mythily (2005) Hybrid control systems and viscosity solutions SIAM Journal on Control and Optimization, 44 (4). pp. 1259-1288. ISSN 0363-0129

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Official URL: http://epubs.siam.org/sicon/resource/1/sjcodc/v44/...

Related URL: http://dx.doi.org/10.1137/040618072


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 quasi-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:Article
Source:Copyright of this article belongs to Society for Industrial and Applied Mathematics.
Keywords:Dynamic Programming Principle; Viscosity Solution; Quasi-variational Inequality; Hybrid Control
ID Code:62293
Deposited On:20 Sep 2011 09:32
Last Modified:18 May 2016 11:39

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