Viability theory
Dynamic Programming for Nonlinear Systems Driven by Ordinaryand Impulsive Controls
SIAM Journal on Control and Optimization
Necessary Conditions for Optimal Impulsive Control Problems
SIAM Journal on Control and Optimization
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Brief On solution concepts and well-posedness of linear relay systems
Automatica (Journal of IFAC)
The Substratum of Impulse and Hybrid Control Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
On the Maximum Principle for Impulsive Hybrid Systems
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Sufficient optimality conditions in hierarchical models of nonuniform systems
Automation and Remote Control
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We consider systems modeled by a differential inclusion subject to impulsive, set valued state resets. We study existence of solutions for this class of systems and derive conditions for a set of states to be viable. From the point of view of hybrid systems, of central interest is the fact that the class of systems and the solution concept considered allow any finite number of left and right accumulation points of the impulse times; in other words, very complex Zeno type behaviors. The results are demonstrated on simple examples that exhibit such behaviors.