Contingent Hybrid Systems

Abstract

This work proposes the first steps for studying resilient control for uncertain hybrid systems. We take a rather radical approach and consider the situations of severe uncertainty. This requires the replacement of classical Kolmogorov probabilities with special concepts from the generalized measure theory. To achieve this goal, we need a rigorous and carefully developed mathematical framework, which constitutes the major contribution of this paper. Technically, the resilience framework of hybrid systems is defined in two steps. First, we introduce the contingent hybrid system that is a mathematical model where uncertainty is quantized using both probabilities and generalized measures. Then, the concept of lithe decision is introduced for this model. The new method combines decision theory with model predictive control and statistics for uncertainty measures.