Abstract
We propose a new class of hybrid (discrete-continuous) dynamical system models with nondeterministic continuous evolutions and switching between discrete modes. Formally, this class is rather similar to the class of stochastic hybrid systems, but it is based on possibility theory. This approach has an advantage over stochastic models when available statistical information is not sufficient for constructing a reliable stochastic model. For example, it may be useful for modeling human-machine-environment systems, because, as it has been argued in the literature, possibility theory describes many aspects of human behavior better than probability theory. In this work we present a motivating example, give a definition and semantics of our systems, consider reachability problems for large subclasses of them, and propose methods to tackle these problems.
Highlights
Hybrid systems [1,2,3] are dynamical systems with interacting continuous-time and discrete-event dynamics
Continuous-time dynamics is usually modeled by differential equations and discrete-event dynamics is usually modeled by automata
In this paper we propose a new class of hybrid systems with uncertain switching, which is based on the possibility theory [6,7,8,9]
Summary
Hybrid systems [1,2,3] are dynamical systems with interacting continuous-time and discrete-event dynamics. In this paper we propose a new class of hybrid systems with uncertain switching, which is based on the possibility theory [6,7,8,9] We argue that this class is well-suited for modeling human-machine systems, e.g. a driver-vehicle system. The paper is organized in the following way: in section 2 we consider the problem of modeling driver-vehicle system and propose a possibilistic model of hybrid system for this problem (on informal level); in section 3 we recall necessary notions of possibility theory; in section 4 we formally define a simple subclass of possibilistic systems with uncertain switching and investigate basic properties and the reachability problem for systems of this class; in section 5 we define a more general class of hybrid possibilistic systems with uncertain switching and investigate its properties and the reachability problem
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