Speaker
Description
The dynamics of a system are not always fully described by a continuous evolution in terms of differential equations, but also by discrete jumps of the state. Jump times and states after the jumps may be stochastic with the probability depending on the actual state of the system. This can be described in the mathematical framework of stochastic hybrid systems. As an extension to classical stochastic hybrid systems described in [1], we introduce stochastic hybrid systems of variable dimension (SHSVD). For these systems, the dimension of the continuous state may switch at jumps.
After an introduction to the concept of a solution to an SHSVD, we will discuss how different notions of stability can be carried over to SHSVD. The focus here will be on the stability of the union of all origins of the possible dimensions. As illustrating examples of the concept, we will present an exponential decay in variable dimension and an oscillator which is held and released with a probability.
We will also present a numerical algorithm to simulate SHSVD which is a combination of a numerical method for solving differential equations and a simulation of an inhomogeneous Poisson process. We will address the situation in which no a-priori bound on the probability density function of a jump occurring is known. Furthermore, we present results of numerical simulations in which the long-term behavior of an SHSVD differs from the long-term behavior of each fixed dimension subsystem.
References:
[1] A. Teel, A. Subbaraman, A. Sferlazza, “Stability analysis for stochastic hybrid systems: A survey,” Automatica, vol. 50, no. 6, pp. 2435-2456, Oct. 2014,
https://doi.org/10.1016/j.automatica.2014.08.006
