Year: 2022
Type: preprint
Abstract: We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations research called risk functionals (i.e., risk measures) to facilitate diverse distributional characterizations. In contrast, classical stochastic stability notions characterize the state energy on average or in probability, which can obscure the variability of stochastic system behavior. After drawing connections between various risk-aware stability concepts for nonlinear systems, we specialize to linear systems and derive sufficient conditions for the satisfaction of some risk-aware stability properties. These results pertain to real-valued coherent risk functionals and a mean-conditional-variance functional. The results reveal novel noise-to-state stability properties, which assess disturbances in ways that reflect the chosen measure of risk. We illustrate the theory through examples about robustness, parameter choices, and state-feedback controllers.
Source: arXiv (Cornell University)
Institution: University of Toronto
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Award: G2614460161
OpenAlex ID: W4309877384