Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach
For control engineers designing discrete implementations of continuous controllers, this work offers preliminary quantitative insights into passivity degradation.
This paper studies how passivity degrades when a continuous controller is replaced by a discrete (symbolic) implementation, providing quantitative results on performance degradation and conditions for boundedness of the closed-loop system.
In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.