State Estimation and Tracking Control for Hybrid Systems by Gluing the Domains

TL;DR

This paper introduces a method to convert hybrid systems with state jumps into continuous systems using domain gluing, simplifying observer and controller design without jump detection.

Contribution

It proposes a novel approach of domain gluing for hybrid systems, enabling jump-free observer and tracking controller design with minimal assumptions.

Findings

Observer design does not require jump detection.

Tracking control does not need to account for plant state jumps.

Provides structural conditions and concrete examples for implementation.

Abstract

We study the design problems of state observers and tracking controllers for a class of hybrid systems whose state jumps. The idea is to utilize the well-known method of gluing the jump set (a part of domain where the jumps take place) onto its image, which converts the hybrid system into a continuous-time system whose state does not jump. Sufficient conditions for this idea to be implemented are listed and discussed with a few concrete examples. In particular, we present a structural condition for an observer design, and, for tracking control, we introduce a feedback to compensate residual discontinuity in the vector field after gluing. The benefits of the proposed approach include that the observer design does not require detection of the state jumps, and that the tracking control does not require the plant state jumps when the reference jumps.