Robust Saturated Stabilization With Measurement Errors: From a Chain of Integrators to Feedforward Systems

• Published in: IEEE transactions on automatic control Vol. 69; no. 3; pp. 1 - 15
• Main Authors: Wang, Mengxi, Liu, Tengfei, Jiang, Zhong-Ping
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loop systems; Closed loops; Control systems design; Coordinate measuring machines; Coordinate transformations; Errors; Event-triggered control; Feedback control; Feedforward systems; Integrators; measurement error; Measurement errors; Measurement uncertainty; Nonlinear systems; robust stabilization; small-gain synthesis; Stabilization; Subsystems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2023.3329342

This paper studies the saturated stabilization problem of a chain of perturbed integrators subject to measurement errors. Inspired by the technique of nested saturation loops, a key strategy is to employ saturated set-valued maps and a generalized coordinate transformation to overcome the difficulty caused by the measurement errors. It is shown that, with the refined controller design, the closed-loop system is transformed into an interconnection of subsystems, each of which can be rendered small-disturbance input-to-state stable (ISS). The small-gain theorem is used to guarantee small-disturbance ISS of the closed-loop system with the measurement errors as the inputs. Interestingly, the proposed methodology yields new solutions to the open problems of measurement feedback control and event-triggered control for a broader class of uncertain, nonlinear feedforward systems.