Low-Gain Stability of Projected Integral Control for Input-Constrained Discrete-Time Nonlinear Systems

We consider the problem of zeroing an error output of a nonlinear discrete-time system in the presence of constant exogenous disturbances, subject to hard convex constraints on the input signal. The design specification is formulated as a variational inequality, and we adapt a forward-backward split...

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Bibliographic Details
Published in:IEEE control systems letters Vol. 6; pp. 788 - 793
Main Author: Simpson-Porco, John W.
Format: Journal Article
Language:English
Published: IEEE 2022
Subjects:
Actuators
Constrained control
Linear systems
Minimization
output regulation
PID control
Power system stability
Regulation
Stability criteria
Steady-state
ISSN:2475-1456, 2475-1456
Online Access:Get full text
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Summary:We consider the problem of zeroing an error output of a nonlinear discrete-time system in the presence of constant exogenous disturbances, subject to hard convex constraints on the input signal. The design specification is formulated as a variational inequality, and we adapt a forward-backward splitting algorithm to act as an integral controller which ensures that the input constraints are met at each time step. We establish a low-gain stability result for the closed-loop system when the plant is exponentially stable, generalizing previously known results for integral control of discrete-time systems. Specifically, it is shown that if the composition of the plant equilibrium input-output map and the integral feedback gain is strongly monotone, then the closed-loop system is exponentially stable for all sufficiently small integral gains. The method is illustrated via application to a four-tank process.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2021.3086682