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arXiv · 2508.12225

Adaptive Control with Set-Point Tracking and Linear-like Closed-loop Behavior

Mohamad T. Shahab
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Abstract

In this paper, we consider the problem of set-point tracking for a discrete-time plant with unknown plant parameters belonging to a convex and compact uncertainty set. We carry out parameter estimation for an associated auxiliary plant, and a pole-placement-based control law is employed. We prove that this adaptive controller provides desirable linear-like closed-loop behavior which guarantees a bound consisting of: exponential decay with respect to the initial condition, a linear-like convolution bound with respect to the exogenous inputs, and a constant scaled by the square root of the constant in the denominator of the parameter estimator update law. This implies that the system has a bounded gain. Moreover, asymptotic tracking is also proven when the disturbance is constant.

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Mohamad T. Shahab. 2025-08-17. Adaptive Control with Set-Point Tracking and Linear-like Closed-loop Behavior. https://arxiv.org/abs/2508.12225

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