{"ID":2881356,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.12225","arxiv_id":"2508.12225","title":"Adaptive Control with Set-Point Tracking and Linear-like Closed-loop Behavior","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.","short_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 con...","url_abs":"https://arxiv.org/abs/2508.12225","url_pdf":"https://arxiv.org/pdf/2508.12225v1","authors":"[\"Mohamad T. Shahab\"]","published":"2025-08-17T03:42:45Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}