Adaptive Control with Set-Point Tracking and Linear-like Closed-loop Behavior
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916904292057088 |
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| author | Shahab, Mohamad T. |
| author_facet | Shahab, Mohamad T. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Control with Set-Point Tracking and Linear-like Closed-loop Behavior Shahab, Mohamad T. Systems and Control Optimization and Control 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. |
| title | Adaptive Control with Set-Point Tracking and Linear-like Closed-loop Behavior |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2508.12225 |