Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.09806 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929572473208832 |
|---|---|
| author | Rezaee, Hamed Renson, Ludovic |
| author_facet | Rezaee, Hamed Renson, Ludovic |
| contents | Control-based continuation (CBC) is a general and systematic method to explore the dynamic response of a physical system and perform bifurcation analysis directly during experimental tests. Although CBC has been successfully demonstrated on a wide range of systems, rigorous and general approaches to designing a noninvasive controller underpinning the methodology are still lacking. In this paper, a noninvasive adaptive control strategy for a wide class of nonlinear systems with unknown parameters is proposed. We prove that the proposed adaptive control methodology is such that the states of the dynamical system track a reference signal in a noninvasive manner if and only if the reference is a response of the uncontrolled system to an excitation force. Compared to the existing literature, the proposed method does not require any a priori knowledge of some system parameters, does not require a persistent excitation, and is not restricted to linearly-stable systems, facilitating the application of CBC to a much larger class of systems than before. Rigorous mathematical analyses are provided, and the proposed control method is numerically demonstrated on a range of single- and multi-degree-of-freedom nonlinear systems, including a Duffing oscillator with multiple static equilibria. It is especifically shown that the unstable periodic orbits of the uncontrolled systems can be stabilized and reached, noninvasively, in controlled conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09806 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Noninvasive Adaptive Control of a Class of Nonlinear Systems With Unknown Parameters Rezaee, Hamed Renson, Ludovic Dynamical Systems Control-based continuation (CBC) is a general and systematic method to explore the dynamic response of a physical system and perform bifurcation analysis directly during experimental tests. Although CBC has been successfully demonstrated on a wide range of systems, rigorous and general approaches to designing a noninvasive controller underpinning the methodology are still lacking. In this paper, a noninvasive adaptive control strategy for a wide class of nonlinear systems with unknown parameters is proposed. We prove that the proposed adaptive control methodology is such that the states of the dynamical system track a reference signal in a noninvasive manner if and only if the reference is a response of the uncontrolled system to an excitation force. Compared to the existing literature, the proposed method does not require any a priori knowledge of some system parameters, does not require a persistent excitation, and is not restricted to linearly-stable systems, facilitating the application of CBC to a much larger class of systems than before. Rigorous mathematical analyses are provided, and the proposed control method is numerically demonstrated on a range of single- and multi-degree-of-freedom nonlinear systems, including a Duffing oscillator with multiple static equilibria. It is especifically shown that the unstable periodic orbits of the uncontrolled systems can be stabilized and reached, noninvasively, in controlled conditions. |
| title | Noninvasive Adaptive Control of a Class of Nonlinear Systems With Unknown Parameters |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2307.09806 |