Nearest Neighbor Control For Practical Stabilization of Passive Nonlinear Systems
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| Format: | Preprint |
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2020
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| _version_ | 1866911895653449728 |
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| author | Almuzakki, M. Z. Jayawardhana, B. Tanwani, A. |
| author_facet | Almuzakki, M. Z. Jayawardhana, B. Tanwani, A. |
| contents | This paper studies static output feedback stabilization of continuous-time (incrementally) passive nonlinear systems where the control actions can only be chosen from a discrete (and possibly finite) set of points. For this purpose, we are working under the assumption that the system under consideration is large-time norm observable and the convex hull of the realizable control actions contains the target constant input (which corresponds to the equilibrium point) in its interior. We propose a nearest-neighbor based static feedback mapping from the output space to the finite set of control actions, that is able to practically stabilize the closed-loop systems. Consequently, we show that for such systems with $m$-dimensional input space, it is sufficient to have $m+1$ discrete input points (other than zero for general passive systems or the target constant input for incrementally passive systems). Furthermore, we present a constructive algorithm to design such $m+1$ nonzero input points that satisfy the conditions for practical stability using our proposed nearest-neighbor control. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2003_13284 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Nearest Neighbor Control For Practical Stabilization of Passive Nonlinear Systems Almuzakki, M. Z. Jayawardhana, B. Tanwani, A. Optimization and Control Systems and Control 93C10, 93C30, 93C62, 93D20 This paper studies static output feedback stabilization of continuous-time (incrementally) passive nonlinear systems where the control actions can only be chosen from a discrete (and possibly finite) set of points. For this purpose, we are working under the assumption that the system under consideration is large-time norm observable and the convex hull of the realizable control actions contains the target constant input (which corresponds to the equilibrium point) in its interior. We propose a nearest-neighbor based static feedback mapping from the output space to the finite set of control actions, that is able to practically stabilize the closed-loop systems. Consequently, we show that for such systems with $m$-dimensional input space, it is sufficient to have $m+1$ discrete input points (other than zero for general passive systems or the target constant input for incrementally passive systems). Furthermore, we present a constructive algorithm to design such $m+1$ nonzero input points that satisfy the conditions for practical stability using our proposed nearest-neighbor control. |
| title | Nearest Neighbor Control For Practical Stabilization of Passive Nonlinear Systems |
| topic | Optimization and Control Systems and Control 93C10, 93C30, 93C62, 93D20 |
| url | https://arxiv.org/abs/2003.13284 |