Improved Small-Signal L2 Gain Analysis for Nonlinear Systems
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909353461678080 |
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| author | Strong, Amy Lavaei, Reza Bridgeman, Leila J. |
| author_facet | Strong, Amy Lavaei, Reza Bridgeman, Leila J. |
| contents | TheL2-gain characterizes a dynamical system's input-output properties, but can be difficult to determine for nonlinear systems. Previous work designed a nonconvex optimization problem to simultaneously search for a continuous piecewise affine (CPA) storage function and an upper bound on the small-signal L2-gain of a dynamical system over a triangulated region about the origin. This work improves upon those results by establishing a tighter upper-bound on a system's gain using a convex optimization problem. By reformulating the relationship between the Hamilton-Jacobi inequality and L2-gain as a linear matrix inequality and then developing novel LMI error bounds for a triangulation, tighter gain bounds are derived and computed more efficiently. Additionally, a combined quadratic and CPA storage function is considered to expand the nonlinear systems this optimization problem is applicable to. Numerical results demonstrate the tighter upper bound on a dynamical system's gain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08034 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Improved Small-Signal L2 Gain Analysis for Nonlinear Systems Strong, Amy Lavaei, Reza Bridgeman, Leila J. Optimization and Control Systems and Control TheL2-gain characterizes a dynamical system's input-output properties, but can be difficult to determine for nonlinear systems. Previous work designed a nonconvex optimization problem to simultaneously search for a continuous piecewise affine (CPA) storage function and an upper bound on the small-signal L2-gain of a dynamical system over a triangulated region about the origin. This work improves upon those results by establishing a tighter upper-bound on a system's gain using a convex optimization problem. By reformulating the relationship between the Hamilton-Jacobi inequality and L2-gain as a linear matrix inequality and then developing novel LMI error bounds for a triangulation, tighter gain bounds are derived and computed more efficiently. Additionally, a combined quadratic and CPA storage function is considered to expand the nonlinear systems this optimization problem is applicable to. Numerical results demonstrate the tighter upper bound on a dynamical system's gain. |
| title | Improved Small-Signal L2 Gain Analysis for Nonlinear Systems |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2309.08034 |