Parameter-Dependent Control Lyapunov Functions for Stabilizing Nonlinear Parameter-Varying Systems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916644081631232 |
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| author | Zhao, Pan |
| author_facet | Zhao, Pan |
| contents | This paper introduces the concept of parameter-dependent (PD) control Lyapunov functions (CLFs) for gain-scheduled stabilization of nonlinear parameter-varying (NPV) systems. It shows that given a PD-CLF, a min-norm control law can be constructed by solving a robust quadratic program. For polynomial control-affine NPV systems, it provides convex conditions, based on the sum of squares programming, to jointly synthesize a PD-CLF and a PD controller while maximizing the PD region of stabilization. Input constraints can be straightforwardly incorporated into the synthesis procedure. Unlike traditional linear parameter-varying (LPV) methods that rely on linearization or over-approximation to get an LPV model, the proposed framework fully captures the nonlinearities of the system dynamics. The theoretical results are validated through numerical simulations, including a 2D rocket landing case study under varying mass and inertia. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06770 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parameter-Dependent Control Lyapunov Functions for Stabilizing Nonlinear Parameter-Varying Systems Zhao, Pan Optimization and Control Systems and Control This paper introduces the concept of parameter-dependent (PD) control Lyapunov functions (CLFs) for gain-scheduled stabilization of nonlinear parameter-varying (NPV) systems. It shows that given a PD-CLF, a min-norm control law can be constructed by solving a robust quadratic program. For polynomial control-affine NPV systems, it provides convex conditions, based on the sum of squares programming, to jointly synthesize a PD-CLF and a PD controller while maximizing the PD region of stabilization. Input constraints can be straightforwardly incorporated into the synthesis procedure. Unlike traditional linear parameter-varying (LPV) methods that rely on linearization or over-approximation to get an LPV model, the proposed framework fully captures the nonlinearities of the system dynamics. The theoretical results are validated through numerical simulations, including a 2D rocket landing case study under varying mass and inertia. |
| title | Parameter-Dependent Control Lyapunov Functions for Stabilizing Nonlinear Parameter-Varying Systems |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2502.06770 |