Further results on synergistic Lyapunov functions and hybrid feedback\n design through backstepping

2020/09/08 by Christopher G. Mayhew, Mayhew, Christopher G., Ricardo G. Sanfelice +3
Engineering · #Control and Stability of Dynamical Systems #Advanced Control Systems Optimization #Adaptive Control of Nonlinear Systems

paper · pdf · doi:10.48550/arxiv.2009.03815

Abstract

We extend results on backstepping hybrid feedbacks by exploiting synergistic\nLyapunov function and feedback (SLFF) pairs in a generalized form. Compared to\nexisting results, we delineate SLFF pairs that are ready-made and do not\nrequire extra dynamic variables for backstepping. From an (weak) SLFF pair for\nan affine control system, we construct an SLFF pair for an extended system\nwhere the control input is produced through an integrator. The resulting hybrid\nfeedback asymptotically stabilizes the extended system when the synergy gap for\nthe original system is strictly positive. To highlight the versatility of SLFF\npairs, we provide a result on the existence of a SLFF pair whenever a hybrid\nfeedback stabilizer exists. The results are illustrated on the 3D pendulum.\n

Citations

• Multiple Lyapunov functions and other analysis tools for switched and hybrid systems

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