2018/05/15 by Raik Suttner, Suttner, Raik
Computer Science · Engineering · #Advanced Control Systems Optimization #Distributed Control Multi-Agent Systems #Dynamical Systems (math.DS) #Extremum Seeking Control Systems #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1805.05991
openalex publication_date 2018/05/15 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
We study convergence and stability properties of control-affine systems. Our\nconsiderations are motivated by the problem of stabilizing a control-affine\nsystem by means of output feedback for states in which the output function\nattains an extreme value. Following a recently introduced approach to extremum\nseeking control, we obtain access to the ascent and descent directions of the\noutput function by approximating Lie brackets of suitably defined vector\nfields. This approximation is based on convergence properties of trajectories\nof control-affine systems under certain sequences of open-loop controls. We\nshow that a suitable notion of convergence for the sequences of open-loop\ncontrols ensures local uniform convergence of the corresponding sequences of\nflows. We also show how boundedness properties of the control vector fields\ninfluence the quality of the approximation. Our convergence results are\nsufficiently strong to derive conditions under which the proposed output\nfeedback control law induces exponential stability. We also apply this control\nlaw to the problem of purely distance-based formation control for nonholonomic\nmulti-agent systems.\n