2020/11/10 by Franck Djeumou, Abraham P. Vinod, Djeumou, Franck +7
Computer Science · Engineering · Medicine · #Advanced Control Systems Optimization #Cardiac Arrest and Resuscitation #FOS: Electrical engineering #FOS: Mathematics #Formal Methods in Verification #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2011.05524
openalex publication_date 2020/11/10 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We develop data-driven algorithms for reachability analysis and control of\nsystems with a priori unknown nonlinear dynamics. The resulting algorithms not\nonly are suitable for settings with real-time requirements but also provide\nprovable performance guarantees. To this end, they merge noisy data from only a\nsingle finite-horizon trajectory and, if available, various forms of side\ninformation. Such side information may include knowledge of the regularity of\nthe dynamics, algebraic constraints on the states, monotonicity, or decoupling\nin the dynamics between the states. Specifically, we develop two algorithms,\n\DaTaReach and \DaTaControl, to over-approximate the\nreachable set and design control signals for the system on the fly.\n\DaTaReach constructs a differential inclusion that contains the\nunknown dynamics. Then, in a discrete-time setting, it over-approximates the\nreachable set through interval Taylor-based methods applied to systems with\ndynamics described as differential inclusions. We provide a bound on the time\nstep size that ensures the correctness and termination of \DaTaReach.\n\DaTaControl enables convex-optimization-based control using the\ncomputed over-approximation and the receding-horizon control framework.\nBesides, \DaTaControl achieves near-optimal control and is suitable\nfor real-time control of such systems. We establish a bound on its\nsuboptimality and the number of primitive operations it requires to compute\ncontrol values. Then, we theoretically show that \DaTaControl\nachieves tighter suboptimality bounds with an increasing amount of data and\nricher side information. Finally, experiments on a unicycle, quadrotor, and\naircraft systems demonstrate the efficacy of both algorithms over existing\napproaches.\n