Modeling of Dynamical Systems via Successive Graph Approximations

2019/10/08 by Nair, Siddharth H., Bujarbaruah, Monimoy, Borrelli, Francesco
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.1910.03719

Abstract

In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using envelopes described by quadratic constraints. The proposed approach is then demonstrated on two control applications: (i) computation of tractable bounds for unmodeled dynamics, and (ii) computation of positive invariant sets. We further highlight the efficacy of the proposed approach via a detailed numerical example.

Related

• Nonlinear Dynamic Systems Parameterization Using Interval-Based Global Optimization: Computing Lipschitz Constants and Beyond
• Set-based state estimation of nonlinear discrete-time systems using constrained zonotopes and polyhedral relaxations
• Iterative data-driven inference of nonlinearity measures via successive graph approximation
• Online Learning and Control Synthesis for Reachable Paths of Unknown Nonlinear Systems
• Adaptation and Parameter Estimation in Systems with Unstable Target Dynamics and Nonlinear Parametrization