Embedding the State Trajectories of Nonlinear Systems via Multimodel Linear Descriptions: A Data-Driven-Based Algorithm

Abstract

In this article, the problem of generating multimodel state space descriptions in a data-driven context to embed the dynamic behavior of nonlinear systems is addressed. The proposed methodology takes advantage of three ingredients: 1) linear time-invariant system behavior; 2) data-driven modeling; and 3) reinforcement learning (RL) technicalities. These elements are properly combined to develop a data-driven algorithm capable to derive an accurate outer convex approximation of the nonlinear evolution. In particular, an actor-critic RL scheme is designed to efficiently comply with the exhaustive research on the whole parameter space. At each iteration, the effectiveness of the obtained uncertain polytopic model is tested by a probabilistic approach based on a confidence level metrics. As the main merits of the proposed approach are concerned, the following aspect clearly stands up: the development of an interdisciplinary methodology that takes advantage of system theory, probabilistic arguments and RL capabilities giving rise to an harmonized architecture in charge to deal with a vast class of nonlinear systems. Finally, the validity of the proposed approach is tested by resorting to benchmark examples that allow to quantify the level of accuracy of the computed convex hull.