Zonotopic Filtering for Uncertain Nonlinear Systems: Fundamentals, Implementation Aspects, and Extensions [Applications of Control]
Alesi Augusto de Paula, Guilherme V. Raffo, Bruno O. S. Teixeira
Abstract
This tutorial provides a comprehensive perspective on the study of zonotopic filtering for nonlinear uncertain dynamical systems. Unlike stochastic methods that characterize the states by means of random vectors, set-based observers estimate deterministic sets that are guaranteed to contain the system states. Among many classes of sets, the focus here is on zonotopes due to their appealing properties that pursue a good tradeoff between precision and computational cost. We start by reviewing the fundamentals of zonotopic filtering together with illustrative examples. As nonlinear systems bring up many challenges for this topic, we choose one of the first nonlinear zonotopic observers proposed in the literature to guide a series of discussions. After presenting this algorithm and understanding its limitations, we extend it by incorporating state inequality constraints. In addition, we motivate the use of linear programs when solving minimum-volume intersections. Additionally, we give a practical discussion on the implementation of discrete-time zonotopic algorithms for sampled-data nonlinear dynamical systems. To better introduce the zonotopic approaches, we briefly review unscented Kalman filtering to trace parallels between the stochastic and set-theoretic frameworks. Then the presented algorithms are experimented and compared in a case study involving a quadrotor unmanned aerial vehicle.