This article focuses on the identification of switched nonlinear systems, which are characterized as a collection of nonlinear dynamical systems. Each nonlinear subsystem is activated by a discrete-valued variable (switching signal). Specifically, we consider the continuous-time switched nonlinear systems in the state-space form in our article. The identification of switched nonlinear systems amounts to simultaneous estimation of the switching signal and the nonlinear dynamic subsystems via all measured state-input vectors. However, the problem is challenging and generally requires a large computational complexity to be solved. In this article, we propose a novel online approach to address the identification problem of switched nonlinear systems, which is capable to handle the measured state-input vectors in sequence. In particular, the principle used for estimating the switching signal is developed based on the subspace method. Subsequently, the integral concurrent learning identifier is extended to identify the dynamics of each subsystem recursively. The effectiveness of the proposed identification approach is demonstrated via simulation results.

No abstract

Piecewise affine (PWA) models are attractive frameworks that can represent various hybrid systems with local affine submodels and polyhedral regions due to their universal approximation properties. The PWA identification problem amounts to estimating both the submodel parameters and the polyhedral partitions from data. In this paper, we propose a novel approach to address the identification problem of PWA systems such that the number of submodels, parameters of submodels, and the polyhedral partitions are obtained. In particular, a cluster-based algorithm is designed to acquire the number of submodels, the initial labeled data set, and initial parameters corresponding to each submodel. Additionally, we develop a modified self-training support vector machine algorithm to simultaneously identify the hyperplanes and parameter of each submodel with the ouputs of the cluster-based algorithm. The proposed algorithm is computationally efficient for region estimation and able to accomplish this task with only a small quantity of classified regression vectors. The effectiveness of the proposed identification approach is illustrated via simulation results.

No abstract