Identification and Control for Singularly Perturbed Systems Using Multitime-Scale Neural Networks

• Published in: IEEE transaction on neural networks and learning systems Vol. 28; no. 2; pp. 321 - 333
• Main Authors: Zheng, Dongdong, Xie, Wen-Fang, Ren, Xuemei
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Artificial Intelligence - trends; Artificial neural networks; Computer simulation; Control stability; Control systems; Convergence; Discrete time systems; Ellipsoids; Feedback control; Identification; Manifolds; Mathematical model; Neural networks; Neural Networks (Computer); Nonlinear Dynamics; Nonlinear systems; optimal bounded ellipsoid (OBE); Order parameters; recurrent high-order neural network (RHONN); Singular perturbation; Singular perturbation methods; singularly perturbed system (SPS); Stability analysis; Time Factors; Uncertainty; Weight
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2015.2508738

Many well-established singular perturbation theories for singularly perturbed systems require the full knowledge of system model parameters. In order to obtain an accurate and faithful model, a new identification scheme for singularly perturbed nonlinear system using multitime-scale recurrent high-order neural networks (NNs) is proposed in this paper. Inspired by the optimal bounded ellipsoid algorithm, which is originally designed for discrete-time systems, a novel weight updating law is developed for continuous-time NNs identification process. Compared with other widely used gradient-descent updating algorithms, this new method can achieve faster convergence, due to its adaptively adjusted learning rate. Based on the identification results, a control scheme using singular perturbation theories is developed. By using singular perturbation methods, the system order is reduced, and the controller structure is simplified. The closed-loop stability is analyzed and the convergence of system states is guaranteed. The effectiveness of the identification and the control scheme is demonstrated by simulation results.