Robust Model Predictive Control of Nonlinear Systems With Unmodeled Dynamics and Bounded Uncertainties Based on Neural Networks

• Published in: IEEE transaction on neural networks and learning systems Vol. 25; no. 3; pp. 457 - 469
• Main Authors: Yan, Zheng, Wang, Jun
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptative systems; Algorithms; Applied sciences; Artificial Intelligence; Artificial neural networks; Computer science; control theory; systems; Computer Simulation; Control theory. Systems; Dynamical systems; Exact sciences and technology; Extreme learning machine (ELM); Humans; Learning; Learning and adaptive systems; Mathematical models; Modelling and identification; Models, Neurological; Neural networks; Neural Networks (Computer); Nonlinear Dynamics; Nonlinear systems; Nonlinearity; Optimal control; Optimization; real-time optimization; recurrent neural networks (RNNs); robust model predictive control (MPC); Robustness; Time Factors; Uncertainty; unmodeled dynamics; Vectors; Extreme learning machine; recurrent neural networks (RNNs); Non linear control; Dynamical system; Jacobi matrix; Modeling; Convex programming; Optimization; Model predictive control; Minimum time; Uncertain system; Feedforward neural nets; Unmodeled dynamics; Efficiency; Minimax problem; System identification; Incomplete information; Dynamic model; Learning algorithm; Linearization; Mathematical programming; Extreme learning machine (ELM); Recurrent neural nets; real-time optimization; Neural network; Non linear system; Real time; Neurophysiology; Robust control; Supervised learning; Residue; Non linear model; Minimax method; Discrete time; Artificial intelligence; Usability; robust model predictive control (MPC)
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2013.2275948

This paper presents a neural network approach to robust model predictive control (MPC) for constrained discrete-time nonlinear systems with unmodeled dynamics affected by bounded uncertainties. The exact nonlinear model of underlying process is not precisely known, but a partially known nominal model is available. This partially known nonlinear model is first decomposed to an affine term plus an unknown high-order term via Jacobian linearization. The linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning. The minimax methodology is exploited to deal with bounded uncertainties. The minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two-layer recurrent neural network. The proposed neurodynamic approach to nonlinear MPC improves the computational efficiency and sheds a light for real-time implementability of MPC technology. Simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach.