Learning From ISS-Modular Adaptive NN Control of Nonlinear Strict-Feedback Systems

• Published in: IEEE transaction on neural networks and learning systems Vol. 23; no. 10; pp. 1539 - 1550
• Main Authors: Cong Wang, Min Wang, Tengfei Liu, Hill, D. J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptative systems; Adaptive neural control; Algorithms; Applied sciences; Approximation methods; Artificial Intelligence; Artificial neural networks; Closed loop systems; Computer science; control theory; systems; Computer Simulation; Connectionism. Neural networks; Control system analysis; Control systems; Control theory. Systems; deterministic learning; Exact sciences and technology; exponential stability; Feedback; International Space Station; Learning; Linear Models; Mathematical analysis; Neural networks; Neural Networks (Computer); Nonlinear Dynamics; Nonlinearity; Orbits; Pattern Recognition, Automated - methods; persistent excitation; Process control. Computer integrated manufacturing; Radial basis function networks; Stability; Stability analysis; strict-feedback systems; Studies; Vectors; Recurrence; Non linear control; Feedback regulation; Exponential stability; Adaptive control; Learning; Time varying system; Efficiency; strict-feedback systems; Tracking error; System identification; Deterministic approach; deterministic learning; Intelligent control; Closed loop; Orbit; Process control; Modular system; Neural network; Non linear system; Affine transformation; Closed feedback; Radial basis function; Neurocontrollers; Input to state stability; Recursive method; Adaptive neural control; persistent excitation
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2012.2205702

This paper studies learning from adaptive neural control (ANC) for a class of nonlinear strict-feedback systems with unknown affine terms. To achieve the purpose of learning, a simple input-to-state stability (ISS) modular ANC method is first presented to ensure the boundedness of all the signals in the closed-loop system and the convergence of tracking errors in finite time. Subsequently, it is proven that learning with the proposed stable ISS-modular ANC can be achieved. The cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using existing methods. To overcome these difficulties, the stable closed-loop system in the control process is decomposed into a series of linear time-varying (LTV) perturbed subsystems with the appropriate state transformation. Using a recursive design, the partial persistent excitation condition for the radial basis function neural network (NN) is established, which guarantees exponential stability of LTV perturbed subsystems. Consequently, accurate approximation of the closed-loop system dynamics is achieved in a local region along recurrent orbits of closed-loop signals, and learning is implemented during a closed-loop feedback control process. The learned knowledge is reused to achieve stability and an improved performance, thereby avoiding the tremendous repeated training process of NNs. Simulation studies are given to demonstrate the effectiveness of the proposed method.