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Robust Stability Of Standard Neural Network Model And Its Application In Robust Control Of Nonlinear Systems

Posted on:2009-09-07Degree:DoctorType:Dissertation
Country:ChinaCandidate:J H ZhangFull Text:PDF
GTID:1118360272477844Subject:Control theory and control engineering
Abstract/Summary:PDF Full Text Request
Robust stability of recurrent neural networks (RNNs) has received much attention in the past decades. Because of the lack of a unified model of RNNs, however, there is no universal approach for this study. Standard neural network model (SNNM) is the interconnection of a linear dynamic system and a bounded static nonlinear operator, which is depicted as a linear differential inclusion (LDI) to be analyzed easily with linear matrix inequalities (LMI) technique. Most delayed or non-delayed RNNs can be transformed into SNNM to be analyzed in a unified way. The robust stability of SNNM is investigated detailed in this dissertation, and is used in the analysis of the robust stability of other RNNs. Moreover, most delayed (or nondelayed) intelligent systems composed of neural networks or T-S fuzzy models can be depicted as SNNM for controller synthesis. Robust control and guaranteed cost control of SNNM are studied in this dissertation. The main contributions of this dissertation are summarized as follows:A brief introduction of SNNM is presented, and several different RNNs are transformed into SNNM to show the transformation procedure and techniques. The approximation capability of SNNM is analyzed. It is approved that SNNM can approximate any dynamic systems to any degree of accuracy. The approximation capability and the learn ability justify the use of SNNM in practical applications.The robust asymptotical stability and exponential stability of continuous (discrete-time) SNNM with norm-bounded uncertainties are investigated. Applying the Lyapunov stability theory and the S-Procedure technique, some criteria for robust stability SNNM are derived. The criteria are presented as LMI. Especially, the criteria for robust exponential stability are formulated as a generalized eigenvalue problem (GEVP), which establish an estimation of the exponential convergence rate and improve the previous results. The numerical simulations show the effectiveness of our results.SNNM is used to describe some delayed(or non-delayed) intelligent systems composed of neural networks and T-S fuzzy models, and design the robust stabilizing controller and guaranteed cost controller based on the description model. State-feedback and output-feedback robust controllers for SNNMs are designed to stabilize the closed-loop systems. The control design equations are formed as a set of LMIs. Most neural-network-based (or fuzzy) intelligent systems can be transformed in to the SNNMs for controller synthesis in a unified way. SNNM provide a new approach for the analysis of RNNs and controller synthesis of nonlinear systems.
Keywords/Search Tags:standard neural network model (SNNM), recurrent neural network, robust stability, robust control, guaranteed cost control, Lyapunov functional, delayed system, intelligent systems, linear matrix inequalities (LMI)
PDF Full Text Request
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