Local modelling and control of nonlinear systems

Abstract

Whilst nonlinear system modelling, analysis and control are fundamentally important to a wide range of industries, they are difficult in practice due to nonlinearities and lack of precise knowledge of the systems, and therefore lack of developed theoretical and instrumental techniques. Among various efforts trying to overcome the difficulties, local schemes play an important role. Local methods are promising because: 1. Naturally any complex nonlinear system exhibits relatively simple behaviour in local areas, and 2. by obtaining simple local models for nonlinear systems, the maturely developed classical techniques such as linear theory can be employed to solve nonlinear problems.

However, currently the proposed local techniques using such as fuzzy system and neural networks are still suffering from the curse of dimensionality, the huge computing load in interpolation areas, and the problem of being unable to provide efficient control strategies for various nonlinear systems in practice. As an attempt to overcome some of the problems, this thesis is devoted to the development of methods for local modelling, control and stability analysis. The work of this thesis can be summarized as: 1. Local modelling: a new fuzzy modelling algorithm and an optimal piecewise locally linear modelling algorithm are developed. The methods are able to derive local models from experimental data of nonlinear systems and avoid the curse of dimensionality. 2. Local Lyapunov stability: new conditions of Lyapunov stability of local systems are derived. The conditions incorporate the input membership or in an interpolation region needs to be searched. This both relaxes the stability conditions and reduces the computation load in solving the stability problems. 3. Controller design: Following the modelling and stability results obtained, this thesis has formulated and solved the problem of robust feedback stabilization for a broad class of fuzzy systems.

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