Adaptive local linear modelling and control of nonlinear dynamical systems

In this chapter, the problem of nonlinear system identification and control system design was addressed under the divide-and-conquer principle. This principle motivated the use of multiple local models for system identification in order to simplify the modelling task. Especially in the case of unknown dynamics, where only input output data from the plant is available, the proposed method is able to approximate the nonlinear dynamics of the plant using a piecewise linear dynamical model that is optimised solely from the available data. Especially when local linear models are used as described, it also became possible to design a piecewise linear controller for the plant, whose design is based on the identified model. The questions of the existence and validity of input-output models as described and utilised was addressed theoretically using the implicit function inversion theorem that points out the observability conditions under which such models are possible to build from input-output data alone. The performance of the proposed local linear modelling scheme and the associated local linear controllers was tested on a variety of nonlinear dynamical systems including chaotic systems, a NASA aircraft and the NASA Langley transonic wind tunnel.

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