ABSTRACT

Nonlinear autoregressive moving average with the exogenous input (NARMAX) model [89,98,99] is a general description of discrete-time nonlinear nonaffine systems. However, the controller design for such a model is quite difficult due to the intrinsic nonlinearity with respect to control input. A common approach to deal with this kind of general nonlinear systems is to convert the original NARMAX model into a linearized one, so as to be easily studied within the relatively welldeveloped linear system framework. There are several typical linearization methods, such as feedback linearization [100-113], Taylor’s linearization [114-118], piecewise linearization [119], orthogonal-function-approximation-based linearization

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[120-122], and so on. However, all of these linearization methods have their own limitations. Feedback linearization intends to find a direct channel between the system output and the control input, for which the accurate mathematical model of the controlled system is needed. As we know, obtaining the accurate model is very difficult and sometimes impossible for a practical plant. Taylor’s linearization uses Taylor expansion around the operating point without high-order terms to obtain a linearized model, which offers an approximate expression of the controlled system. Taylor’s linearization has found many successful applications in practice, but also encounters some difficulties in theoretical analysis for control system design due to the omitted high-order terms. Piecewise linearization executes Taylor expansion in a piecewise manner to improve linearization accuracy. More information, however, such as the switching instant and the dwell time of the piecewise linearized dynamics of a controlled plant, is needed. Orthogonalfunction-approximation-based linearization utilizes a set of orthogonal basis functions to approximate the nonlinear model of a controlled plant. A large number of parameters, however, will appear in the linearized model, and the number of the parameters will increase exponentially as more orthogonal basis functions are involved, which leads to a heavy computational burden for parameter identification algorithms and complexity in controller design.