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Multi-state dependent parameter model identification and estimation

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This chapter describes an important generalisation of the State Dependent Parameter (SDP) approach to the modelling of nonlinear dynamic systems to include Multi-State Dependent Parameter (MSDP) nonlinearities. The recursive estimation of the MSDP model parameters in a multivariable state space occurs along a multi-path trajectory, employing the Kalman Filter and Fixed Interval Smoothing algorithms. The novelty of the method lies in redefining the concepts of sequence (predecessor, successor), allowing for its use in a multi-state dependent context, so producing efficient parameterisation for a fairly wide class of non-linear, stochastic dynamic systems. The format of the estimated model allows its direct use in control system design. Two worked examples in Matlab are included.