5 Non-Linear Dynamic System Model : 4.5.1 From linear model to nonlinear model Many physical systems are characterized by nonlinear relationships between various phys- ical variables. Taking an example of the speech process, we can use a dynamic system model to describe the speech production process. The state equation can be used to describe the dynamic articulation process, while the observation equation be used to

doi:10.1201/9781482276237-24

Chapter

Chapter

ABSTRACT

The kernel function in the RBF should have the desirable "localized" property. The Gaussian function above satisfies such a property. Another common "localized" kernel function is

yj (x) = (11x112 + a2 ) (4.39) In a scalar form, each element of the RBF nonlinear function in Eq. 4.36 can be

written as

hi(x) = Wij • yj(x), 1 < i < I. (4.40) J=I

Typically, the analytical forms of nonlinear functions, such as the MLP and RBF described above, make the associated nonlinear dynamic systems difficult to analyze and make the estimation problems difficult to solve. Approximations are frequently used to gain computational simplifications while sacrificing accuracy for approximating the nonlinear functions.