Design method of exact model matching control for finite Volterra series systems

The model matching problem for a class of polynomial non-linear discrete input–output systems with cross-products. An algorithmic approach

“…Though there is already a clear understanding of the linear problem (Astrom and Witenmark 1984;Glad and Ljung 2000), the non-linear case is still being examined and is the subject matter of a large number of papers: see for instance (Glad 1990;Kotsios and Kalouptsidis 1993b;Yamanaka et al 1997;Conte, Moog and Perdon 1999), to mention but a few.…”

“…The model matching problem for input -output discrete systems has already attracted a lot of attention. Though there is already a clear understanding of the linear problem [17], [21], the non-linear case is still being examined and is the subject matter of a large number of papers (see for instance [11], [25], [22], to mention but a few). In this paper we examine the Model Matching Problem (MMP) for non-linear discrete systems of the form (1), or F [y(t), u(t)] = 0, F a δǫ-polynomial, by using the entire algebraic background that has been previously developed.…”

“…By means of those tools we managed to solve the problem only for input-output systems with nonlinear output, linear input and without cross-products between input and output signals. Extension of those results can be found at [12], [14], [15], [25]. The aim of the current paper is to present a solution of the model matching problem for a general class of nonlinear input-output systems with nonlinearities in the output, in the input, and with cross-products.…”