An iterative parametric estimation method for Hammerstein large-scale systems: a simulation study of hydraulic process

Adaptive Control Scheme for Large‐Scale Interconnected Systems Described by Hammerstein Models

“…The objective of this control design is to follow a time‐varying reference signal and to reduce the noise effects acting on each system output. In this sense, we retain the following assumptions: the polynomials A i ( q −1 , k ), B i ( q −1 , k ), B ij ( q −1 , k ), A ij ( q −1 , k ) and C i ( q −1 ) have the same order in order to facilitate the problem formulation; the approximated errors , and are negligible; the structure of the submodel (1) is fixed, the delays d i , d ij and t ij are known, in such a way that d i < d ij and d i < t ij ; the parameters b i , 1 ( k ), b ij , 1 ( k ) and γ j , 1 are well‐known at each discrete‐time k , in such a way that b i , 1 ( k ) = b ij , 1 ( k ) = γ j , 1 = 1, ∀ k , in order to overcome the implementation difficulties of the parametric estimation ; the sequence { e i ( k )} constituted of independent random variables and generated as Gaussian distributed with zero average and constant variance ; the sequences { e i ( k )} and { u i ( k ), y i ( k ), u j ( k ), y j ( k ); i , j = 1, … , N ; j ≠ i } are independent. …”

Improved Discrete Techniques of Time‐Delay and Order Estimation for Large‐Scale Interconnected Nonlinear Systems

“…In the literature, several presentations are used to describe the dynamics of this class of systems. We can cite input-output discrete models [11], continuous statespace models [1,2], and block-oriented mathematical models [10,[12][13][14]. In this framework, we consider the class of largescale systems which consist of several interconnected Hammerstein subsystems operating in a stochastic environment with unknown time-varying parameters and described by the following dynamic equation:…”

“…From [12], we propose that ,1 , ,1 ( ), and ,1 ( ) are constant and known, in such a way that ,1 = ,1 ( ) = ,1 ( ) = 1, ∀ , in order to avoid the posed problem. In this case, each output ( ) of the considered interconnected system becomes…”

“…The formulation of the parametric estimation problem for this class of large-scale systems, which is described by the discrete model (5), was proved by Elloumi and Kamoun [12]. In this instance, the developed parameter estimation procedure is based on the adjustable model and the prediction error method, starting from the knowledge of several measured input-output signals resulting from the considered process.…”

“…These works preoccupied more particularly the large-scale systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14], the nonlinear systems , and the nonstationary systems [12][13][14]. The class of large-scale systems can be found in different fields as transportation processes, power processes, communication networks, space structures, and others.…”