Tối ưu mạng máy tính theo độ tin cậy và chi phí

Tối ưu mạng máy tính theo độ tin cậy và chi phí.Tiếp cận các hệ thống phức tạp trình bày khái niệm về hệ thống phức tạp, cách tiếp cận chúng, đặc biệt chú trọng tới các nguyên lý tiếp cận hệ thống. Lược đồ nghiên cứu tổ chức xây dựng và quản lý hệ thống trình bày lược đồ nghiên cứu chung nhất, nêu rõ các bước phát triển hệ thống, phương pháp tiếp cận hệ thống, phương pháp nghiên cứu phân tích hệ thống, tóm lược hai giai đoạn trung tâm và phân biệt của vòng đời phát...
Nội dung trích xuất từ tài liệu:
Tối ưu mạng máy tính theo độ tin cậy và chi phí T~p chi Tin hoc va Dieu khign hoc, T.16, S.l (2000), 25-34 CONTINUOUS TIME SYSTEM IDENTIFICATION: A SELECTED CRITICAL SURVEY Part II - INPUT ERROR METHODS AND OPTIMAL PROJECTION EQUATIONS NGO MINH KHAI, HOANG MINH, TRUONG NHU TUYEN, NGUYEN NGOC SAN Abstract. The part I and the part II of the paper refer to a critical survey on significant results available in the literature for identification of systems, linear in the present part and nonlinear in the following one. The most important trends in identification approaches to linear systems are from the development of optimal projection equations, which are argued by the complexity of numerical calculations and of practical applications. The perturbed a quasilinear and on Neuro-Fuzzy trends in representing nonlinear systems, i.e., functional series expansions of Wiener and Volterra, Modeling Robustness and structured numerical estimators are included. The limitations and applicability of the methods are discussed throughout. 4. INPUT ERROR METHODS It has been shown in [36,44- 48] that by adopting input error methods one can avoid the direct use of time derivatives of system input signals. However, in the input error derivation, few.terms and their relative are to be cleared first. 4.1. Definitions and lemmas Definition 1. The model that is in antiparallel with the system having the output and input of the system as its respective input and output is named as a model inverse of the system [36,p.12]. According to the above definition, the system of dynamical equations and its equivalence in the state variable description for describing model inverse of the system are readily obtained [36, p. 12, 13]. Definition 2. A description of the model inverse in the state variable space with minimal number of parameters is called canonical [14], for which realization of model inverse is also minimal and corresponding to this minimal, the dimension of matrix A is its order [36, p. 13]. Definition 3. Parameters of the model for a system are determinable if those of its model inverse are known and vice verse [36, p. 18]. Definition 4. A model of well specified structure having known parameters is called an assumed model (AM) [36,p.25]. Definition 5. Let the response y(t) of a high order model to an input u(t) be given. A low order model is said to be the reduced model of the given one if the low order model has the response y(t) to an input close to u( t) or has a response close to y( t) to the same u( t) [36, p. 18]. Following lemmas are restated, their proofs are available in [36, p. 14-18]. Lemma 1. A realization of model inverse is minimal if and only if it is controllable and. observable iointly. Lemma 2. Let a iointly controllable/observable model and a model inverse for a system be given. Assume that for an augmented of the model and model inverse, there exists a nonnegative definite steady state covariance matrix of the appropriate dimension satisfying Lyapunov equation. tu;« augmented system is stabilizable if and only if the model inverse is asymptotically stable. 26 NGO MINH KHAI, HOANG MINH, TRUONG NHU TUYEN, NGUYEN NGOC SAN Lemma 3. If the model is a minimal realization of the system, then there exists also a minimal realization for its model inverse. 4.2. Derivation of the input error With the use of model inverse Assume that an AM is in parallel with a system. As parameters and order of AM are different from those of the system, for ensuring the output of the model to be matched with that of the system, AM should have a requested input different from the system input signal. Discrepancy between AM and the system is reflected at the input side of the system in term in terms of difference of two input signals. This difference between the two inputs is referred to as an input error. Assume that a linear, continuous time system having input vector u(t) and output vector y(t) is modeled by the use of eqn. (2.1). By the definition 1, for the model there exists a model inverse described by: n1 ~ diudt) q n1 ~ diy](t) Lai,k(t) dti = LL.Bi,]k(t)dti' for k = 1, ... , p, (4.1) i=O ]=1 i=O where superscript 0 on parameters means that the parameters are to be estimated. If the order and parameters of the model inverse are known, then it follows an AM, from definitions 1 and 3. Considering the coefficients of zero derivatives of the requested inputs be 1, the requested signal at the k-th input of AM is obtained: q n1 di ~(t) n1 di ~ (t) Uk(t) = LL.Bi,]k(t) ~~i - Lai,k(t) ~;i ' for k = 1, ... .v, (4.2) ]=1i=0 i=1 where parameters are known values, y](t) for j = 1, ... , q are the response at the j-th output of the system. The input error vector in this case is obtained by defining the error at the k-input first then wr it ing for all k input: e.; (t) = u(t) - u(t), ...