Goodwin, G. C. and Sin, K. S. (1984). Adaptive Filtering Prediction and Control. Prentice-Hall, Englewood Cliffs, NJ.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....smoother instead of the Kalman filter, since smoothing involves additional data in the estimation procedure. As a consequence, the estimation error variance is further decreased, and with a large lag length (delay) the performance approaches that of a noncausal Wiener filter for stationary signals [3]. In order to obtain a Kalman fixed lag smoother we represent the AR signal model (2) in state space form s(n 1) A(n)s(n) u(n) 0; 0 : 4) In contrast to (2) the d 1 dimensional state vector s(n) now consists of the current signal sample s(n) and d delayed samples where d ....

G. C. Goodwin, "Adaptive filtering prediction and control", Chapter 7, Prentice-Hall, Inc., 1984.

....according to J for the so obtained augmented state space representation of the system. The resulting controller incorporates a self adjusting mechanism, in that it selects a control input that realizes an appropriate compromise between the control and the identification objectives (dual action, [1]) However, such an optimal dual control problem is doable only in a few simple cases where computing the solution to the optimization problem is actually feasible. A computationally feasible though sub optimal approach to the design of self adjusting controllers is the so called switching ....

G. C. Goodwin, K. S. Sin, Adaptive filtering prediction and control. Englewood Cli#s, Prentice-Hall, 1984.

....smoother instead of the Kalman filter, since smoothing involves additional data in the estimation procedure. As a consequence, the estimation error variance is further decreased, and with a large lag length (delay) the performance approaches that of a noncausal Wiener filter for stationary signals [4]. In order to obtain a Kalman fixed lag smoother we represent the AR signal model (1) in state space form s(n 1) A(n)s(n) u(n) 0; 0 Delta T : 3) In contrast to (1) the d 1 dimensional state vector s(n) now consists of the current signal sample s(n) and d delayed samples ....

G. C. Goodwin, "Adaptive filtering prediction and control", Chapter 7, Prentice-Hall, Inc., 1984.

.... not the required inner product of the parameter error vector ( 0 yy n QQand input vector ( nVnd y , but instead this inner product is filtered by the FIR filter is not strictly positive real (SPR) except for the case of 0 dB = i.e. convergence cannot be assured [48]. Therefore, the controller of Figure 2 is disqualified as viable explicit rate congestion controller. 10 ( yndnd y Q u(n d) ynndV Figure 2 A Direct Adaptive Controller System for Controlling MA Plant That MAY NOT CONVERGE. 3.2.2 An Unrealizable Controller Consider a ....

....Section 4.1 are lifted. In their place, Assumption 5 is made, as well as the minor Assumption 6 and Assumption 7. This leads to a cleaner proof with stronger global stability results. 4.2.2.1 Proof of Convergence and Global Stability The update equation (39) is identical to Equation (3.3. 19) of [48]. From (15) 39) and (14) en n n = Qy , and from Lemma 3.3.2 of [48] 1 2 lim 0 n T nn . yy , nk n = QQfor any finite k. 40) From (15) 13) and (14) T en ndV nndV n n ndV n nndV n nndV n = ....

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G. Goodwin and K. Sin, Adaptive Filtering Prediction and Control, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1984.

....on the so obtained augmented state space representation of the process. The resulting controller incorporates a self adjusting mechanism, in that it selects a control input that realizes an appropriate compromise between the control and the identification objectives (dual action, see, e.g. [1]) However, such an optimal dual control approach is generally di#cult, except in a few simple cases, where computing the solution to the optimization problem is actually feasible. A computationally feasible though sub optimal approach to the design of self adjusting controllers is the ....

....# #J # (#, #) 1 #J # (#, #) if #) is # stable 1, otherwise, 2.2) where J # (#, #) is some positive cost criterion (e.g. an H 2 or H# cost) and # is a positive constant. The criterion J thus combines both stability and performance. Note that J # is normalized so that J takes values in [0, 1]. This is done for technical reasons related to the implementation of the cautious switching logic. We can then formalize the required richness of the candidate controller set as follows. Assumption 2.3. J : sup ### inf ### J(#, #) 1. This means that for any admissible model, there is a ....

G.C. Goodwin and K.S. Sin. Adaptive filtering prediction and control. Prentice-Hall, 1984.

.... Delta Delta r 1 z r 0 : 3.6) Since in our application we want the system output y(k) to converge to a constant level, we specify the reference output signal as ym (k) c 6= 0, which is characterized in the zdomain as Qm (z)y m (z) 0; Qm (z) z Gamma 1: 3. 7) The adaptive controller [13] applied to our QoS proxy cache system (3.2) is u(k) a j (k)u(k Gamma j) b j (k) y m (k Gamma j) Gamma y(k Gamma j) 3.8) Web Cache R(z) P(z) y=H[0] H[1] u=S[0] S[1] Estimation Controller y m =Desired Ratio of Hit Rates Controller Design Controller Parameters Plant ....

....In the next two subsections we describe how the cache parameters and controller parameters are estimated and updated respectively. 3.2. 1 Parameter Estimation To estimate the web cache system parameters pn Gammaj and r n Gammaj , we use a standard gradient algorithm from control literature [13]. The input u(k) and output y(k) measurements are fit to the model described in equation (3.2) Define the vector OE(k) u(k Gamma n) Delta Delta Delta ; u(k Gamma 1) y(k Gamma n) Delta Delta Delta ; y(k Gamma 1) 3.9) Then the cache model(3.2) can be expressed as y(k) ....

Goodwin, G. C., and K. S. Sin. Adaptive Filtering Prediction and Control. Prentice Hall, 1984.

....Adaptive control, controller parametrization, dynamic modeling, high frequency gain matrix, LDU decomposition, multivariable systems, web cache. 1 Introduction Adaptive control of multivariable systems has been a major research topic with both theoretical and practical challenges [4] 8] [9], 15] 16] 18] Recently, continuing effort has been made to relax conditions on systems to be admissible to a stable adaptive control scheme [10] 11] 14] 20] especially, a certain positive definiteness condition on the system high frequency gain matrix in the continuous time case. ....

....any bounded initial conditions. An important concept used in designing multivariable model reference control schemes is the zero structure at infinity of the plant transfer matrix G(D) This structure is characterized by the Hermite normal form [15] or equivalently, the interactor matrix [4] [9], 21] or its modified version [18] a triangular polynomial matrix m (D) of the form: m (D) 6 6 6 6 6 6 p 1 (D) 0 Delta Delta Delta Delta Delta Delta 0 p 21 (D) p 2 (D) 0 Delta Delta Delta 0 p N Gamma1 1 (D) Delta Delta Delta p N Gamma1 N Gamma2 (D) p N Gamma1 ....

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Goodwin, G. C. and K. S. Sin, Adaptive Filtering Prediction and Control, Prentice-Hall, Englewood Cliffs, N. J., 1984.

....of an effective new approach of using adaptive control in web cache systems for performance guarantees in the presence of system uncertainties. 1 Introduction Adaptive control of multivariable systems has been a major research topic with both theoretical and practical challenges [4] 7] [8], 13] Recently, continuing effort has been made to relax conditions on systems to be admissible to a stable adaptive control scheme [9] 12] 15] especially, a certain positive definiteness condition on the system high frequency gain matrix in the continuous time case. Inspired by recent ....

....input signal, find the feedback control u(k) for the plant (3.1) with unknown G(D) such that y(k) tracks ym (k) asymptotically and all signals in the closed loop system are bounded. An important concept used in designing multivariable model reference control schemes is the interactor matrix [8] of the plant transfer matrix G(D) a triangular polynomial matrix m (D) which has a stable inverse and has the key property that lim D 1 m (D)G(D) K p , the high frequency gain matrix of G(D) is finite and nonsingular. For the system model (2.4) D 0 (3.3) if det[B] 6= 0, and for the ....

Goodwin, G. C. and K. S. Sin, Adaptive Filtering Prediction and Control, Prentice-Hall, 1984.

....and control of dynamical systems has been an active area of research for the last three decades. Although methods for controlling linear time invariant plants with unknown parameters had been pursued since the 1960s, it was not until the last decade that stable adaptive laws were established [1] [4] Recent advances in nonlinear control theory and, in particular, feedback linearization techniques [5, 6] have initiated activity aimed at developing adaptive control schemes for nonlinear plant models [7] 10] This area, which came to be known as adaptive totlitear cottrol, deals with ....

....of their rguments. This cn esily be chieved if the sigmoid used is smooth function. The logistic function nd the hyperbolic tngent re examples of popular sigmoids that lso stisfy the smoothness condition. By the Mean Value Theorem there exists f [0f, 0] i. e, f : 0f (1 ) 0 for some ) [0, 1], such that Now let where B(Mf) denotes a ball of radius Mf. Therefore, the higher order terms satisfy Using the same procedure we have oo where 0g : 0g 0j and 0o(X , 0v) satisfies and the constant 6g is defined as sup cs(yr, g[ 3.37) 3.39) Vx x, V (M) 3.40) From now ....

G.C. Goodwin and K.S. Sin, Adaptive Filtering Prediction and Control, Englewood Cliffs, N J, Prentice-Hall, 1984.

....data pairs ( xi, xi2 . Xiq] Yi) i = 1, 2 . p . Here W is the weight matrix and its element, wj, are defined by 1 d (d is the distance between the j th example and the corresponding cluster centre) j = 1, 2 . p. We can rewrite equations (4) with the use of a recursive LSE formula [8] as follows: P = A r A) b =PArWy, 5) In DENFIS, we use a weighted recursive LSE with a forgetting factor defined as follows. Let the k th row vector of a matrix A is denoted as ak r and the k th element ofy is denoted as yk. Then b can be calculated iteratively as follows: f b = bk w ....

Goodwin, G. C., Sin, K. S., "Adaptive Filtering Prediction and Control", Prentice-Hall, Englewood Cliffs, N.J., 1984.

....( eff yn N nun d = 2.4) Note that Fulton and Li do not use forward looking estimates of ( yn, therefore the notation ( yninstead of ( yndn is used. Assuming for now that the plant in (2. 4) is a valid model, a simple Minimum Prediction Error Adaptive Controller (Direct Approach) [63] can be created to determine, at time n , the control signal ( un that minimizes ( 2 Eyndyndn . As with the design of most adaptive controllers, for the purposes of analysis, it is assumed that the parameter oeff N = is constant within the time interval needed to ....

....knowledge of d is assumed, a Normalized Least Mean Squares (NLMS) 64] formulation is possible: 29 ( 2 1 eff eff eff N nNn undynundNn und = 2.5) 1 eff yndn un Nn = 2.6) Update equation (2. 5) converges to the desired value if 02 [63]. All poles and zeros of (2.4) are at the origin, thus within the unit circle, leading to the result of Lemma 2.1. ######### For the adaptive controller of (2.5) and (2.6) applied to the plant (2.4) 1. yn and ( un are bounded sequences, 2. lim 0 n yn y nn d = ....

[Article contains additional citation context not shown here]

G. Goodwin and K. Sin, Adaptive Filtering Prediction and Control, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1984.

....are deterministic based on ordinary differential equations. However, to be usable in a Kalman filtering framework it is crucial that the model contain both deterministic and stochastic components stochastic differential equations. Such models can be learned effectively from training data [9, 5]. In this paper we develop two significant elaborations for stochastic dynamical models. The first concerns modelling object classes for objects in motion. The second addresses the efficient modelling of couplings between tracked objects. 1.1 Shape and Motion Variability The first problem ....

C.G. Goodwin and K.S. Sin. Adaptive filtering prediction and control. PrenticeHall, 1984.

....system expressed in rational proper transfer function form using the differentiation operator p: y(t) u(t) A(p) G(p) A(p) pn an lp i . alp ao B(p) b,p bm lp m 1 . blp bo This can be converted to an equivalent state space form using a canonical representation [6]: p(t) A(t) Bu(t) 2) y(t) CT(t) bu(t) Note that if G(p) is strictly proper then b equivalent shift operator state space description is: 0. Assuming zero order hold sampling, the qk = Mk Nu (4) y = S Tu (5) Where M,N,S and T are given by [12] M = e A5 N = A i(eAS I)B =C T = ....

....front end anti aliasing filters can be relaxed. Since these filters have to be taken into account in system estimation this is a major advantage. There is a smoother progression in control input to the plant. If slow sampling is used then the control input can be a sequence of large step changes [6]. This can feed significant energy into high frequency mechanical resonances. Rapid sampling ensures a smooth sequence of smaller changes to achieve the same bandwidth. 3. The discrete time response is a better approximation to the desired continuous time response. 4. Higher closed loop ....

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G.C. Goodwin and K.W. Sin. Adaptive Filtering Prediction and Control. Prentice- Hall, Inc., New Jersey, 1984.

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Goodwin, G. C. and Sin, K. S. (1984). Adaptive Filtering Prediction and Control. Prentice-Hall, Englewood Cliffs, NJ.

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Goodwin, G. C. and Sin, K. S. 1984. Adaptive Filtering Prediction and Control. Prentice-Hall, Englewood Cliffs, New Jersey. 34

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G.C. Goodwin and K.S. Sin. Adaptive filtering prediction and control. PrenticeHall, 1984.

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G. C. Goodwin and K. S. Sin. Adaptive Filtering Prediction and Control. Prentice-Hall, 1984.

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G. Goodwin and K. Sin, Adaptive Filtering Prediction and Control, Prentice-Hall, Inc., New Jersey, 1984.

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G. GOODWIN AND K. SIN, Adaptive Filtering Prediction and Control, Prentice-Hall, Inc., New Jersey, 1984.

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G. GOODWIN AND K. SIN, Adaptive Filtering Prediction and Control, Prentice-Hall, Inc., New Jersey, 1984.

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G.C. Goodwin and K.W. Sin. Adaptive Filtering Prediction and Control. Prentice-Hall, Inc., New Jersey, 1984.

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G. C. Goodwin and K. S. Sin, "Adaptive Filtering, Prediction and Control," Prentice-Hall, Info.and Sys. Sci. Ser., 1985.

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Goodwin, G. C., Sin, K. S., "Adaptive Filtering Prediction and Control", Prentice-Hall, Englewood Cliffs, N. J., 1984 27

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G. C. Goodwin, "Adaptive filtering prediction and control", Chapter 7, Prentice-Hall, Inc., 1984.

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Goodwin, GC and Sin, KS. 1984. Adaptive Filtering Prediction and Control. Information and Systems Science, Prentice Hall. NJ.

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