Johansen T. A. and Foss B. A., A narmax model representation for adaptive control based on local model-Modeling, Identification and Control, 13(1):2539, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....local linearisations of the system arise an accurate non linear model of the system. Hence, if we design a controller for each local identification we are very likely to obtain a multi linear controllers system adapted for the control of the entire non linear system. Following Johansen and Foss (Johansen and Foss, 1992) and Murray Smith and Hunt (Murray Smith and Hunt, 1995) we call such a multi controllers system a Linear Controllers Network (LCN) This controller will not suffer from the stability plasticity dilemma since different controllers will be adapted for different regions of the system. Hence, and ....

....each control error at time t 1, the controller connected to the basis function the most activated is selected . Hence, the output of the network corresponds to the output of the selected controller. This is very different of what is achieved by the so call local model network first introduced by (Johansen and Foss, 1992) or its control version the local controllers network (see for a review of that later (MurraySmith and Hunt, 1995) In that case the basis function used are Gaussian. Therefore the activity of each basis function can be used to weight its connected controller output. In a global term the output ....

Johansen, T. A. and B. A. Foss (1992). A narmax model representation for adaptive control based on local model. Modeling, Identification, and control 13(1), 25--39.

....1. Equation 2 is a locally (not globally) valid representation of Equation 1 [1] 2. all physical significance is lost. For these reasons, the formulation of Equation 1 is prefered to that of Equation 2 for the purposes of this paper. Local model networks (LMN) were introduced by Johansen and Foss [7, 8] as a means of decomposing NARMAX models like Equation 2 into an insightful structure for system identification and control. Further developments have been reported by Murray Smith [9, 10] More recently, Johansen and Foss have investigated a local model network representation of the ODE ....

....u d i x l i (0) x0 Gamma x e i y l i = C i x l i D i u l i (10) 2. 2 Global and Local state LMN S C 1 S S S u y B 1 S S l 1 1 1 r 1 x y B S S l r x y B S S l r x u u i C i i i N N N C N N N u L y L A 1 A A N e e e l e e e Figure 1: Local state LMN Following Johansen and Foss [8][7] N of these linearised models are created indexed by i together with an operating point vector OE and N validity functions ae i (OE) The N validity functions interpolate the N linearised models to create a (non dynamic) approximations f and g to the functions f and g of Equation 1 as ....

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T. A. Johansen and B. A. Foss, A NARMAX Model Representation for Adaptive Control Based on Local Models, Modeling, Identification, and Control, 13(1):25--39, 1992.

....can be memory intensive with regard to the complexity of the problem. The number of hidden units can be reduced by using a more complex function linear or not instead of the weighted parameter W. This is what is achieved by the so called Local Model Network (LMN) which was first introduced by [38]. This system (see fig. 11) enables each clustering unit to cover larger areas of the input space. In addition, as highlights [37] considering a priori knowledge on the cluster of the input space cover by each unit it can be possible to use different kind of appropriate functions. For this it is ....

T. A. Johansen and B. A. Foss, "A narmax model representation for adaptive control based on local model," Modeling, Identification, and control, vol. 13, no. 1, pp. 25--39, 1992.

....the use of local models f i ( provides a much richer model structure which results in the requirement for fewer units to reach a given degree of model fidelity. Typically, local linear models are used. The interpretation of the GBFN as a local model network has been considered by Johansen [7, 8, 9]. In the local model framework the input to the basis functions are required to capture the non linear effects in the system. Thus, the x i can be interpreted as operating point vectors. The basis functions use the operating point vectors to partition the space into a set of overlapping regions ....

T. A. Johansen and B. A. Foss, "A NARMAX model representation for adaptive control based on local models," Modelling, Identification and Control, vol. 13, no. 1, pp. 25--39, 1992.

....the system it is forgetting previous adaptations concerning other regions. A simple way to have a control system valid for all system s operating conditions is to use a certain number of controllers each one locally valid for a different operating region of the system. Following Johansen and Foss (Johansen and Foss, 1992) and Murray Smith and Hunt (Murray Smith and Hunt, 1995) we call such a multi controllers system a Local Controllers Network (LCN) The problem of the LCN was the necessity to have some important a priori knowledge about the system in order to determine the adequate operating region for each ....

....1 jcenter j Gammacenter i j is used to maintain the same shape of the sigmoid function (see figure 3) whatever the scale of the single dimension clustering space is. This is to avoid to normalise the clustering space (as it is achieved when applying the local models network of Johansen and Foss (Johansen and Foss, 1992)) The parameter ff in the variable p is the coefficient that drives the sharpness of the sigmoid. We use here ff = 10, which leads to the sigmoid shape depicted in figure 3. From figure 3, and taking the rbf i for example, you can see that the activation Act i of the rbf i will tend to 1 when ....

Johansen, T. A. and B. A. Foss (1992). A narmax model representation for adaptive control based on local model. Modeling, Identification, and control 13(1), 25--39.

....to the use of a weighted parameter to approximate a function. The number of basis functions can be reduced by using a more complex function, linear or not, instead of the weighted parameter W (4) This is what is achieved by the so called Local Model Network (LMN) that was first introduced by (Johansen and Foss 1992). Instead of the weighted parameter W a linear function is connected to each basis function. The function is then decomposed into linear segments. The local model is valid so long the relevant part of the function is linear. So, this system enables each basis function to cover larger areas of the ....

Johansen, T. A. and B. A. Foss (1992). `A narmax model representation for adaptive control based on local model'. Modeling, Identification, and control 13(1), 25--39.

....and Athans, 1990; Shamma and Athans, 1992) There are a couple of algorithms that have been recently developed for this purpose. One of them is the Local Model Network introduced in (Poggio and Girosi, 1990) and further extended for modelling and control purposes by (Johansen and Foss, 1993; Johansen and Foss, 1992). The control version of the LMN is the Local Controller Network . The concept underlying the other controller network has been introduced in (Middleton et al. 1988) and further extended in (Morse, 1990; Morse et al. 1992; Weller and Goodwin, 1994) and is know as the hysteresis switching ....

Johansen, T. A. and B. A. Foss (1992). A narmax model representation for adaptive control based on local model. Modeling, Identification, and control 13(1), 25--39.

....local linearisations of the system arise an accurate non linear model of the system. Hence, if we design a controller for each local identification we are very likely to obtain a multi linear controllers system adapted for the control of the entire non linear system. Following Johansen and Foss (Johansen and Foss, 1992) and Murray Smith and Hunt (Murray Smith and Hunt, 1995) we call such a multi controllers system a Controllers Network (CN) This controller will not suffer from the stability plasticity dilemma since different controllers will be adapted for different regions of the system. Hence, and as ....

....use of a polynomial function even of very low order (e.g. cubic polynomial) enables a very accurate local identification and control of the system. Hence it is not necessary to perform a weighted sum of the controllers output to obtain a smooth interpolation between controllers, as did originally (Johansen and Foss, 1992) when developing the local model network. Let us now sketch the behaviour of the CN feedback control system (see fig. 4) Note that by controller we are not referring to the MRAC in particular because we believe that other kinds of controllers (e.g. General Predictive Controller) could be used as ....

Johansen, T. A. and B. A. Foss (1992). A narmax model representation for adaptive control based on local model. Modeling, Identification, and control 13(1), 25--39.

....several alternatives and choosing the one that gives the largest decrease in a validation criterion. The LSA algorithm also involves local linear models and smooth interpolation between the local models by the use of Gaussian functions. The approach was originally developed for NARMAX models [Johansen and Foss 92a, Johansen and Foss 92b] but has been extended to general nonlinear dynamic and static models. The algorithm involves no projection of the input variables as a result of being developed in a system identi cation context. It is therefore best suited for lower dimensional problems, and all the ....

....will lead to a rough or even discontinuous f , which is undesirable. One way is to assign a normalized and smooth weight or interpolation function to each local model. Such a function is often of the form wm (x) ae m (x) P M j=1 ae j (x) 3. 2) where ae m is a scalar local validity function [Johansen and Foss 92a] which should indicate the validity or relevance of the local model as a function of the position of x in input space. Furthermore, ae m should be nonnegative, smooth, and have the property of being close to 0 if x is far from the center of a local model. The use of smooth validity functions, ....

T. A. Johansen and B. A. Foss. A NARMAX model representation for adaptive control based on local models. Modeling, Identiøcation, and Control, vol. 13, no. 1, pp. 2539, 1992. Bibliography 90

....un normalised case where points given different weightings. Normalised networks are attractive for a number of practical reasons. Because the space is covered to same degree at every point, they are often less sensitive to poor centre selection. In addition, it is desirable for many applications [10] that the cumulative sum of all basis functions at any point equals unity. Werntges [11] discusses the advantages of normalisation in RBF nets, promoting the advantages of a partition of unity produced by normalisation, but not considering the side effects discussed in this paper. The ....

T. Johansen and B. Foss, "A NARMAX model representation for adaptive control based on local models," Modelling, Identification and Control, vol. 13, no. 1, pp. 25--39, 1992.

....(Equation 9) are used ffl a generalised predictive control formulation is used ffl the models are explicitly used to overcome the stability plasticity dilemma. As discussed by Zbikowski, Hunt, Dzieli nski, Murray Smith, and Gawthrop (1994) and by Gawthrop (1996) the Local Model Network of Johansen and Foss(1993, 1992) provides a conceptually powerful combination of general Neural Network ideas with conventional linear control techniques to provide an approach to the control of nonlinear systems. The Local Model Network may also be regarded as a multiple model approach. This approach may be contrasted with the ....

Johansen, T. A. and B. A. Foss (1992). A NARMAX model representation for adaptive control based on local models. Modeling, Identification, and Control 13 (1), 25--39.

....space in order to select and dispatch the input vectors to various modules. The most advanced algorithm in this respect is the local model network (LMN) Poggio and Girosi, 1990; Stokbro et al. 1990; Jones and al. 1991) which has been further extended for modelling and control purposes by (Johansen and Foss, 1992; Johansen and Foss, 1993) Note that the LMN is a generalisation of the basis function neural network (Powell, 1987) that was developed in first place for classification purposes. Moreover it has very close connections to the fuzzy model developed by (Takagi and Sugeno, 1985; Sugeno and Kang, ....

....advantage of this method is the facility to transform the LMN into a local controller network. Since each local model is linear there are several straightforward methods arising from control theory that can be used to transform the linear models into a local linear controllers. The early work of (Johansen and Foss, 1992; Johansen and Foss, 1993) used a proportional and integral (PI) design method to transform each model into a controller. In (Gawthrop, 1996; Gawthrop and Ronco, 1996) the models are used to develop predictive controllers. A pole placement technique is used in (Hunt and Johansen, 1996; Gollee and ....

Johansen, T. A. and B. A. Foss (1992). A narmax model representation for adaptive control based on local model. Modeling, Identification, and control 13(1), 25--39.

....dispatch the input vectors to various computing modules (models or controllers) The most advanced algorithm in this respect is the local model network (LMN) Poggio and Girosi, 1990; Stokbro et al. 1990; Jones and al. 1991) which has been further extended for modelling and control purposes by (Johansen and Foss, 1992; Johansen and Foss, 1993) Note that the LMN is a generalisation of the basis function neural network (Powell, 1987) that was developed in first place for classification purposes. Note that the fuzzy models developed by (Takagi and Sugeno, 1985; Sugeno and Kang, 1986) can also be interpreted as ....

....of this model network is the facility to transform each local linear model into a controller and as a result transform this scheme into a controller network. There are several straightforward methods arising from control theory that can be used to achieve this transformation. The early work of (Johansen and Foss, 1992; Johansen and Foss, 1993) used a proportional and integral (PI) design method to transform each model into a controller. In (Gawthrop, 1996; Gawthrop and Ronco, 1996; Gawthrop and Ronco, 1999; Foss et al. 1995) the models are used to develop predictive controllers. A pole placement technique is ....

Johansen, T. A. and B. A. Foss (1992). A narmax model representation for adaptive control based on local model. Modeling, Identification, and control 13(1), 25--39.

....the only general and systematic approach to designing a non linear controller out of a non linear model. One of these neural networks is the Local Model Network (LMN) introduced in (Poggio and Girosi, 1990) and further extended for modelling and control purposes by (Johansen and Foss, 1993; Johansen and Foss, 1992). The control version of the LMN is the Local Controller Network (LCN) The idea underlying the second type of neural network was introduced in (Middleton et al. 1988) and further extended in (Morse, 1990; Morse et al. 1992; Weller and Goodwin, 1994) and coined as the hysteresis switching ....

Johansen, T. A. and B. A. Foss (1992). A narmax model representation for adaptive control based on local model. Modeling, Identification, and control 13(1), 25--39.

....is presented. LOCAL MODEL NETWORKS ae 2 ae nA y ae 1 f 1 ( P f nA ( f 2 ( OE Theta Theta Theta Theta Theta Theta Theta Theta Theta OE y 1 y 2 ynA Figure 1 General architecture of a local model network Local model networks were developed by Johansen and Foss (Johansen and Foss 1992, 1993) A local model network is a set of models weighted by some activation function as in Figure 1. The same input signal is fed to each model and the outputs are weighted according to some scheduling variable or variables, j, where y(t) is the model network output, r i (j) is the (1) basis ....

.... TIME LOCAL MODEL NETWORK To evaluate the output of a local model network, the output of each local model must be calculated, then multiplied by the relevant basis function, then summed to give the network output (Figure 1) For a discrete system, this updating can be done at the sampling interval (Johansen and Foss 1992), but this update time is not so obvious for continuous systems. Each model is integrated over some time interval, t u , where y i is the local model output, f i is the function (4) describing the local model, and t is the start time of the interval. The outputs of these models at the end of this ....

Johansen, T.A. and B.A. Foss, 1992, "A NARMAX model representation for adaptive control based on local models", Modelling, Identification and Control, vol.

....the only general and systematic approach to designing a non linear controller out of a non linear model. One of these neural networks is the Local Model Network (LMN) introduced in (Poggio and Girosi, 1990) and further extended for modelling and control purposes by (Johansen and Foss, 1993; Johansen and Foss, 1992). The control version of the LMN is the Local Controller Network (LCN) The idea underlying the other network was introduced in (Middleton et al. 1988) and further extended in (Morse, 1990; Morse et al. 1992; Weller and Goodwin, 1994) and coined as the hysteresis switching algorithm . This ....

....be used as building block of the controller networks. One of the gated controller networks uses a spatial clustering approach to select the controllers at each instant: the Clustered Controller Network (CCN) that shares many common features with the Local Controller Network (LCN) developed by (Johansen and Foss, 1992; Jo28 hansen and Foss, 1993) The main difference in the CCN is that, whatever the system characteristics, the clustering used for the selection of the controllers is achieved on a single quantity. This simplification is justified by several important advantages. The main advantages are the ....

Johansen, T. A. and B. A. Foss (1992). A narmax model representation for adaptive control based on local model. Modeling, Identification, and control 13(1), 25--39.

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Johansen T. A. and Foss B. A., A narmax model representation for adaptive control based on local model-Modeling, Identification and Control, 13(1):2539, 1992.

No context found.

T. A. Johansen and B. A. Foss, "A NARMAX model representation for adaptive control based on local models," Modelling, Identification and Control, vol. 13, no. 1, pp. 25--39, 1992.

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