Adaptive systems in control and signal processing 1992 : by L Dugard; M MʼSaad; Yoan D Landau; International Federation

By L Dugard; M MʼSaad; Yoan D Landau; International Federation of Automatic Control

Adaptive structures stay a really fascinating box of theoretical study, prolonged through methodological reports and a growing number of purposes. The plenary papers, invited periods and contributed periods enthusiastic about many points of adaptive structures, reminiscent of structures id and modelling, adaptive regulate of nonlinear structures and theoretical matters in adaptive keep watch over. additionally coated have been methodological features and purposes of adaptive keep watch over, clever tuning and adaptive sign processing.

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This suggests the idea to approximate ER t �ogm(x , 8)] through ERt �og m(x , 8 )] L; { ER - R' �og m(x, 8 )J } = L; [g (8 )] = 0 . ( 1 4) Assume that the linear operators L; and E can be inter­ changed [this may imply some constraints on integrability of the function log m(x , 8 ) ]. d. 's R equiva­ lent in the sense of ( 13) , one has to store only the values of ER{L; �ogm(x , 8)]} for i = 1 , . . , n. This motivates the following definition. Definition 1. ' is said to be an admissible statistic for the model ( 1 ) if their entries, for i = 1, .

We also assume that Ro E M, namely Proposition 1 (maximum entropy estimation). d. f.

1 . Process model, Estimation model and error system (3. 1 1 ) (3. 1 2) The process model in this paper is From (3. > 11 with k 1 = cs / Amin(-\)I) (3. j� l -n (4) 0 E RP where 0=0 * are unknown process parameters, we have also the inputs u and state variables X are availables. ) II X II � = Assumption I. The process state vector is bounded with c9 S II X II S c 1 0, c9>0. It can be ensured by some control schemes. ) . ( 3 . 1 4) 31 To estimate the unknown parameters of introduce an estimation model as X where A(X,0)X = 'lfE R"'" + g(X)u + 'lfX is a Hurwitz matrix and X = the process.

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