By Mario A. Jordán, Jorge L. Bustamante
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Extra resources for DISCRETE TIME SYSTEMS Edited by Mario A. Jordán and Jorge L. Bustamante
1999). Observers design for a class of nonlinear systems with time-varying delay, CDC’1999, Phoenix, Arizona USA. December . Alessandri, A. (2004). Design of observers for Lipschitz nonlinear systems using LMI, NOLCOS, IFAC Symposium on Nonlinear Control Systems, Stuttgart, Germany . , Feron, E. & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory, SIAM Studies in Applied Mathematics, Philadelphia, USA. , Boutayeb, M. & Ragot, J. (2005). Observers based synchronization and input recovery for a class of chaotic models, Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference , Seville, Spain.
Thus, the primary aim of this paper is to propose two distributed fusion predictors using fusion formula with matrix weights, and analysis their statistical properties and relationship between them. Then, through a comparison with an optimal centralized predictor, performance of the novel predictors is evaluated. This chapter is organized as follows. In Section 2, we present the statement of the continuous-discrete prediction problem in a multisensor environment and give its optimal solution. In Section 3, we propose two fusion predictors, derived by using the fusion formula and establish the equivalence between them.
T+Δ t+Δ t+Δ t+Δ t+Δ (N) ˆ … , ,x Theorem 1: Let xˆ (1) are the local predictors of an unknown state x t+Δ . Then t+Δ t+Δ a. (N) The weights a(1) t+Δ ,… ,a t+Δ satisfy the linear algebraic equations N N i=1 i=1 (ij) (iN) ⎤ -Pt+Δ =0, ∑ a(i) ∑ a(i)t+Δ ⎡⎣Pt+Δ t+Δ =I n , ⎦ b. j=1,… ,N-1; (12) (ii) (i) (i) ˆ (i) The local covariance Pt+Δ =cov(x(i) t+Δ ,x t+Δ ) , x t+Δ =x t+Δ -x t+Δ satisfies (8) and local crossij ) j) ) covariance Pt(+Δ = cov( xt( i+Δ , xt( +Δ ) , i ≠ j describes the time update and observation update equations: ⎧ P(ij)- =F P(ij)- +P(ij)- F T +Q , P(ij)- =P(ij) , t ≤ τ ≤ t , τ τ τ τ τ k-1 k τ=t k-1 t k-1 ⎪ τ T ⎪⎪ (ij) (ij) (j) (j) (i) (i) ⎨ Pt k = I n +L t k H tk Pt k I n +L t k H tk , t=t k , ⎪ (ij) ⎪ Ps(ij) =FsPs(ij) +Ps(ij)FsT +Q s , Ps=t =Pt(ij) , t k ≤ s ≤ t+Δ; k k ⎪⎩ ( c.