Design of finite dimensional robust H_∞ distributed consensus filters for dissipative PDE systems with sensor networks

Abstract

SUMMARYThis paper presents a design method of finite dimensional robust H 1 distributed consensus filters (DCFs) for a class of dissipative nonlinear partial differential equation (PDE) systems with a sensor network, for which the eigenvalue spectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement. Initially, the modal decomposition technique is applied to the PDE system to derive a finite dimensional ordinary differential equation system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Then, based on the slow subsystem, a set of finite dimensional robust H 1 DCFs are developed to enforce the consensus of the slow mode estimates and state estimates of all local filters for all admissible nonlinear dynamics and observation spillover, while attenuating the effect of external disturbances. The Luenberger and consensus gains of the proposed DCFs can be obtained by solving a set of linear matrix inequalities (LMIs). Furthermore, by the existing LMI optimization technique, a suboptimal design of robust H 1 DCFs is proposed in the sense of minimizing the attenuation level. Finally, the effectiveness of the proposed DCFs is demonstrated on the state estimation of one dimensional Kuramoto-Sivashinsky equation system with a sensor network.

Local design of distributed H∞‐consensus filtering over sensor networks under multiplicative noises and deception attacks

“…The following theorem provides sufficient criterion to guarantee the stochastic vector dissipative-like property of system (10), which further infers the desired performance (8) for the error dynamics (7). Theorem 1.…”

“…Then, the locally augmented dynamics (10) is stochastic vector dissipative-like over the finite horizon  with respect to the vector supply rate S( k , k , k ). Moreover, the error dynamics (7) satisfies the H ∞ -consensus performance criterion (8).…”

“…In this section, a simulation example is presented to illustrate the effectiveness of the proposed design scheme. Consider a sensor network with 10 nodes, whose topology is represented by a digraph  = (, , ) with the set of nodes  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and the set of edges  = {(2, 1), (3, 2), (4, 3), (5, 4), (6, 5), (7,6), (8,7), (9,8), (10,9), (1, 10)}. Obviously, p i = q i = 1 for i = 1, 2, … , 10.…”

Reliable control design for composite‐driven scheme based on delay networked T‐S fuzzy system

“…Now, the problem addressed in this paper is formulated as follows. Design a state feedback fuzzy controller in the form of (9) for the fuzzy time-delay system (2) such that the closed-loop system in (13) is stable for any time-varying delay satisfying (14).…”

“…In NCSs, the concept of allied limited bandwidth frequently generates data transmission delays, disorder, and data packet dropouts, which degrade the system performance and also complicate the stabilization of the plant. [9][10][11][12][13] In the last decade, numerous approaches had been developed to tackle with these channel-delay problems, for example, dissipative control design, 14,15 the identification, filtering, and estimation, [16][17][18][19][20] output feedback control, [21][22][23][24][25][26] NCS, [27][28][29][30][31][32] and multiagent system. [33][34][35] Moreover, numerous work is based on a time-triggered mechanism, which can deteriorate the performance of the utilization of limited channel capacity.…”