Distributed Consensus Observers-Based H Control of Dissipative PDE Systems Using Sensor Networks

This paper considers the problem of finite dimensional output feedback H ∞ control for a class of nonlinear spatially distributed processes described by highly dissipative partial differential equations (PDEs), whose state is observed by a sensor network (SN) with a given topology. This class of sys...

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Veröffentlicht in:IEEE transactions on control of network systems Jg. 2; H. 2; S. 112 - 121
Hauptverfasser: Wu, Huai-Ning, Wang, Hong-Du
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IEEE 01.06.2015
Schlagworte:
Bilinear matrix inequality
Control design
Eigenvalues and eigenfunctions
Observers
Partial differential equation
Spatially distributed processes
Tin
Topology
Vectors
sensor networks (SNs)
distributed consensus observers
partial differential equation (PDE)
Bilinear matrix inequality (BMI)
H_{\infty} control
spatially distributed processes
ISSN:2325-5870, 2372-2533
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Zusammenfassung:This paper considers the problem of finite dimensional output feedback H ∞ control for a class of nonlinear spatially distributed processes described by highly dissipative partial differential equations (PDEs), whose state is observed by a sensor network (SN) with a given topology. This class of systems typically involves a spatial differential operator whose eigenspectrum can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. Motivated by this fact, the modal decomposition and singular perturbation techniques are initially applied to the PDE system to derive a finite-dimensional ordinary differential equation model, which accurately captures the dominant dynamics of the PDE system. Subsequently, based on the slow system and the SN topology, a set of finite-dimensional distributed consensus observers is constructed to estimate the state of the slow system. Then, a centralized control scheme, which only uses the available estimates from a specified group of SN nodes, is proposed for the PDE system. An H ∞ control design is developed in terms of a bilinear matrix inequality (BMI), such that the closed-loop PDE system is exponentially stable and a prescribed level of disturbance attenuation is satisfied for the slow system. Furthermore, a suboptimal H ∞ controller is also provided to make the attenuation level as small as possible, which can be obtained via a local optimization algorithm that treats the BMI as a double linear matrix inequality. Finally, the proposed method is applied to the control of the 1-D Kuramoto-Sivashinsky equation system.
ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2014.2378874