Distributed Control with Integral Quadratic Constraints

Fang, Hui; Antsaklis, Panos J.

doi:10.3182/20080706-5-kr-1001.00097

Cited by 10 publications

(11 citation statements)

References 26 publications

(31 reference statements)

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“…To address this issue, [23] and [24] propose an efficient method for robust stability analysis of interconnected uncertain systems with an interconnection matrix that is normal, and [18] considers stability analysis and design methods for networks of certain systems with uncertain interconnections. A similar problem is also considered in [25]. In [26], the authors consider robust stability analysis of interconnected uncertain systems using IQC-based analysis, and they show that when the interconnection matrix is unitarily diagonalizable, the analysis problem can be decomposed into smaller problems that are easier to solve.…”

Section: Related Workmentioning

confidence: 99%

Distributed robust stability analysis of interconnected uncertain systems

Andersen

Hansson

Pakazad

et al. 2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Abstract-This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic constraints. This approach yields a sparse linear matrix inequality which can be decomposed into a set of smaller, coupled linear matrix inequalities. This allows us to solve the analysis problem efficiently and in a distributed manner. We also show that the decomposed problem is equivalent to the original robustness analysis problem, and hence our method does not introduce additional conservativeness.

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Section: Related Workmentioning

confidence: 99%

Distributed robust stability analysis of interconnected uncertain systems

Andersen

Hansson

Pakazad

et al. 2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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“…In [15] and [16], the authors consider robust stability analysis of interconnected systems where the uncertainty lies in the interconnections among the subsystems. In these papers, the authors consider the use of IQCs to describe the uncertain interconnections, and they provide coupled LMIs to address the stability analysis and control design for such systems.…”

Section: Introductionmentioning

confidence: 99%

Robust Stability Analysis of Sparsely Interconnected Uncertain Systems

Andersen

Pakazad

Hansson

et al. 2014

IEEE Trans. Automat. Contr.

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In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem.

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“…for v = in,out. Then, premultiplying and postmultiplying inequality (19) by diag((Π + 3 P out ) T , (Π 1 P in ) T , I, I) and its transpose, respectively, where Π 1 and Π 3 are defined in Equation 23, we get the following equivalent condition:…”

Section: Algorithmmentioning

confidence: 99%

“…Specifically, the subsystems can be homogeneous (all described by the same model) [13][14][15] or heterogeneous (different models). [16][17][18][19][20][21] The interconnection topology can be of varying complexity, for instance, highly structured 14,17 or an arbitrary graph. 16,18,21 This work considers heterogeneous subsystems and extends the results of the work of Farhood et al 22 on linear time-varying (LTV) subsystems to the LPV setting.…”

mentioning

confidence: 99%

Distributed control of LPV systems over arbitrary graphs with communication latency

Farhood

2017

Intl J Robust & Nonlinear

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Summary This paper focuses on spatially distributed control systems where the controller sensing and actuation topology is inherited from that of the plant. Specifically, this paper considers distributed systems composed of discrete‐time linear parameter‐varying subsystems interconnected over general graph structures. These distributed systems are subject to a communication latency of one sampling period, where the information sent by a subsystem at the current time step is received by the target subsystem at the next time step. Analysis and synthesis conditions are derived for control design in this setting using a parameter‐dependent Lyapunov approach with the ℓ2‐induced norm as the performance measure. Fast and easy‐to‐implement algorithms are also provided for constructing the controller in real time. The techniques developed are finally applied to a leader‐follower formation problem with intermittent communications.

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Distributed Control with Integral Quadratic Constraints

Cited by 10 publications

References 26 publications

Distributed robust stability analysis of interconnected uncertain systems

Distributed robust stability analysis of interconnected uncertain systems

Robust Stability Analysis of Sparsely Interconnected Uncertain Systems

Distributed control of LPV systems over arbitrary graphs with communication latency

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