Optimal controllers for spatially invariant systems with delayed communication requirements

Voulgaris, Petros G.; Bianchini, Gianni; Bamieh, Bassam

doi:10.1016/s0167-6911(03)00181-6

Cited by 39 publications

(32 citation statements)

References 6 publications

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“…Reference [2] demonstrates closure results for cone causal systems using Markov parameter descriptions. The following proposition proves closure results for C -causal systems using state-space descriptions.…”

Section: Closure Of C Under Lftsmentioning

confidence: 99%

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On the state-space design of optimal controllers for distributed systems with finite communication speed

Fardad

Jovanović

2008

2008 47th IEEE Conference on Decision and Control

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We consider the problem of designing optimal distributed controllers whose impulse response has limited propagation speed. We introduce a state-space framework in which such controllers can be described. We show that the optimal control problem is not convex with respect to certain state-space design parameters, and demonstrate a reasonable relaxation that renders the problem convex. This relaxation is associated with an iterative numerical scheme known as the Steiglitz-McBride (SM) algorithm. We improve the SM algorithm by using the algebraic Lyapunov equation to relieve time integration, thus significantly reducing computational costs.

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Section: Closure Of C Under Lftsmentioning

confidence: 99%

“…References [2] and [3] introduce the subspaces of "cone causal" and "funnel causal" systems, respectively. These subspaces describe how information from every controller propagates through the similar but more general characterization, termed "quadratic invariance," is introduced in [4].…”

Section: Introductionmentioning

confidence: 99%

On the state-space design of optimal controllers for distributed systems with finite communication speed

Fardad

Jovanović

2008

2008 47th IEEE Conference on Decision and Control

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“…Additionally, methods and/or solutions exist for special instances of this problem, such as the two-player systems considered in [15], [16], and spatially invariant systems [17], [18], [19].…”

Section: Introductionmentioning

confidence: 99%

A heuristic for sub-optimal ℌ<inf>2</inf> decentralized control subject to delay in non-quadratically-invariant systems

Matni

Doyle

2013

2013 American Control Conference

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Inspired by potential applications to the smart grid, we develop a heuristic for sub-optimal, but acceptable, control of decentralized systems subject to non-quadratically invariant (non-QI) delay patterns. We do so by exploiting a recently developed solution to the decentralized H2 model matching problem subject to delays, which decomposes the controller into a centralized, but delayed, component and a decentralized FIR component. In particular, we present an iterative procedure that exploits this decomposition to design a sub-optimal decentralized H2 controller for non-QI systems that is guaranteed a priori to be stable, and to perform no worse than a controller computed with respect to a QI subset of the non-QI constraint set. We then apply this procedure to a smart-grid frequency regulation problem.

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“…Related work, exploiting a specific interconnection structure for spatial invariance and identical linear subsystems with nearest neighbour coupling, is discussed in [18][19][20][21]. In [22], decentralised state feedback controllers are proposed for infinite interconnections of discrete-time systems, satisfying the spatial invariance property.…”

Section: Introductionmentioning

confidence: 99%

“…Design methods to synthesise optimal H 2 controllers for distributed discrete time systems have been proposed in [21]. In [19], a development mainly based on [20], proposed distributed dynamic output control for heterogenous systems interconnected over arbitrary graphs based on robust H ∞ control and dissipativity arguments.…”

Section: Introductionmentioning

confidence: 99%

Static output feedback stabilisation and synchronisation of complex networks with ℋ︁₂ performance

Menon¹,

Edwards²

2009

Int. J. Robust Nonlinear Control

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SUMMARYIn this paper global stabilisation of a complex network is obtained by applying local decentralised static output feedback control, ensuring guaranteed bounds on quadratic performance. Necessary conditions for stabilisation of a complex network with quadratic performance are derived as a convex LMI representation. In addition, a centralised static output feedback controller is designed and its quadratic performance is compared with that of the decentralised one. Strict positive realness conditions on the node level dynamics allow nonlinearities/uncertainties, which satisfy sector conditions, to be considered. Two examples are used to demonstrate the efficacy of the approach. The first one is a randomly generated academic example with 10 nodes. The second example is based on a network formed from the interconnection of 20 Chua circuits. In both cases controllers are developed with H 2 bounded performance using only measured output information.

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Optimal controllers for spatially invariant systems with delayed communication requirements

Cited by 39 publications

References 6 publications

On the state-space design of optimal controllers for distributed systems with finite communication speed

On the state-space design of optimal controllers for distributed systems with finite communication speed

A heuristic for sub-optimal ℌ<inf>2</inf> decentralized control subject to delay in non-quadratically-invariant systems

Static output feedback stabilisation and synchronisation of complex networks with ℋ︁₂ performance

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Optimal controllers for spatially invariant systems with delayed communication requirements

Cited by 39 publications

References 6 publications

On the state-space design of optimal controllers for distributed systems with finite communication speed

On the state-space design of optimal controllers for distributed systems with finite communication speed

A heuristic for sub-optimal &#x210C;<inf>2</inf> decentralized control subject to delay in non-quadratically-invariant systems

Static output feedback stabilisation and synchronisation of complex networks with ℋ︁2 performance

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Resources

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A heuristic for sub-optimal ℌ<inf>2</inf> decentralized control subject to delay in non-quadratically-invariant systems

Static output feedback stabilisation and synchronisation of complex networks with ℋ︁₂ performance