Linear Systems Theory

Hespanha, João P.

doi:10.2307/j.ctvc772kp

Cited by 126 publications

(213 citation statements)

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“…When T is equal to N (i.e., the dimension of the state space), the matrix is referred to as the controllability matrix of the system2. A system is controllable if, for every initial condition , there exists an input signal able to steer the system to any arbitrary final state in at most N time steps.…”

Section: Resultsmentioning

confidence: 99%

“…A system is controllable if, for every initial condition , there exists an input signal able to steer the system to any arbitrary final state in at most N time steps. Kalman’s controllability criterion2 states that a system is controllable, if and only if, .…”

Section: Resultsmentioning

confidence: 99%

“…In particular, if the system is controllable and the initial state is the origin (i.e., x 0 = 0), the input signal that steers the system to can be explicitly computed as ref. 2…”

Section: Resultsmentioning

confidence: 99%

“…In this direction, control theory equips us with powerful mathematical notions, such as controllability and controllability subspace 23, to determine the set of dynamic states that are achievable (in finite time) by carefully choosing external driving signals. Even though most of these tools require full access to the network dynamics, in many practical scenarios, either the dynamics leads to a ill-posed controllability problem4 or only the topology of the dynamic network is available.…”

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confidence: 99%

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Trade-offs between driving nodes and time-to-control in complex networks

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Barabási

et al. 2017

Sci Rep

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Recent advances in control theory provide us with efficient tools to determine the minimum number of driving (or driven) nodes to steer a complex network towards a desired state. Furthermore, we often need to do it within a given time window, so it is of practical importance to understand the trade-offs between the minimum number of driving/driven nodes and the minimum time required to reach a desired state. Therefore, we introduce the notion of actuation spectrum to capture such trade-offs, which we used to find that in many complex networks only a small fraction of driving (or driven) nodes is required to steer the network to a desired state within a relatively small time window. Furthermore, our empirical studies reveal that, even though synthetic network models are designed to present structural properties similar to those observed in real networks, their actuation spectra can be dramatically different. Thus, it supports the need to develop new synthetic network models able to replicate controllability properties of real-world networks.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…In particular, if the system is controllable and the initial state is the origin (i.e., x 0 = 0), the input signal that steers the system to can be explicitly computed as ref. 2…”

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

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Trade-offs between driving nodes and time-to-control in complex networks

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Barabási

et al. 2017

Sci Rep

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“…For the purpose of state estimation, it is necessary to transform the hydrodynamic load model to time domain. A transfer function on the form of has a realization that is both controllable and observable when transferred into state space …”

Section: Low‐fidelity Owt Modelmentioning

confidence: 99%

Wave disturbance rejection for monopile offshore wind turbines

et al. 2018

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The dimensions of offshore wind turbine (OWT) support structures are governed by fatigue considerations. For 6‐ to 10‐MW OWTs, wave loads are often dominating in terms of fatigue utilization. The present work proposes a control scheme to reduce the wave‐induced fatigue loads in OWT support structures. The control scheme applies collective pitch control to increase both the damping and stiffness of the fore‐aft vibration modes. With conventional active tower damping, efficient wave disturbance rejection is restricted to a narrow frequency range around the first fore‐aft modal frequency. The proposed control scheme achieves efficient wave disturbance rejection across a broader frequency range. Here, tower feedback control is implemented via an auxiliary control loop. Based on a low‐fidelity model, the effect of the tower feedback loop on the stability margins of the basic controller is analysed. The results show that, within certain boundaries, the stability margins are improved by the stiffness term in the tower feedback loop. Consequently, the need to reduce the bandwidth of the basic controller to accommodate tower feedback control is relaxed. Based on time‐domain simulations carried out in an aero‐hydro‐servo‐elastic simulation tool, the lifetime effects of the proposed control scheme are analysed. Compared with conventional active tower damping, a more favourable trade‐off between adverse side effects and the support structure's fatigue damage is achieved with the proposed control scheme.

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