H-Infinity Optimal Control for Systems With a Bottleneck Frequency

Bergeling, Carolina; Pates, Richard; Rantzer, Anders

doi:10.1109/tac.2020.3010263

Cited by 16 publications

(7 citation statements)

References 35 publications

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“…It is also interesting to note that standard consensus algorithm [35] also arises as a special case of the above, by setting p = 0 and A to be an incidence matrix. The corresponding circuit can in fact be realised without transformers, and Theorem 4 again demonstrates that this simple algorithm has excellent robustness properties 4 .…”

Section: Now Perform the Coordinate Transformationmentioning

confidence: 81%

“…The dynamics of the generation buses are coupled through the dynamics of the transmission network. After linearisation, the transmission network dynamics are 4 A small technical point here is that (ii) no longer holds, and the realisation in (4. 16) is neither controllable nor observable.…”

Section: Now Perform the Coordinate Transformationmentioning

confidence: 99%

“…−1 B K + D K . We can thus find a lower bound on the achievable H ∞ performance (as suggested in [4]) by solving the static optimisation problem A least squares argument (see [31,Lemma 1]) shows that K = G (0)…”

Section: Next Note Thatmentioning

confidence: 99%

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Passive and reciprocal networks: From simple models to simple optimal controllers

Pates¹

2022

Preprint

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Networks constructed out of resistors, inductors, capacitors and transformers form a compelling subclass of simple models. Models constructed out of these basic elements are frequently used to explain phenomena in largescale applications, from inter-area oscillations in power systems, to the transient behaviour of optimisation algorithms. Furthermore they capture the dynamics of the most commonly applied controllers, including the PID controller. In this paper we show that the inherent structure in these networks can be used to simplify, or even solve analytically, a range of simple optimal control problems. We illustrate these results by designing and synthesising simple, scalable, and globally optimal control laws for solving constrained least squares problems, regulating electrical power systems with stochastic renewable sources, studying the robustness properties of consensus algorithms, and analysing heating networks.

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Section: Now Perform the Coordinate Transformationmentioning

confidence: 81%

Section: Now Perform the Coordinate Transformationmentioning

confidence: 99%

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Passive and reciprocal networks: From simple models to simple optimal controllers

Pates¹

2022

Preprint

Self Cite

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“…Theorem 1 shows that the controlled system (3) is in a real sliding mode with respect to the integral sliding function s I (t) (6) under the integral sliding mode controller u(t) (7). This sliding mode is also the first layer sliding mode of the controlled system (3). It also shows that s I (t) is bounded with a prescribed upper boundary 𝜖 I , which is independent to the faults f (t) or disturbances 𝜔(t).…”

Section: 𝜎(𝜏)D𝜏mentioning

confidence: 94%

“…With the rapid requirements of the realistic industrial process, not only the stability but also the satisfactory performances of system need to be guaranteed. [1][2][3] On the other side, the practical system dynamics usually consist of many nonlinearities, lots of results of robust control on nonlinear systems have been reported. [4][5][6][7][8] Robust control typically focuses on the controller design to ensure the stability of system with some required performances under unreliable surroundings.…”

Section: Introductionmentioning

confidence: 99%

Robust sliding mode control for a class of nonlinear systems with actuator failures and disturbances: A dual‐layer sliding mode strategy

Dong

2023

Intl J Robust & Nonlinear

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This paper studies the problem of robust sliding mode control (SMC) for a class of nonlinear systems subject to actuator failures and disturbances. By employing a novel integral sliding function constructed with an nested sliding mode controller "𝜈(t)," a dual-layer sliding mode control is established. The first layer is an integral sliding mode generated by the actuator output, the second one is a linear sliding mode generated by "𝜈(t)." Indeed, the linear sliding mode is nested to the integral sliding mode for the system under consideration. Compared with the state-of-the-art integral sliding mode controls (ISMCs), not only the inherent robustness of ISMC is retained, but also the time derivative of integral sliding function in integral sliding motion dynamics can be compensated by "𝜈(t)," so that the robustness of integral sliding motion is further enhanced. Furthermore, due to the generation of the nested linear sliding mode, it decouples the matched integral sliding function time derivative of integral sliding motion dynamics from the mismatched disturbance. This decoupling facilitates the design of "𝜈(t)" through  ∞ control theory, then, the closed-loop systems are ensured to be asymptotically stable with  ∞ performance. Lastly, with two classes of barrier functions exploited for the design of sliding mode controllers, both sliding modes cannot be lost for system responses even in the presence of unforeseen actuator failures and disturbances. In simulation, an IEEE 6 bus power system is offered to demonstrate the superiorities of the theoretical results.

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Nonlinear output feedback control laws based on linear ones for improving ultimate bound

Furtat,

Gushchin,

Kopysova

2024

Journal of the Franklin Institute

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H-Infinity Optimal Control for Systems With a Bottleneck Frequency

Abstract: H-infinity Optimal Control for Systems with a Bottleneck Frequency

Cited by 16 publications

References 35 publications

Passive and reciprocal networks: From simple models to simple optimal controllers

Passive and reciprocal networks: From simple models to simple optimal controllers

Robust sliding mode control for a class of nonlinear systems with actuator failures and disturbances: A dual‐layer sliding mode strategy

Nonlinear output feedback control laws based on linear ones for improving ultimate bound

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