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8. Phase limitations of multipliers at harmonics

Author

Heath, William Paul, Carrasco, Joaquin, and Zhang, Jingfan

Subjects
Mathematics - Optimization and Control
Abstract

We present a phase condition under which there is no suitable multiplier for a given continuous-time plant. The condition can be derived from either the duality approach or from the frequency interval approach. The condition has a simple graphical interpretation, can be tested in a numerically efficient manner and may be applied systematically. Numerical examples show significant improvement over existing results in the literature. The condition is used to demonstrate a third order system with delay that is a counterexample to the Kalman Conjecture.

Published
2021

18. Duality bounds for discrete-time Zames-Falb multipliers

Author

Zhang, Jingfan, Carrasco, Joaquin, and Heath, William

Subjects
Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Systems and Control
Abstract

We develop phase limitations for the discrete-time Zames-Falb multipliers based on the separation theorem for Banach spaces. By contrast with their continuous-time counterparts they lead to numerically efficient results that can be computed either in closed form or via a linear program. The closed-form phase limitations are tight in the sense that we can construct multipliers that meet them with equality. We discuss numerical examples where the limitations are stronger than others in the literature. The numerical results complement searches for multipliers in the literature; they allow us to show, by construction, that the set of plants for which a suitable Zames-Falb multiplier exists is non-convex., Comment: 16 pages, 12 figures, submitted to IEEE TAC

Published
2020
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20. Discrete-time Zames-Falb multipliers

Author

Zhang, Jingfan, Heath, William, and Carrasco Gomez, Joaquin

Subjects
Zames-Falb multipliers, Absolute stability, Nonlinear systems
Abstract

A Lurye system is a feedback interconnection between a linear plant and a nonlinear operator that belongs to some class of nonlinear operators. The stability problem of Lurye systems has been being a core topic in control theory for the last 70 years due to the lack of necessary and sufficient conditions in general. In this thesis, we study the absolute stability of discrete-time Lurye systems where the nonlinearities are sector-bounded and slope-restricted. For completeness' sake, we review the searches over two subclasses of Zames-Falb multipliers, infinite impulse response (IIR) and finite impulse response (FIR) Zames-Falb multipliers. The search leads to the lower bound of the maximum slope bound of the nonlinearities that preserve the absolute stability of a Lurye system. The numerical results obtained by FIR multipliers are less conservative than all existing literature. As a contribution, this thesis shows the equivalence between the second-order FIR searches and previous literature using Lyapunov functions. The main contribution of this thesis is the development of tractable duality conditions for Zames-Falb multipliers. The result allows us to find an upper bound of the maximum slope of the nonlinearities where linear time-invariant (LTI) Zames-Falb multipliers can guarantee the absolute stability. As a result, it is shown that the search over FIR Zames-Falb multipliers are very efficient as we can show that there is no suitable LTI multipliers when the FIR search fails to find a multiplier besides numerical precision. The significance of these results is two folds. First, they can be used as the stopping criterion in the iterative process in selecting the order of FIR multipliers. Second, they may be used to show unstable behaviour if the recent conjecture on the necessity of the LTI Zames-Falb multipliers for the absolute stability is shown to be true. Inspired by the sound result of FIR Zames-Falb multipliers, we propose a novel parametrisation of a class of Lyapunov-Lurye functionals (LLFs), which are the time-domain equivalence to FIR Zames-Falb multipliers. It may have some advantages to analyse Lurye systems in pure time domain, and the numerical results are less conservative than all existing Lyapunov methods. In addition to the absolute stability problem, the exponential convergence rate of stable Lurye systems has aroused the interest in recent years as the first order optimisation algorithms for convex objective functions can be modelled as Lurye systems. In this thesis, a convex search over the suitable subclass of Zames-Falb multipliers has been developed leading to less-conservative upper bound of the convergence rate of Lurye systems with slope-restricted nonlinearities. However, it remains open to analyse the conservativeness of the results.

Published
2021

23. P450-mediated dehydrotyrosine formation during WS9326 biosynthesis proceeds via dehydrogenation of a specific acylated dipeptide substrate

Author

Zhang, Songya, Zhang, Lin, Greule, Anja, Tailhades, Julien, Marschall, Edward, Prasongpholchai, Panward, Leng, Daniel J., Zhang, Jingfan, Zhu, Jing, Kaczmarski, Joe A., Schittenhelm, Ralf B., Einsle, Oliver, Jackson, Colin J., Alberti, Fabrizio, Bechthold, Andreas, Zhang, Youming, Tosin, Manuela, Si, Tong, and Cryle, Max J.

Published
2023
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24. Soil Carbon Stock and Potential Carbon Storage in the Mangrove Forests of Guangdong

Author

Qin Guoming, Zhang Jingfan, Zhou Jinge, Lu Zhe, and Wang Faming

Subjects
mangrove, blue carbon, carbon density, carbon stock, guangdong province, Geography (General), G1-922
Abstract

Mangroves occur in coastal intertidal zones and play an important role in terrestrial and marine carbon cycles. Accurate estimations of mangrove carbon stocks and sequestration potential can help quantify the contribution of mangroves to addressing climate change and achieving carbon neutrality goals. The carbon stocks and burial rates of different mangrove communities and regions in Guangdong Province were studied through literature collection and data integration. The soil carbon densities of the Rhizophora stylosa and Bruguiera gymnorhiza communities were 0.27 and 0.23 Gg C/hm2, respectively, while the soil carbon density of the Kandelia obovata community was the lowest at only 0.13 Gg C/hm2. The area of mangroves in Guangdong Province is 9,106.2 hm2, the total carbon stock is 1,542.02 Gg C, and the soil carbon density is 0.23 Gg C/hm2. The total carbon reserves of mangroves in thirteen regions are in the following order: Zhanjiang (894.5 Gg C) > Yangjiang (195.4 Gg C) > Jiangmen (97.7 Gg C) > Zhuhai (91.0 Gg C) > Maoming (59.6 Gg C) > Shantou (51.4 Gg C) > Zhongshan (49.2 Gg C) > Huizhou (36.1 Gg C) > Guangzhou (35.1 Gg C) > Shenzhen (18.3 Gg C) > Shanwei (10.8 Gg C) > Dongguan (2.83 Gg C) > Chaozhou (0.11 Gg C). Using the 210Pb method, the sediment accretion rate was found to be 13.47 mm/a. Qi'ao Island had the highest sediment compaction rate of 31.5 mm/a, followed by Zhenhai Bay, with 16.5 mm/a, Shenzhen Futian, with 15.9 mm/a, and Leizhou Bay, with the lowest sediment compaction rate of 7.3 mm/a. The carbon sequestration capacity of Guangdong province is approximately 2.96 Gg C/a, with the Leizhou Peninsula having the highest (6.05 Gg C/a) and Futian, Shenzhen having the lowest (0.66 Gg C/a) capacities. The carbon storage of mangroves in Guangdong Province was 1,542.02 Gg C, which was higher than that in other regions. The carbon sequestration capacity of the mangroves was relatively strong. Therefore, the protection and restoration of local mangroves may substantially contribute to the mitigation of climate change while providing additional benefits. This assessment, on a provincial scale, provides insights into blue carbon sequestration capacity, thus contributing to the synchronous progression of blue carbon management.

Published
2023
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26. Noncausal FIR Zames-Falb Multiplier Search for Exponential Convergence Rate

Author

Zhang, Jingfan, Seiler, Peter, and Carrasco, Joaquin

Subjects
Mathematics - Optimization and Control
Abstract

In the existing literature, there are two approaches to estimate tighter bounds of the exponential convergence rate of stable Lure systems. On one hand, the classical integral quadratic constraint (IQC) framework can be applied under loop-transformation, so the stability of the new loop implies the convergence of the original loop. On the other hand, it is possible to modify the IQC framework, the so-called rho-IQC framework, in such a way that the convergence rate is directly obtained over the original loop. In this technical note, we extend the literature results from the search for a causal finite impulse response (FIR) Zames-Falb multiplier to the noncausal case. We show that the multipliers by the two approaches are equivalent by a change of variable. However, the factorisation of the Zames-Falb rho-IQC is restricted compared to the Zames-Falb IQC, so an unified factorisation is proposed. Finally, numerical examples illustrate that noncausal multipliers lead to less-conservative results.

Published
2019

29. Convex searches for discrete-time Zames-Falb multipliers

Author

Carrasco, Joaquin, Heath, William P., Ahmad, Nur Syazreen, Wang, Shuai, and Zhang, Jingfan

Subjects
Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Systems and Control
Abstract

In this paper we develop and analyse convex searches for Zames--Falb multipliers. We present two different approaches: Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) multipliers. The set of FIR multipliers is complete in that any IIR multipliers can be phase-substituted by an arbitrarily large order FIR multiplier. We show that searches in discrete-time for FIR multipliers are effective even for large orders. As expected, the numerical results provide the best $\ell_{2}$-stability results in the literature for slope-restricted nonlinearities. Finally, we demonstrate that the discrete-time search can provide an effective method to find suitable continuous-time multipliers., Comment: 12 pages

Published
2018
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34. Contributions of plant‐ and microbial‐derived residuals to mangrove soil carbon stocks: Implications for blue carbon sequestration

Author

Qin, Guoming, primary, He, Weijun, additional, Sanders, Christian J., additional, Zhang, Jingfan, additional, Zhou, Jinge, additional, Wu, Jingtao, additional, Lu, Zhe, additional, Yu, Mengxiao, additional, Li, Yingwen, additional, Li, Yongxing, additional, Lambers, Hans, additional, Li, Zhian, additional, and Wang, Faming, additional

Published
2024
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36. A Fast Hybrid Image Encryption Method for Networked Inverted Pendulum Visual Servo Control Systems

Author

Yang, Lisi, Du, Dajun, Zhang, Changda, Zhang, Jingfan, Fei, Minrui, Rakić, Aleksandar, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Prates, Raquel Oliveira, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Fei, Minrui, editor, Li, Kang, editor, Yang, Zhile, editor, Niu, Qun, editor, and Li, Xin, editor

Published
2020
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44. Enhanced abundance of generalist and litter saprotrophs explain increased tropical forest soil carbon with long‐term nitrogen deposition

Author

Lu, Zhe, primary, Li, Hui, additional, Sayer, Emma J., additional, Liu, Zhanfeng, additional, Li, Luhua, additional, Chen, Yao, additional, Qin, Guoming, additional, Li, Jintian, additional, Zhou, Jinge, additional, Huang, Xingyun, additional, Zhang, Jingfan, additional, Wu, Jingtao, additional, Thapa, Poonam, additional, and Wang, Faming, additional

Published
2023
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46. Phase Limitations of Multipliers at Harmonics

Author

Heath, William P., Carrasco, Joaquin, and Zhang, Jingfan

Abstract

The absolute stability of a Lurye system with a monotone nonlinearity is guaranteed by the existence of a suitable O'Shea–Zames–Falb (OZF) multiplier. We develop a numerically tractable phase condition under which there can be no suitable OZF multiplier for the transfer function of a given continuous-time plant. We provide its graphical interpretation. The condition may be tested in a systematic manner and leads to significantly improved results compared with the condition in the literature from which it is derived. Our results are useful to evaluate the performance of numerical searches for OZF multipliers.

Published
2024
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