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Linear-like properties arise naturally in the adaptive control setting

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2021年第6期35卷 965-990页

作者： Miller, Daniel E. Shahab, Mohamad T. Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

Classical discrete-time adaptive controllers typically provide asymptotic stabilization and tracking;usually the affect of the noise is at best bounded-input bounded-output. Recently we have shown that if you design a discrete-time adaptive controller in just the right way, then in a variety of situations you not only obtain exponential stability, but also a bounded gain on the noise in every p-norm, as well as a never-before-seen linear-like convolution bound on the input-output behavior. Quite surprisingly, the approach is very natural, and relies on the use of the unmodified, original projection algorithm to carry out parameter estimation;if the set of plant uncertainty is not convex, then a multi-estimator and switching are used. The goal of this paper is to provide an overview of the approach, discuss the results-to-date, and list some of the open problems.

关键词： adaptive control bounded gain convolution bound exponential stability projection algorithm

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Simulation of mooring Lines in complex bathymetries using a finite element method

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OCEAN ENGINEERING 2023年 272卷

作者： Deske, Paula Rodnguez-Luis, Alvaro Guanche, Ranl Univ Cantabria Ave los Castros Santander 39005 Spain Univ Cantabria Environm Eydraut Inst Avda Isabel Torres15 Parque Cientif & Tecnol Cant Santander 39011 Spain

This paper presents a novel method for the modeling of the seabed interaction of mooring lines in complex bathymetries, known as "continuous projection method". This method is able to calculate ground normal and friction forces for any seafloor surface. This provides an improvement in the mooring systems simulation, as it captures additional non-linearities on the mooring line performance due to seabed *** method is based on constructing a triangulation for the seabed and projecting mooring line nodes by using the vertex normal vectors of each triangle, ensuring the continuity of the projection. For the sake of the computational cost reduction, the line nodes are first projected into the closest triangles. Also, whenever the floor is flat, inclined or horizontal, a point-to-plane projection expression is used instead. The projection method described has been implemented to a finite element model. The initial condition problem was solved with a static approach, based on finding the static equilibrium with Newton-Armijo algorithm. This improves other static approaches which use the catenary equation, and that are only valid for a flat *** model was successfully verified against the analytical solution of an inextensible catenary line in a slope. Furthermore, the simulation results were validated against experimental scale tests on a single chain mooring line with three different seafloor structures: one flat floor and two different sloped steps. For each of them, static and dynamic regular tests were performed. Moreover, high and low frequency fairlead movements were imposed in the dynamic tests, aiming to validate the model both in cases with and without snapping loads. Overall, the obtained results were coherent and allow to validate the accuracy of the proposed model. Finally, a mooring line over an irregular seabed surface was studied, comparing the results obtained by directly applying the developed method for complex bathymetries, by interpola

关键词： Complex bathymetry projection algorithm Mooring lines Numerical model Finite element methoo

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Classification and Applications of Randomized Functional Numerical algorithms for the Solution of Second-Kind Fredholm Integral Equations

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Journal of Mathematical Sciences (United States) 2021年第5期254卷 589-605页

作者： Voytishek, A.V. Institute of Computational Mathematics and Mathematical Geophysics Siberian Branch of the Russian Academy of Sciences Novosibirsk Russian Federation Novosibirsk State University Novosibirsk Russian Federation

Systematization of numerical randomized functional algorithms for approximation of solutions to second-kind Fredholm integral equation is performed in this paper. Three types of algorithms are emphasized: projection algorithms, grid algorithms, and projection-grid algorithms. Disadvantages of grid algorithms that require calculation of values of the kernel of integral equations at fixed points are revealed (practically, the kernels of equation have integrable singularities and this calculation is impossible). Thus, for applied problems related to the solution of second-kind Fredholm integral equations, projection or projection-grid randomized algorithms are more convenient. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： 45B05 65C05 65C40 computational kernel grid algorithm numerical solution projection algorithm randomized algorithm second-kind Fredholm integral equation

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Adaptive tracking control of the leader-following multi-agent system with uncertainties

Adaptive tracking control of the leader-following multi-agen...

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第35届中国控制与决策会议

作者： Xinghong Zhang Xiuli Zheng School of Electrical Engineering and Automation Henan Institute of Technology

The adaptive tracking control problem of the multi-agent system is *** dynamics of each agent is of unknown parameter and can only receive different intensities of information from its different *** identify parameters,the improved projection algorithm is adopted,and based on each parameter estimate update law,the decentralized adaptive controllers are ***,a numerical example is provided to illustrate that each parameter estimate error is bounded and each agent tracks the desired reference trajectory.

关键词： adaptive tracking multi-agent system uncertainties projection algorithm

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projection methods for high numerical aperture phase retrieval

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INVERSE PROBLEMS 2021年第12期37卷 125005-125005页

作者： Nguyen Hieu Thao Soloviev, Oleg Luke, Russell Verhaegen, Michel Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands Can Tho Univ Sch Educ Dept Math Can Tho Vietnam Flexible Opt BV Polakweg 10-11 NL-2288 GG Rijswijk Netherlands Univ Gottingen Inst Numer & Angew Math D-37083 Gottingen Germany

We develop for the first time a mathematical framework in which the class of projection algorithms can be applied to high numerical aperture (NA) phase retrieval. Within this framework, we first analyze the basic steps of solving the high-NA phase retrieval problem by projection algorithms and establish the closed forms of all the relevant projection operators. We then study the geometry of the high-NA phase retrieval problem and the obtained results are subsequently used to establish convergence criteria of projection algorithms in the presence of noise. Making use of the vectorial point-spread-function (PSF) is, on the one hand, the key difference between this paper and the literature of phase retrieval mathematics which deals with the scalar PSF. The results of this paper, on the other hand, can be viewed as extensions of those concerning projection methods for low-NA phase retrieval. Importantly, the improved performance of projection methods over the other classes of phase retrieval algorithms in the low-NA setting now also becomes applicable to the high-NA case. This is demonstrated by the accompanying numerical results which show that available solution approaches for high-NA phase retrieval are outperformed by projection methods.

关键词： phase retrieval high numerical aperture projection algorithm nonconvex optimization inconsistent feasibility

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NLTV-Gabor-based models for image decomposition and denoising

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SIGNAL IMAGE AND VIDEO PROCESSING 2020年第2期14卷 305-313页

作者： Liu, Xinwu Chen, Yue Hunan Univ Sci & Technol Sch Math & Computat Sci Xiangtan 411201 Hunan Peoples R China Zhejiang Normal Univ Coll Math & Comp Sci Jinhua 321004 Zhejiang Peoples R China

By using the nonlocal total variation (NLTV) as the regularization and Gabor functions as the fidelity, this paper proposes two novel models for image decomposition and denoising. The presented models closely incorporate the advantages of the NLTV and Gabor wavelets-based methods. These improvements are aimed at overcoming the drawbacks of staircase artifacts and loss of edge details caused by the traditional variational frameworks. Furthermore, on the basis of Chambolle's projection algorithm, we introduce two extremely efficient numerical methods to solve the resulting optimization problems. Finally, compared with several popular and powerful numerical methods, this article confirms the superiorities of the developed strategies for image decomposition and denoising in terms of visual quality and quantitative assessments.

关键词： Image decomposition Image denoising Nonlocal total variation Gabor functions projection algorithm

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Adaptive tracking with exponential stability and convolution bounds using vigilant estimation

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MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS 2020年第3期32卷 241-291页

作者： Miller, Daniel E. Shahab, Mohamad T. Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

Classical discrete-time adaptive controllers provide asymptotic stabilization and tracking;neither exponential stabilization nor a bounded noise gain is typically proven. In our recent work, it is shown, in both the pole placement stability setting and the first-order one-step-ahead tracking setting, that if the original, ideal, projection algorithm is used (subject to the common assumption that the plant parameters lie in a convex, compact set and that the parameter estimates are restricted to that set) as part of the adaptive controller, then a linear-like convolution bound on the closed-loop behaviour can be proven;this immediately confers exponential stability and a bounded noise gain, and it can be leveraged to provide tolerance to unmodelled dynamics and plant parameter variation. In this paper, we solve the much harder problem of adaptive tracking;under classical assumptions on the set of unmodelled parameters, including the requirement that the plant be minimum phase, we are able to prove not only the linear-like properties discussed above, but also very desirable bounds on the tracking performance. We achieve this by using a modified version of the ideal projection algorithm, termed as vigilant estimator: it is equally alert when the plant state is large or small and is turned off when it is clear that the disturbance is overwhelming the estimation process.

关键词： Adaptive control projection algorithm Exponential stability Bounded gain Convolution bound

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Distributed Containment Control of Fractional-order Multi-agent Systems with Double-integrator and Nonconvex Control Input Constraints

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2020年第7期18卷 1728-1742页

作者： Yuan, Xiao-Lin Mo, Li-Po Yu, Yong-Guang Ren, Guo-Jian Beijing Technol & Business Univ Sch Math & Stat 11 FuCheng Rd Beijing 100048 Peoples R China Beijing Jiaotong Univ Dept Math 3 ShangYuanCun Beijing 100044 Peoples R China

This paper mainly considers the distributed containment control problem for continuous-time fractional-order multi-agent systems (FOMASs) with double-integrator, where the control input of each agent is constrained to lie in a nonconvex set. A distributed projection containment control algorithm is designed for each follower. To finish the convergence analysis, the original closed-loop system is first changed into an equivalent one by a proper model transformation and the method of the L-1 interpolation approximation is introduced to deal with the projection operator. Then, by using the properties of the convex hull and the Mittag-Leffler function, it is shown that the largest distance between the followers and the convex hull spanned by leaders tends to zero asymptotically, while all agents' control inputs are constrained to stay in their corresponding nonconvex constraint sets. Finally, numerical simulations are provided to verify the effectiveness of the theoretical results.

关键词： Distributed containment control fractional-order multi-agent systems nonconvex constrains projection algorithm

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Phase Retrieval with Sparse Phase Constraint

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SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE 2020年第1期2卷 246-263页

作者： Nguyen Hieu Thao Luke, David Russell Soloviev, Oleg Verhaegen, Michel Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands Can Tho Univ Sch Educ Dept Math Can Tho Vietnam Univ Gottingen Inst Numer & Angew Math D-37083 Gottingen Germany Flexible Opt BV NL-2288 GG Rijswijk Netherlands

In this paper, we propose and investigate the phase retrieval problem with the a priori constraint that the phase is sparse (SPR), which encompasses a number of practical applications, for instance, in characterizing phase-only objects such as microlenses, in phase-contrast microscopy, in optical path difference microscopy, and in Fourier ptychography, where the phase object occupies a small portion of the whole field. The considered problem is strictly more general than the sparse signal recovery problem, which assumes the sparsity of the signal because the sparsity of the signal trivially implies the sparsity of the phase, but the converse is not true. As a result, existing solution algorithms in the literature of sparse signal recovery cannot be applied to SPR and there is an appeal for developing new solution methods for it. In this paper, we propose a new regularization scheme which efficiently captures the sparsity constraint of SPR. The idea behind the proposed approach is to perform a metric projection of the current estimated signal onto the set of all the signals whose phase satisfies the sparsity constraint. The main challenge here is that the latter set is not convex and its associated projector in general does not admit a closed form. One novelty of our analysis is to establish an explicit form of that projector when restricted to those points which are relevant to the solutions of SPR. Note that this result is fundamentally different from the widely known calculation form for projections onto intensity constraint sets. Based on this new result, we propose an efficient solution method, named the sparsity regularization on phase (SROP) algorithm, for the SPR problem in the challenging setting where only one point-spread-function image is given, and we analyze its convergence. The algorithm is the combination of the Gerchberg-Saxton (GS) algorithm with the projection step described above. In view of the GS algorithm being equivalent to the alternating pro

关键词： phase retrieval sparsity constraint nonconvex optimization prox-regularity projection algorithm linear convergence

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Enforcing Intra-Regional Constraints in Tie-Line Scheduling: A projection-Based Framework

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IEEE TRANSACTIONS ON POWER SYSTEMS 2019年第6期34卷 4751-4761页

作者： Tan, Zhenfei Zhong, Haiwang Wang, Jianxiao Xia, Qing Kang, Chongqing Tsinghua Univ State Key Lab Power Syst Beijing 100084 Peoples R China Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China

Inter-regional power trading plays a crucial role in optimal resource utilization. However, intra-regional operation constraints are currently not well considered in practical implementation, which may lead to internal congestions and economic loss. In this paper, a non-iterative tie-line scheduling framework taking account of both intra- and inter-regional network constraints is proposed. Based on projection theory, admissible set of tie-line injections (ASTI) is defined as the allowable range of tie-line power injections that can be met by a regional system. Then, the ASTI is implemented in tie-line scheduling to ensure the feasibility of the tie-line schedule result for each region. Requirements for practical algorithms that calculate the ASTI in power system applications are analyzed, and a novel vertex-oriented projection algorithm is proposed to efficiently calculate the ASTI. Case studies based on several IEEE and Polish test systems verify the validity and efficiency of the proposed projection algorithm. Simulations based on a four-region system demonstrate the effectiveness of the proposed tie-line scheduling framework.

关键词： Tie-line scheduling congestion management admissible set projection algorithm economic dispatch

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