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Approximate Controllability of Continuity Equation of Transformers

IEEE CONTROL systems LETTERS 2024年 8卷 964-969页

作者： Adu, Daniel Owusu Gharesifard, Bahman Univ Georgia Fac Math Athens GA 30605 USA Univ Calif Los Angeles Dept Elect & Comp Engn Los Angeles CA 90095 USA

Building on the recent work by Geshkovski et al. (2023) which provides an interacting particle system interpretation of Transformers with a continuous-time evolution, we study the controllability attributes of the corresponding continuity equation across the landscape of probability space curves. In particular, we consider the parameters of the Transformer's continuous-time evolution as control inputs. We prove that given an absolutely continuous probability measure and a non-local Lipschitz velocity field that satisfy a continuity equation, there exist control inputs such that the measure and the non-local velocity field of the Transformer's continuous-time evolution approximate them, respectively, in the p-Wasserstein and L-p-sense, where 1 <= p < infinity.

关键词： distributed parameter systems machine learning neural networks

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Guaranteed Cost Boundary Control of the Semilinear Heat Equation

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IEEE CONTROL systems LETTERS 2024年 8卷 898-903页

作者： Selivanov, Anton Wang, Pengfei Fridman, Emilia Univ Sheffield Dept Automatic Control & Syst Engn Sheffield S1 3JD England Tel Aviv Univ Sch Elect Engn IL-6997801 Tel Aviv Israel

We consider a 1D semilinear reaction-diffusion system with controlled heat flux at one of the boundaries. We design a finite-dimensional state-feedback controller guaranteeing that a given quadratic cost does not exceed a prescribed value for all nonlinearities with a predefined Lipschitz constant. To this end, we perform modal decomposition and truncate the highly damped (residue) modes. To deal with the nonlinearity that couples the residue and dominating modes, we combine the direct Lyapunov approach with the S-procedure and Parseval's identity. The truncation may lead to spillover: the ignored modes can deteriorate the overall system performance. Our main contribution is spillover avoidance via the L-2 separation of the residue. Namely, we calculate the L-2 input-to-state gains for the residue modes and add them to the control weight in the quadratic cost used to design a controller for the dominating modes. A numerical example demonstrates that the proposed idea drastically improves both the admissible Lipschitz constants and guaranteed cost bound compared to the recently introduced direct Lyapunov method.

关键词： Costs Heating systems Mathematical models Eigenvalues and eigenfunctions System performance Lyapunov methods Upper bound distributed parameter systems modal decomposition heat equation

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Extremum Seeking for a Class of Wave Partial Differential Equations With Kelvin-Voigt Damping

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IEEE CONTROL systems LETTERS 2024年 8卷 43-48页

作者： Silva, Paulo Cesar Souza Pellanda, Paulo Cesar Oliveira, Tiago Roux de Andrade, Gustavo Artur Krstic, Miroslav Mil Inst Engn Dept Def Engn BR-22290270 Rio De Janeiro Brazil Univ Estado Rio De Janeiro Dept Elect & Telecommun Engn BR-20550900 Rio de Janeiro Brazil Univ Fed Santa Catarina Dept Automat & Syst Engn BR-88040900 Florianopolis Brazil Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

This letter presents the design and analysis of gradient extremum seeking applied to scalar static maps within the context of infinite-dimensional dynamics governed by Partial Differential Equations (PDEs) of wave type featuring a small amount of Kelvin-Voigt damping. Notably, this particular class of PDEs for extremum seeking still needs to be explored in the existing literature. First, to compensate for the influence of PDE actuation dynamics, we employ a boundary control law via backstepping transformation and averaging-based estimates of the gradient and Hessian. Finally, we prove the local exponential convergence to a small neighborhood surrounding the unknown optimal point by means of an Input-to-State Stability analysis, as well as by employing Lyapunov functionals and averaging theory in infinite dimensions.

关键词： Adaptive control backstepping distributed parameter systems extremum seeking optimization

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On constructing boundaries for boundary value problems: the general case

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MULTIDIMENSIONAL systems AND SIGNAL PROCESSING 2023年第2期34卷 521-541页

作者： Mukherjee, Mousumi Pal, Debasattam Indian Inst Technol Dept Elect Engn Mumbai 400076 Maharashtra India

In this paper, we provide a constructive method of specifying initial/boundary conditions for linear unforced systems of partial differential equations (PDEs) with real constant coefficients. In the literature, one of the ways of specifying initial/boundary data is by specifying the values of certain derivatives of the solution trajectories at the origin. These derivatives correspond to a standard monomial set and is obtained using Grobner basis. This method of specifying initial data often lacks physical interpretation. In this paper, we propose a method of specifying initial/boundary data by restricting trajectories to subsets of the domain having an algebraic structure given by a hyper-cubic strip of infinite length and finite width;such special subsets are known as characteristic sets. We provide a method of constructing characteristic sets of this form. We further show that every unforced system of linear PDEs with real constant coefficients admits a characteristic set of the above-mentioned form. This provides a complete answer to the question of initial/boundary conditions for systems of linear PDEs with real constant coefficients.

关键词： distributed parameter systems Boundary control Characteristic sets

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Input shaping prefilter for vibration mitigation of distributed parameter system

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MECHATRONICS 2023年 93卷

作者： Heining, Andre Sawodny, Oliver Univ Stuttgart Inst Syst Dynam Stuttgart Germany

An increasing speed of a motion change in conjunction with lightweight elastic structures lead to large elastic deflections. In order to maintain a sufficient positioning accuracy, vibration damping is mandatory. This can be achieved directly by a feedback loop or indirectly by shaping the reference signal. Based on a G2-norm optimal filter that takes the desired rigid body acceleration and elastic mode dynamics into account and returns a force signal, a reshaped velocity signal for reducing the elastic oscillation is generated. The method is validated on a test setup comprising a linearly moving slide with an upright beam and measurements show a major reduction in the beam oscillation.

关键词： Vibration and modal analysis Linear systems distributed parameter systems Input and excitation design

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A Lyapunov Approach for the Exponential Stability of a Damped Timoshenko Beam

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第12期68卷 8287-8292页

作者： Mattioni, Andrea Wu, Yongxin Le Gorrec, Yann Univ Grenoble Alpes GIPSA Lab CNRS Grenoble INP F-38000 Grenoble France Univ Bourgogne Franche Compte FEMTO ST Res Lab AS2M Dept F-25000 Besancon France

In this technical note, we consider the stability properties of a viscously damped Timoshenko beam equations with spatially varying parameters. With the help of the port-Hamiltonian framework, we first prove the existence of solutions and show, by the use of an appropriate Lyapunov function, that the system is exponentially stable and has an explicit decay rate. The explicit exponential bound is computed for an illustrative example for which we provide some numerical simulations.

关键词： distributed parameter systems exponential stability port-Hamiltonian systems viscous damping

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Cooperative Filtering and parameter Identification for Advection-Diffusion Processes Using a Mobile Sensor Network

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IEEE TRANSACTIONS ON CONTROL systems TECHNOLOGY 2023年第2期31卷 527-542页

作者： You, Jie Zhang, Ziqiao Zhang, Fumin Wu, Wencen Rensselaer Polytech Inst Dept Elect Comp & Syst Engn Troy NY 12180 USA Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30318 USA San Jose State Univ Dept Comp Engn San Jose CA 95192 USA

This article presents an online parameter identification scheme for advection-diffusion processes using data collected by a mobile sensor network. The advection-diffusion equation is incorporated into the information dynamics associated with the trajectories of the mobile sensors. A constrained cooperative Kalman filter is developed to provide estimates of the field values and gradients along the trajectories of the mobile sensors so that the temporal variations in the field values can be estimated. This leads to a co-design scheme for state estimation and parameter identification for advection-diffusion processes that is different from comparable schemes using sensors installed at fixed spatial locations. Using state estimates from the constrained cooperative Kalman filter, a recursive least-square (RLS) algorithm is designed to estimate unknown model parameters of the advection-diffusion processes. Theoretical justifications are provided for the convergence of the proposed cooperative Kalman filter by deriving a set of sufficient conditions regarding the formation shape and the motion of the mobile sensor network. Simulation and experimental results show satisfactory performance and demonstrate the robustness of the algorithm under realistic uncertainties and disturbances.

关键词： Robot sensing systems Mathematical models Trajectory Kalman filters Sensors Inverse problems parameter estimation distributed parameter systems Kalman filters multi-robot systems system identification

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MMC-HVDC AC side line protection based on positive sequence fault component current ratio

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IET GENERATION TRANSMISSION & DISTRIBUTION 2023年第19期17卷 4375-4385页

作者： Huang, Hanqing Wang, Zengping North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewable Beijing 102206 Peoples R China

The high-voltage direct current (HVDC) transmission based on modular multilevel converter shows the weak feed characteristic of limited fault current amplitude when connected to the traditional AC power grid, which leads to the risk of sensitivity reduction or even failure of the traditional pilot protection. Here, a modular multi-level converter (MMC)-HVDC AC side transmission line protection scheme based on positive sequence fault component current ratio is proposed. The positive sequence fault component current of the MMC-HVDC side is calculated by using the positive sequence fault component current of the power grid side, and the fault is identified through the significant difference between the ratio of the positive sequence fault component current of the MMC-HVDC side and the actual positive sequence fault component current of the MMC-HVDC side in the case of internal and external faults. This method has the advantages of simple principle, low requirement for synchronous data, not affected by capacitive current and strong resistance to high resistance. The simulation results show that the algorithm can correctly partition internal and external faults, and is not affected by fault location, fault type and operation mode of converter station, and has high sensitivity and reliability. Here, a modular multi-level converter (MMC)-high-voltage direct current (HVDC) AC side transmission line protection scheme based on positive sequence fault component current ratio is proposed. The positive sequence fault component current of the MMC-HVDC side is calculated by using the positive sequence fault component current of the power grid side, and the fault is identified through the significant difference between the ratio of the positive sequence fault component current of the MMC-HVDC side and the actual positive sequence fault component current of the MMC-HVDC side in the case of internal and external ***

关键词： distributed parameter systems power system protection power transmission protection

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Continuification Control of Large-Scale Multiagent systems in a Ring

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IEEE CONTROL systems LETTERS 2023年 7卷 841-846页

作者： Maffettone, Gian Carlo Boldini, Alain Di Bernardo, Mario Porfiri, Maurizio Scuola Super Meridionale Modeling & Engn Risk & Complex I-80138 Naples Italy NYU Tandon Sch Engn Ctr Urban Sci & Progress Brooklyn NY 11201 USA NYU Dept Mech & Aerosp Engn Tandon Sch Engn Brooklyn NY 11201 USA Univ Naples Federico II Dept Elect Engn & Informat Technol I-80125 Naples Italy NYU Tandon Sch Engn Dept Biomed Engn Brooklyn NY 11201 USA

In this Letter, we propose a method to control large-scale multiagent systems swarming in a ring. Specifically, we use a continuification-based approach that transforms the microscopic, agent-level description of the system dynamics into a macroscopic, continuum-level representation, which we employ to synthesize a control action towards a desired distribution of the agents. The continuum-level control action is then discretized at the agent-level in order to practically implement it. To confirm the effectiveness and the robustness of the proposed approach, we complement theoretical derivations with numerical simulations.

关键词： Agents-based systems distributed parameter systems large-scale systems

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Safe PDE Backstepping QP Control With High Relative Degree CBFs: Stefan Model With Actuator Dynamics

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第12期68卷 7195-7208页

作者： Koga, Shumon Krstic, Miroslav Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

High-relative-degree control barrier functions play a prominent role in automotive safety and in robotics. In this article, we launch a generalization of this concept for PDE control, treating a specific, physically relevant model of thermal dynamics where the boundary of the PDE moves due to a liquid-solid phase change-the so-called Stefan model. The familiar quadratic programming (QP) design is employed to ensure safety but with CBFs that are infinite-dimensional (including one control barrier "functional") and with safe sets that are infinite-dimensional as well. Since, in the presence of actuator dynamics, at the boundary of the Stefan system, this system's main CBF is of relative degree 2, an additional CBF is constructed, by backstepping design, which ensures the positivity of all the CBFs without any additional restrictions on the initial conditions. It is shown that the "safety filter" designed in this article guarantees safety in the presence of an arbitrary operator input. This is similar to an automotive system in which a safety feedback law overrides-but only when necessary-the possibly unsafe steering, acceleration, or braking by a vigorous but inexperienced driver. Simulations have been performed for a process in metal additive manufacturing, which show that the operator's heat-and-cool commands to the Stefan model are being obeyed but without the liquid ever freezing.

关键词： Additive manufacturing (AM) control barrier function (CBF) distributed parameter systems nonlinear control quadratic program safety Stefan problem

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