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Contraction Analysis of Continuation Method for Suboptimal Model Predictive Control

IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 3261-3266页

作者： Shima, Ryotaro Ito, Yuji Miyano, Tatsuya Toyota Cent Res & Dev Labs Inc Green Fuel Res Domain Nagakute Aichi 4801192 Japan Toyota Cent Res & Dev Labs Inc Appl Math Res Domain Nagakute Aichi 4801192 Japan

This letter analyzes the contraction property of the nonlinear systems controlled by suboptimal model predictive control (MPC) using the continuation method. We propose a contraction metric that reflects the hierarchical dynamics inherent in the continuation method. We derive a pair of matrix inequalities that elucidate the impact of suboptimality on the contraction of the optimally controlled closed-loop system. A numerical example is presented to verify our contraction analysis. Our results are applicable to other MPCs than stabilization, including economic MPC.

关键词： Measurement Trajectory Linear matrix inequalities Vectors Predictive control Convergence Stability criteria optimization Numerical stability Mathematical models Predictive control for nonlinear systems optimization algorithms time-varying systems

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Feedback-Based optimization With Sub-Weibull Gradient Errors and Intermittent Updates

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IEEE CONTROL SYSTEMS LETTERS 2022年 6卷 2521-2526页

作者： Ospina, Ana M. Bastianello, Nicola Dall'Anese, Emiliano Univ Colorado Dept Elect Comp & Energy Engn Boulder CO 80309 USA Univ Padua Dept Informat Engn I-35131 Padua Italy

This letter considers a feedback-based projected gradient method for optimizing systems modeled as algebraic maps. The focus is on a setup where the gradient is corrupted by random errors that follow a sub-Weibull distribution, and where the measurements of the output - which replace the input-output map of the system in the algorithmic updates - may not be available at each iteration. The sub-Weibull error model is particularly well-suited in frameworks where the cost of the problem is learned via Gaussian Process (GP) regression (from functional evaluations) concurrently with the execution of the algorithm;however, it also naturally models setups where nonparametric methods and neural networks are utilized to estimate the cost. Using the sub-Weibull model, and with Bernoulli random variables modeling missing measurements of the system output, we show that the online algorithm generates points that are within a bounded error from the optimal solutions. In particular, we provide error bounds in expectation and in high probability. Numerical results are presented in the context of a demand response problem in smart power grids.

关键词： Costs Noise measurement Random variables Measurement uncertainty Convergence Computational modeling Particle measurements optimization optimization algorithms

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Distributed Stochastic Dual Subgradient for Constraint-Coupled optimization

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IEEE CONTROL SYSTEMS LETTERS 2022年 6卷 644-649页

作者： Camisa, Andrea Notarnicola, Ivano Notarstefano, Giuseppe Univ Bologna Dept Elect Elect & Informat Engn I-40136 Bologna Italy

In this letter we consider a distributed stochastic optimization framework in which agents in a network aim to cooperatively learn an optimal network-wide policy. The goal is to compute local functions to minimize the expected value of a given cost, subject to individual constraints and average coupling constraints. In order to handle the challenges of the distributed stochastic context, we resort to a Lagrangian duality approach that allows us to derive an associated stochastic dual problem with a separable structure. Thus, we propose a distributed algorithm, without a central coordinator, that exploits consensus iterations and stochastic approximation to find an optimal solution to the problem, with attractive scalability properties. We demonstrate convergence of the proposed scheme and validate its behavior through simulations.

关键词： optimization Couplings Stochastic processes Resource management Distributed algorithms Minimization IEEE members optimization algorithms large-scale systems distributed control stochastic optimization

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A framework for bilevel optimization that enables stochastic and global variance reduction algorithms

arXiv

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arXiv 2022年

作者： Dagréou, Mathieu Ablin, Pierre Vaiter, Samuel Moreau, Thomas Inria CEA Université Paris-Saclay Palaiseau France CNRS Université Côte d’Azur LJAD Nice France CNRS Université Paris-Dauphine PSL-University Paris France

Bilevel optimization, the problem of minimizing a value function which involves the arg-minimum of another function, appears in many areas of machine learning. In a large scale empirical risk minimization setting where the number of samples is huge, it is crucial to develop stochastic methods, which only use a few samples at a time to progress. However, computing the gradient of the value function involves solving a linear system, which makes it difficult to derive unbiased stochastic estimates. To overcome this problem we introduce a novel framework, in which the solution of the inner problem, the solution of the linear system, and the main variable evolve at the same time. These directions are written as a sum, making it straightforward to derive unbiased estimates. The simplicity of our approach allows us to develop global variance reduction algorithms, where the dynamic of all variables is subject to variance reduction. We demonstrate that SABA, an adaptation of the celebrated SAGA algorithm in our framework, has O(T1 ) convergence rate, and that it achieves linear convergence under Polyak-Lojasciewicz assumption. This is the first stochastic algorithm for bilevel optimization that verifies either of these properties. Numerical experiments validate the usefulness of our method. © 2022, CC BY.

关键词： optimization algorithms

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A Linear Model for Irrigation Canals Operating in Real Time Applied in ASCE Test Cases

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WATER 2025年第9期17卷 1368-1368页

作者： Bonet, Enrique Yubero, Maria Teresa Bascompta, Marc Alfonso, Pura Univ Politecn Catalunya UPC Dept Min Ind & ICT Engn Les Bases Ave 61-73 Manresa 08242 Spain

In the context of irrigation canal flow, numerical models developed to accurately estimate canal behavior based on gate trajectories are often highly complex. Consequently, hardware limitations make it significantly more challenging to implement these models locally at gate devices. In this regard, one of the most significant contributions of this paper is the concept of the hydraulic influence matrix (HIM) and its application as a linear model to estimate the water surface flow in irrigation canals, integrated within an irrigation canal controller to facilitate real-time operations. The HIM model provides a significant advantage by quickly and accurately computing water level and velocity perturbations in open-flow canals. This capability empowers watermasters to apply this linear free-surface model in both unsteady and steady flow conditions, enabling real-time applications in control algorithms. The HIM model was validated by comparing water-level estimates under various perturbations with results from software using the full Saint-Venant equations. The test involved introducing a 10% perturbation in gate movement over a specified time period in two different test cases, resulting in a flow discharge increase of more than 10% in each test case. The results showed maximum absolute errors below 7 cm and 0.2 cm, relative errors of 0.7% and 0.023%, root mean square errors ranging from 2.4 to 0.07 cm, and Nash-Sutcliffe efficiency values of approximately 0.95 in the first and second test cases, respectively, when compared to the full Saint-Venant equations. This highlights the high precision of the HIM model, even when subjected to significant disturbances. However, larger gate movement disturbances (exceeding 10%) should be planned in advance rather than managed in real time.

关键词： optimization algorithms real time control mathematical flow models irrigation canals

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Proximal Gradient Dynamics: Monotonicity, Exponential Convergence, and Applications

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IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 2853-2858页

作者： Gokhale, Anand Davydov, Alexander Bullo, Francesco UC Santa Barbara Ctr Control Dynam Syst & Computat Santa Barbara CA 93106 USA

In this letter we study the proximal gradient dynamics. This recently-proposed continuous-time dynamics solves optimization problems whose cost functions are separable into a nonsmooth convex and a smooth component. First, we show that the cost function decreases monotonically along the trajectories of the proximal gradient dynamics. We then introduce a new condition that guarantees exponential convergence of the cost function to its optimal value, and show that this condition implies the proximal Polyak-& Lstrok;ojasiewicz condition. We also show that the proximal Polyak-& Lstrok;ojasiewicz condition guarantees exponential convergence of the cost function. Moreover, we extend these results to time-varying optimization problems, providing bounds for equilibrium tracking. Finally, we discuss applications of these findings, including the LASSO problem, certain matrix based problems and a numerical experiment on a feed-forward neural network.

关键词： Convergence Cost function Heuristic algorithms Trajectory Machine learning algorithms Costs Prediction algorithms Neuroscience Machine learning Encoding optimization algorithms nonconvex optimization nonlinear systems

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The Whale optimization Algorithm in Abrasive Water Jet Machining of Tool Steel 27

The Whale Optimization Algorithm in Abrasive Water Jet Machi...

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27th International Conference on Knowledge Based and Intelligent Information and Engineering Sytems, KES 2023

作者： Kawecka, Elzbieta The Jacob of Paradies University Faculty of Technology Teatralna 25 Gorzów Wielkopolski66-400 Poland

The paper presents possibility of Whale optimization Algorithm application into abrasive waterjet (AWJ) machining of tool steel. Based on the control parameters of the process of cutting tool steel with AWJ, the objective function was determined using the Response Surface Methodology (RSM). Then the process of optimization and established the set of control parameters which the value of the objective function reaches the extremum value was carried out. Also, the effectiveness of this algorithm for optimizing the parameters of the studied process was determined. The calculated on the basis WOA value of optimum was comparison with value of the best effect determined experimentally. © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0)

关键词： Abrasive Water Jet (AWJ) AWJ cutting process meta-heuristic algorithms optimization algorithms Whale optimization Algorithm (WOA)

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Iterative Learning-Based Trajectory optimization Using Fourier Series Basis Functions

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IEEE CONTROL SYSTEMS LETTERS 2022年 6卷 2180-2185页

作者： Drallmeier, Joseph A. Siegel, Jason B. Stefanopoulou, Anna G. Univ Michigan Dept Mech Engn Ann Arbor MI 48109 USA

This letter presents an iterative, online trajectory optimization algorithm for systems performing repetitive processes. While typical iterative learning techniques are formulated for tracking control applications, a precise definition of the tracking reference is required. In repetitive applications where the optimal tracking reference is not fully defined, there exists an opportunity to improve system performance by altering the trajectory of the system based on information rich signals from previous cycles. In this letter, we develop an algorithm to optimize the parameterized trajectory of a system in real time utilizing constrained optimization of a cost function generated from the performance values of the previous cycle. Simulation results are used to illustrate the implementation of this iterative trajectory optimization framework while also benchmarking the performance against a norm optimal iterative learning controller with perfect system knowledge.

关键词： Cost function Trajectory optimization Indium tin oxide Uncertainty Manipulator dynamics Iterative algorithms Indexes optimization iterative learning control optimization algorithms

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Stochastic Learning Rate With Memory: optimization in the Stochastic Approximation and Online Learning Settings

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IEEE CONTROL SYSTEMS LETTERS 2022年 7卷 419-424页

作者： Mamalis, Theodoros Stipanovic, Dusan Voulgaris, Petros Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Univ Illinos Urbana Champaign Coordinated Sci Lab Urbana IL 61801 USA Univ Nevada Dept Mech Engn Reno NV 89557 USA

In this letter, multiplicative stochasticity is applied to the learning rate of stochastic optimization algorithms, giving rise to stochastic learning-rate schemes. In-expectation theoretical convergence results of Stochastic Gradient Descent equipped with this novel learning rate scheme under the stochastic setting, as well as convergence results under the online optimization settings are provided. Empirical results consider the case of an adaptively uniformly distributed multiplicative stochasticity and include not only Stochastic Gradient Descent, but also other popular algorithms equipped with a stochastic learning rate. They demonstrate noticeable optimization performance gains with respect to their deterministic-learning-rate versions.

关键词： Stochastic processes Convergence optimization Training data Upper bound Minimization Loss measurement optimization algorithms stochastic systems convergence machine learning

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algorithms for influence maximization in socio-physical networks

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JOURNAL OF COMBINATORIAL optimization 2023年第1期45卷 1-28页

作者： Gehlot, Hemant Sundaram, Shreyas Ukkusuri, Satish, V Indian Inst Technol Kanpur Dept Civil Engn Kanpur 208016 Uttar Pradesh India Purdue Univ Elmore Family Sch Elect & Comp Engn W Lafayette IN 47907 USA Purdue Univ Lyles Sch Civil Engn W Lafayette IN 47907 USA

Given a directed graph (referred to as social network), the influence maximization problem is to find k nodes which, when influenced (or activated), would maximize the number of remaining nodes that get activated under a given set of activation dynamics. In this paper, we consider a more general version of the problem that includes an additional set (or layer) of nodes that are termed as physical nodes, such that a node in the social network is connected to one physical node. A physical node exists in one of two states at any time, opened or closed, and there is a constraint on the maximum number of physical nodes that can be opened. In this setting, an inactive node in the social network becomes active if it has at least one active neighbor in the social network and if it is connected to an opened physical node. This problem arises in scenarios such as disaster recovery, where a displaced social group (an inactive social node) decides to return back after a disaster (switches to active state) only after a sufficiently large number of groups in its social network return back and some infrastructure components (physical nodes) in its neighborhood are repaired (brought to the open state). We first show that this general problem is NP-hard to approximate within any constant factor. We then consider instances of the problem when the mapping between the social nodes and the physical nodes is bijective and characterize optimal and approximation algorithms for those instances.

关键词： optimization algorithms Social networks Influence maximization Disaster recovery

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