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Robust eigenvalue assignment for time-delay systems

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Robust eigenvalue assignment for time-delay systems

IEEE Annual Conference on Decision and Control

作者： Robert Schmid Thang Nguyen Department of Electrical and Electronic Engineering University of Melbourne Australia Department of Engineering University of Exeter UK

ISBN: (纸本)9781467360890

We consider the problem of robust pole assignment for a linear time invariant plant with state feedback subject to time delay in the control input. For systems with a known time delay, we offer a parametric formula for the feedback gain matrix that will assign a desired set of closed-loop eigenvalues to the time-delay system. Secondly we consider systems subject to small input time delays and introduce an unconstrained optimisation algorithm for the computation of a state feedback matrix to deliver the desired pole placement in a manner that minimises the sensitivity of the eigenvalues to input time delays. The performance of the algorithm is compared against an alternative robust pole placement method from the recent literature and found to give significantly reduced time delay sensitivity.

关键词： Delay systems pole assignment State feedback eigenvalues time delay control control input optimization algorithms information matrix

Optimal and least restrictive supervisory control: safety verification methods for human-driven vehicles at traffic intersections

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Optimal and least restrictive supervisory control: safety ve...

IEEE Annual Conference on Decision and Control

作者： Gabriel Rodrigues de Campos Fabio Della Rossa Alessandro Colombo DEIB at Politecnico di Milano Italy

ISBN: (纸本)9781479978878

We consider a cooperative conflict resolution problem at traffic intersections. Our goal is to design a least restrictive supervisor able to identify the optimal corrections to a human-decided input with respect to a given performance index, while keeping the system safe. Here, safety is formulated in terms of a maximal safe controlled invariant set. Leveraging results from scheduling theory, we characterize the preorder of the optimal solution set and propose an efficient optimization algorithm providing Pareto optimal solutions. We illustrate the application of the proposed algorithm through simulations in which vehicles crossing an intersection are optimally overridden by the supervisor only when necessary to maintain safety.

关键词： vehicle performance indicators Scheduling Theory Safety Verification Preorder Optimal Solution Set Supervisory control Conflict Resolution Supervisors Human Traffic optimal solution optimization algorithms

Ontologies for Models and algorithms in Applied Mathematics and Related Disciplines

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arXiv 2023年

作者： Schembera, Björn Wübbeling, Frank Kleikamp, Hendrik Biedinger, Christine Fiedler, Jochen Reidelbach, Marco Shehu, Aurela Schmidt, Burkhard Koprucki, Thomas Iglezakis, Dorothea Göddeke, Dominik Institute of Applied Analysis and Numerical Simulation University of Stuttgart Germany Institute of Applied Mathematics: Analysis and Numerics University of Münster Germany Fraunhofer Institute for Industrial Mathematics Kaiserslautern Germany Zuse Institute Berlin Germany Weierstrass Institute for Applied Analysis and Stochastics Berlin Germany University Library University of Stuttgart Germany University of Stuttgart Germany

In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data, the Mathematical Research Data Initiative has developed, merged and implemented ontologies and knowledge graphs. This contributes to making mathematical research data FAIR by introducing semantic technology and documenting the mathematical foundations accordingly. Using the concrete example of microfracture analysis of porous media, it is shown how the knowledge of the underlying mathematical model and the corresponding numerical algorithms for its solution can be represented by the ontologies. © 2023, CC BY.

关键词： optimization algorithms

Modified Recursive QAOA for Exact Max-Cut Solutions on Bipartite Graphs: Closing the Gap Beyond QAOA Limit

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arXiv 2024年

作者： Bae, Eunok Kwon, Hyukjoon Vijendran, V. Lee, Soojoon Seoul02455 Korea Republic of Department of Quantum Science and Technology Research School of Physics Australian National University Acton2601 Australia 2 Fusionopolis Way Innovis #08-03 Singapore138634 Singapore Department of Mathematics Research Institute for Basic Sciences Kyung Hee University Seoul02447 Korea Republic of

Quantum Approximate optimization Algorithm (QAOA) is a quantum-classical hybrid algorithm proposed with the goal of approximately solving combinatorial optimization problems such as the MAX-CUT problem. It has been considered a potential candidate for achieving quantum advantage in the Noisy Intermediate-Scale Quantum era and has been extensively studied. However, the performance limitations of low-level QAOA have also been demonstrated across various instances. In this work, we first analytically prove the performance limitations of level-1 QAOA in solving the MAX-CUT problem on bipartite graphs. To this end, we derive an upper bound for the approximation ratio based on the average degree of bipartite graphs. Second, we demonstrate that Recursive QAOA (RQAOA), which recursively reduces graph size using QAOA as a subroutine, outperforms the level-1 QAOA. However, the performance of RQAOA exhibits limitations as the graph size increases. Finally, we show that RQAOA with a restricted parameter regime can fully address these limitations. Surprisingly, this modified RQAOA always finds the exact maximum cut for any bipartite graphs and even for a more general graph with parity-signed weights. © 2024, CC BY.

关键词： optimization algorithms

Worst-Case Performance of Rendezvous Networks in the Presence of Adversarial Nodes

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Worst-Case Performance of Rendezvous Networks in the Presenc...

IEEE/RSJ International Conference on Intelligent Robots and Systems

作者： Hyongju Park Seth Hutchinson Department of Mechanical and Science Engineering at the University of Illinois. Electrical and Computer Engineering at the University of Illinois.

ISBN: (纸本)9781467363563

In this paper, we consider the performance of distributed control algorithms for networked robotic systems when one or more robots fail to execute the optimal policy. In particular, we investigate the performance of the circumcenter algorithm with connectivity maintenance [1]-[3] when one or more adversarial agents act maliciously to maximally disrupt convergence of the remaining, cooperative agents. To this end, we formulate a performance objective for each adversary node in terms of the circumradii of its cooperative neighbors in a communication graph which does not require omniscience of adversaries as is often assumed in the literature (e.g., [4], [5]). We provide an optimization algorithm based on finite-horizon dynamic programming, and obtain solutions through numerical simulation. Our results show that in general adversarial nodes are able not only to impede convergence toward consensus, but can also affect global changes in the topology of the communication graph for the cooperative agents.

关键词： circumcenter algorithm communication graph cooperative agents rendezvous Ganglia Converge optimization algorithms Agents optimal strategy Circumcentre Line graph

High-Dimensional Sparse Data Low-rank Representation via Accelerated Asynchronous Parallel Stochastic Gradient Descent

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arXiv 2024年

作者： Hu, Qicong Wu, Hao College of Computer and Information Science Southwest University Chongqing China

Data characterized by high dimensionality and sparsity are commonly used to describe real-world node interactions. Low-rank representation (LR) can map high-dimensional sparse (HDS) data to low-dimensional feature spaces and infer node interactions via modeling data latent associations. Unfortunately, existing optimization algorithms for LR models are computationally inefficient and slowly convergent on large-scale datasets. To address this issue, this paper proposes an Accelerated Asynchronous Parallel Stochastic Gradient Descent (A2PSGD) for High-Dimensional Sparse Data Low-rank Representation with three fold-ideas: a) establishing a lock-free scheduler to simultaneously respond to scheduling requests from multiple threads;b) introducing a greedy algorithm-based load balancing strategy for balancing the computational load among threads;c) incorporating Nesterov's accelerated gradient into the learning scheme to accelerate model convergence. Empirical studies show that A2PSGD outperforms existing optimization algorithms for HDS data LR in both accuracy and training time. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

Complexity order of multiple resource algorithms

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arXiv 2024年

作者： Teh, Run Yan Thenabadu, Manushan Drummond, Peter D. Centre for Quantum Science and Technology Theory Swinburne University of Technology Melbourne3122 Australia

Algorithmic efficiency is essential to reducing energy use and time taken for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random ensemble competes with the time-step. We define the complexity order of an algorithm needing multiple resources as the exponent of inverse total error with respect to the total resources used. The optimum order c is predicted for cases involving competing, factorable resources. As an illustration, this is applied to computing averages in a stochastic differential equation, with numerical examples that agree with earlier literature, as well as with the more general analytic theory that is obtained here. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

A preconditioned second-order convex splitting algorithm with a difference of varying convex functions and line search

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arXiv 2024年

作者： Shen, Xinhua Shang, Zaijiu Sun, Hongpeng School of Mathematics Renmin University of China China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Shanghai Institute for Mathematics and Interdisciplinary Sciences Shanghai200092 China

This paper introduces a preconditioned convex splitting algorithm enhanced with line search techniques for nonconvex optimization problems. The algorithm utilizes second-order backward differentiation formulas (BDF) for the implicit and linear components and the Adams-Bashforth scheme for the nonlinear and explicit parts of the gradient flow in variational functions. The proposed algorithm, resembling a generalized difference-of-convex-function approach, involves a changing set of convex functions in each iteration. It integrates the Armijo line search strategy to improve performance. The study also discusses classical preconditioners such as symmetric Gauss-Seidel, Jacobi, and Richardson within this context. The global convergence of the algorithm is established through the Kurdyka-Lojasiewicz properties, ensuring convergence within a finite number of preconditioned iterations. Numerical experiments demonstrate the superiority of the proposed second-order convex splitting with line search over conventional difference-of-convex-function algorithms. © 2024, CC BY-NC-ND.

关键词： optimization algorithms

Cyclades: Conflict-free Asynchronous Machine Learning 16

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Cyclades: Conflict-free Asynchronous Machine Learning

Annual Conference on Neural Information Processing Systems

作者： Xinghao Pan Maximilian Lam Stephen Ti Dimitris Papailiopoulos Ce Zhang Michael I. Jordan Kannan Ramchandran Chris Re Benjamin Recht Department of Electrical Engineering and Computer Science UC Berkeley Berkeley CA Department of Computer Science Stanford University Palo Alto CA Department of Electrical Engineering and Computer Science UC Berkeley Berkeley CADepartment of Statistics UC Berkeley Berkeley CA

ISBN: (纸本)9781510838819

We present Cyclades, a general framework for parallelizing stochastic optimization algorithms in a shared memory setting. Cyclades is asynchronous during model updates, and requires no memory locking mechanisms, similar to Hog-??wild!-type algorithms. Unlike HOGWILD!, Cyclades introduces no conflicts during parallel execution, and offers a black-box analysis for provable speedups across a large family of algorithms. Due to its inherent cache locality and conflict-??free nature, our multi-core implementation of Cyclades consistently outperforms Hogwild!-type algorithms on sufficiently sparse datasets, leading to up to 40% speedup gains compared to Hogwild!, and up to 5× gains over asynchronous implementations of variance reduction algorithms.

关键词： Cyclades Asynchronous parallel execution shared memory large family asynchronous machines optimization algorithms Model updating Conflict (Psychology) algorithms