Designing large-scale control systems to satisfy complex specifications is hard in practice, as most formal methods are limited to systems of modest size. Contract theory has been proposed as a modular alternative, in...
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Designing large-scale control systems to satisfy complex specifications is hard in practice, as most formal methods are limited to systems of modest size. Contract theory has been proposed as a modular alternative, in which specifications are defined by assumptions on the input to a component and guarantees on its output. However, current contract-based methods for control systems either prescribe guarantees on the state of the system, going against the spirit of contract theory, or are not supported by efficient computational tools. In this paper, we present a contract-based modular framework for discrete-time dynamical control systems. We extend the definition of contracts by allowing the assumption on the input at a time k to depend on outputs up to time k - 1, which is essential when considering feedback systems. We also define contract composition for arbitrary interconnection topologies, and prove that this notion supports modular design, analysis and verification. This is done using graph theory methods, and specifically using the notions of topological ordering and backwardreachable nodes. Lastly, we present an algorithm for verifying vertical contracts, which are claims of the form "the conjunction of given component-level contracts implies given contract on the integrated system". These algorithms are based on linear programming, and scale linearly with the number of components in the interconnected network. A numerical example is provided to demonstrate the scalability of the presented approach, as well as the modularity achieved by using it. (c) 2024 Elsevier Ltd. All rights reserved.
In this note, a novel methodology that can extract a number of analysis results for linear time-invariant systems (LTI) given only a single trajectory of the considered system is proposed. The superiority of the propo...
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ISBN:
(数字)9781665473385
ISBN:
(纸本)9781665473385
In this note, a novel methodology that can extract a number of analysis results for linear time-invariant systems (LTI) given only a single trajectory of the considered system is proposed. The superiority of the proposed technique relies on the fact that it provides an automatic and formal way to obtain a valuable information about the controlled system by only having access to a single trajectory over a finite period of time (i.e., the system dynamics is assumed to be unknown). At first, we characterize the stability region of LTI systems given only a single trajectory dataset by constructing the associated Lyapunov function of the system. The Lyapunov function is found by formulating and solving a linear programming (LP) problem. Then, we extend the same methodology to a variety of essential analysis results for LTI systems such as deriving bounds on the output energy, deriving bounds on output peak, deriving L-2 and RMS gains. To illustrate the efficacy of the proposed data-driven paradigm, a comparison analysis between the learned LTI system metrics and the true ones is provided.
In this paper, we consider three related cost-sparsity induced optimal input selection problems for structural controllability using a unifying linear programming (LP) framework. More precisely, given an autonomous sy...
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ISBN:
(数字)9781665451963
ISBN:
(纸本)9781665451963
In this paper, we consider three related cost-sparsity induced optimal input selection problems for structural controllability using a unifying linear programming (LP) framework. More precisely, given an autonomous system and a constrained input configuration where whether an input can directly actuate a state variable, as well as the corresponding (possibly different) cost, is prescribed, the problems are, respectively, selecting the minimum number of input links, selecting the minimum cost of input links, and selecting the input links with the cost as small as possible while their cardinality is not exceeding a prescribed number, all to ensure structural controllability of the resulting systems. Current studies show that in the dedicated input case (i.e., each input can actuate only a state variable), the first and second problems are polynomially solvable by some graphtheoretic algorithms, while the general nontrivial constrained case is largely unexploited. In this paper, we formulate these problems as equivalent integer linear programming (ILP) problems. Under a weaker constraint on the prescribed input configurations than most of the currently known ones with which the first two problems are reportedly polynomially solvable, we show these ILPs can be solved by simply removing the integer constraints and solving the corresponding LP relaxations, thus providing a unifying algebraic method, rather than graph-theoretic, for these problems with polynomial time complexity. The key to our approach is the observation that the respective constraint matrices of the ILPs are totally unimodular.
Secret sharing is a central topic in information-theoretical cryptography. In a secret sharing scheme a random secret is distributed among participants so that only the qualified subsets of parties can recover the sec...
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ISBN:
(纸本)9781665421607;9781665421591
Secret sharing is a central topic in information-theoretical cryptography. In a secret sharing scheme a random secret is distributed among participants so that only the qualified subsets of parties can recover the secret. In this paper we improve previously known [13] lower bounds on the size of the largest share for several specific access structures. Our approach is based on non-Shannon-type information inequalities. We employ the linear programming (LP) technique that permits to apply new information inequalities indirectly. To reduce computational complexity of the involved linear programs we extensively use symmetry considerations.
The growing power consumption of heterogeneous clusters has attracted great interests from both academia and industry. Although there have been extensive studies on energy-efficient task scheduling algorithms to addre...
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ISBN:
(数字)9781665497268
ISBN:
(纸本)9781665497268
The growing power consumption of heterogeneous clusters has attracted great interests from both academia and industry. Although there have been extensive studies on energy-efficient task scheduling algorithms to address this problem, most of them are task-centric. However, as a task is fine-grained enough, the scheduling algorithm can put more efforts on utilizing different power characteristics of heterogeneous servers, which has not been fully explored. This paper presents a linear programming-based Energy-efficient Load Balancing (LP-ELB) scheme for heterogeneous clusters. The power model of each sever in the cluster is obtained in advance, and the overall optimization problem is formulated as a mixed integer linear programming problem. LP-ELB tackles this problem through a two-phase heuristic: a server selection phase for choosing a minimal set of servers, and a load partition phase for calculating load distribution. An optimal solution to the relaxed problem in the second phase can be provided finally. Experiments on both simulated and real-world testbeds validate the effectiveness of the proposed method, and reveal that LP-ELB is superior to competitor algorithms, such as Round-Robin and power-aware Weighted Round-Robin.
The environmental problem continues to be an issue that cannot be neglected. As agriculture would largely affect the environment and is highly related to our daily diet, our project is to solve the diet problem by foc...
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ISBN:
(纸本)9781510655201;9781510655195
The environmental problem continues to be an issue that cannot be neglected. As agriculture would largely affect the environment and is highly related to our daily diet, our project is to solve the diet problem by focusing on the environmental impact brought by the food we eat. Instead of discussing every impact of one specific category of food on the environment, we investigated how a diet would affect carbon emissions, water use, land use, and the combination of them when the nutritional demands can also be fulfilled below budget. We collected the nutrition contents and price of foods in different categories, used linear programming to build the mathematical model which includes all the constraints such as budget and nutritional requirements and aims at minimizing the environmental impacts of the diet. We compared the results between the diet with and without meat consumption, found that meat would largely affect the environment. We also customized the diet for American high school students whose nutritional requirements and living styles are different from the others and the general diet for adults from 19 to 35.
Velocity Planning for self-driving vehicles in a complex environment is one of the most challenging tasks. It must satisfy the following three requirements: safety with regards to collisions;respect of the maximum vel...
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ISBN:
(纸本)9781728196817
Velocity Planning for self-driving vehicles in a complex environment is one of the most challenging tasks. It must satisfy the following three requirements: safety with regards to collisions;respect of the maximum velocity limits defined by the traffic rules;comfort of the passengers. In order to achieve these goals, the jerk and dynamic objects should be considered, however, it makes the problem as complex as a non-convex optimization problem. In this paper, we propose a linear programming (LP) based velocity planning method with jerk limit and obstacle avoidance constraints for an autonomous driving system. To confirm the efficiency of the proposed method, a comparison is made with several optimization-based approaches, and we show that our method can generate a velocity profile which satisfies the aforementioned requirements more efficiently than the compared methods. In addition, we tested our algorithm on a real vehicle at a test field to validate the effectiveness of the proposed method.
This paper provides a basic background consisting of mathematical concepts of linear programming (LP) and implementation to process the images. This analysis consists of a basic introduction to optimization techniques...
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ISBN:
(纸本)9783031126383;9783031126376
This paper provides a basic background consisting of mathematical concepts of linear programming (LP) and implementation to process the images. This analysis consists of a basic introduction to optimization techniques used for and image processing. Image processing consists of various problem domains like segmentation, color-based segmentation, multiple objects tracking problems in video streams, image registration and image de-noising etc. Various algorithmic approaches devised to address these challenges using LP. The use of linear programming facilitates the designing of digital filters, utilization of prior knowledge for occlusion detection and efficient data fitting for image restoration along with the enhancement of the image quality. Reconstructed image exhibits optimal results then counterparts. LP helps in minimizing errors using estimators, extended dynamic programming for object tracking. It is also capable to separate meaningful regions, or interactive colors and with the integration of correlation clustering for segmentation of images. This analysis gives a insights versatility of the linear programming to implement, integrate and solving any problem. The analysis helps to conclude the future scopes and ideas to target and modify the problem.
In a universe full of fuzziness and uncertainty, it is an absolute blessing if some information is reliable to some degree. Considering the amount of uncertainty, Zadeh proposed the idea of Z -number, which carries bo...
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In a universe full of fuzziness and uncertainty, it is an absolute blessing if some information is reliable to some degree. Considering the amount of uncertainty, Zadeh proposed the idea of Z -number, which carries both uncertainty and the reliability of the information. Uncertain information can be reliably conveyed using Z -numbers. On the other hand, one of the important and widely used decision -making techniques is linear programming. Currently, linear programming has been extensively explored using fuzzy information. Decisions made using linear programming with uncertain data are highly uncertain due to the lack of reliability of the information. An effective decision -making method is multi -objective linear programming (MOLP), in which the decision -maker attempts to draw conclusions from information containing conflicting attributes. In the MOLP problem, there may be different solution vectors corresponding to each objective function. One needs to find a compromise solution vector that satisfies each objective function to a certain extent based on the decision maker's suggested preferences. In this study, we use Z -number and MOLP to model the Z -number MOLP problem (ZMOLPP). Furthermore, we propose a strategy for solving ZMOLPP by transforming it into a crisp MOLP problem, and finally converting this crisp MOLP problem into a single -objective linear programming problem (LPP) using different shape functions. Additionally, we compare the results with existing MOLP problems in fuzzy settings to validate the proposed strategy.
When informing decisions with experimental data, it is often necessary to quantify the distribution tails of uncertain system responses using limited data. To maximize the information content of the data, one is natur...
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When informing decisions with experimental data, it is often necessary to quantify the distribution tails of uncertain system responses using limited data. To maximize the information content of the data, one is naturally led to use experimental design. However, common design techniques minimize global statistics such as the average estimation or prediction variance. Novel methods for optimal experimental design that target distribution tails are developed. To achieve this, pre asymptotic estimates of the data uncertainty are produced via an upper bound on a prescribed quantile, computed using quantile regression. Two optimal design problems are formulated: (i) Minimize the variance of the upper bound;and (ii) Minimize the Conditional Value-at-Risk of the upper bound. Additionally, each design problem is augmented with an added cardinality constraint to bound the number of experiments. These optimal design problems are reduced to continuous and mixed-integer linear programming problems. Consequently, the proposed methods are extremely efficient, even when applied to large datasets. The application of the proposed design formulation is demonstrated through a sensor placement problem in direct field acoustic testing.
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