Average-energy games

Bouyer, Patricia; Markey, Nicolas; Randour, Mickaël; Larsen, Kim Guldstrand; Laursen, Simon

doi:10.1007/s00236-016-0274-1

Cited by 31 publications

(70 citation statements)

References 37 publications

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“…Quantitative infinite-duration games have received considerable attention, e.g., in the form of games with mean-payoff conditions [2,18,30,38] and other payoff conditions [6,22,38], energy conditions [4,15,24,33], quantitative logics for specifying winning conditions [1,19,26,36,37], variations of the classical parity condition [11,12,13,20,31], and other models [3,5,7]. Weighted limit games are related to some of these models.…”

Section: Related Workmentioning

confidence: 99%

Optimal Strategies in Weighted Limit Games

Murano¹,

Rubin²,

Zimmermann³

2020

Electron. Proc. Theor. Comput. Sci.

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We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a Büchi-style winning condition requiring to produce infinitely many play prefixes that satisfy a given regular specification. Quality of plays is measured in the maximal weight of infixes between successive play prefixes that satisfy the specification. * We would like to thank Alexander Weinert for fruitful discussions leading to this work and the reviewers for their detailed feedback, which considerably improved the paper.

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Section: Related Workmentioning

confidence: 99%

Optimal Strategies in Weighted Limit Games

Murano¹,

Rubin²,

Zimmermann³

2020

Electron. Proc. Theor. Comput. Sci.

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“…Obviously, along with the already introduced lower and upper minimax joint spectral radii µ(A, B) and η(A, B), the quantities (16) and (17) could also claim the role of numeric quantities that characterize the stabilizability of a controlled system AB, governed by equation (6).…”

Section: Other Minimax Characteristics Of Matrix Productsmentioning

confidence: 99%

Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems

Kozyakin¹

2019

Discrete &Amp; Continuous Dynamical Systems - B

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To estimate the growth rate of matrix products An · · · A1 with factors from some set of matrices A, such numeric quantities as the joint spectral radius ρ(A) and the lower spectral radiusρ(A) are traditionally used. The first of these quantities characterizes the maximum growth rate of the norms of the corresponding products, while the second one characterizes the minimal growth rate. In the theory of discrete-time linear switching systems, the inequality ρ(A) < 1 serves as a criterion for the stability of a system, and the inequalityρ(A) < 1 as a criterion for stabilizability.For matrix products AnBn · · · A1B1 with factors Ai ∈ A and Bi ∈ B, where A and B are some sets of matrices, we introduce the quantities µ(A, B) and η(A, B), called the lower and upper minimax joint spectral radius of the pair {A, B}, respectively, which characterize the maximum growth rate of the matrix products AnBn · · · A1B1 over all sets of matrices Ai ∈ A and the minimal growth rate over all sets of matrices Bi ∈ B. In this sense, the minimax joint spectral radii can be considered as generalizations of both the joint and lower spectral radii. As an application of the minimax joint spectral radii, it is shown how these quantities can be used to analyze the stabilizability of discrete-time linear switching control systems in the presence of uncontrolled external disturbances of the plant.

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“…. , B k ∈ B for which equality (7) holds. Correspondingly, the statement of Theorem 1 is valid under weaker assumptions.…”

Section: Remarks and Open Questionsmentioning

confidence: 99%

On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices

Kozyakin

2018

Discrete Dynamics in Nature and Society

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We consider the problem of convergence to zero of matrix products ⋅ ⋅ ⋅ 1 1 with factors from two sets of matrices, ∈ A and ∈ B, due to a suitable choice of matrices { }. It is assumed that for any sequence of matrices { } there is a sequence of matrices { } such that the corresponding matrix products ⋅ ⋅ ⋅ 1 1 converge to zero. We show that, in this case, the convergence of the matrix products under consideration is uniformly exponential; that is, ‖ ⋅ ⋅ ⋅ 1 1 ‖ ≤ , where the constants > 0 and ∈ (0, 1) do not depend on the sequence { } and the corresponding sequence { }. Other problems of this kind are discussed and open questions are formulated.

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Average-energy games

Cited by 31 publications

References 37 publications

Optimal Strategies in Weighted Limit Games

Optimal Strategies in Weighted Limit Games

Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems

On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices

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