Markov Chains With Maximum Entropy for Robotic Surveillance

George, Mishel; Jafarpour, Saber; Bullo, Francesco

doi:10.1109/tac.2018.2844120

Cited by 28 publications

(20 citation statements)

References 25 publications

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“…This chain can be computed for a directed graph with unitary weights via solving a convex program. Further, if the graph is undirected, the MaxEntropyRate chain can be computed efficiently using the method in [13]; (iii) the Markov chain that minimizes the (weighted) Kemeny constant, abbreviated as the MinKemeny chain.…”

Section: Numerical Resultsmentioning

confidence: 99%

Markov Chains With Maximum Return Time Entropy for Robotic Surveillance

Duan

George

Bullo

2020

IEEE Trans. Automat. Contr.

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Motivated by robotic surveillance applications, this paper studies the novel problem of maximizing the return time entropy of a Markov chain, subject to a graph topology with travel times and stationary distribution. The return time entropy is the weighted average, over all graph nodes, of the entropy of the first return times of the Markov chain; this objective function is a function series that does not admit in general a closed form.The paper features theoretical and computational contributions. First, we obtain a discrete-time delayed linear system for the return time probability distribution and establish its convergence properties. We show that the objective function is continuous over a compact set and therefore admits a global maximum; a unique globally-optimal solution is known only for complete graphs with unitary travel times. We then establish upper and lower bounds between the return time entropy and the well-known entropy rate of the Markov chain. To compute the optimal Markov chain numerically, we establish the asymptotic equality between entropy, conditional entropy and truncated entropy, and propose an iteration to compute the gradient of the truncated entropy. Finally, we apply these results to the robotic surveillance problem. Our numerical results show that, for a model of rational intruder over prototypical graph topologies and test cases, the maximum return time entropy chain performs better than several existing Markov chains. arXiv:1803.07705v2 [math.OC]

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Section: Numerical Resultsmentioning

confidence: 99%

Markov Chains With Maximum Return Time Entropy for Robotic Surveillance

Duan

George

Bullo

2020

IEEE Trans. Automat. Contr.

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“…Stochastic vehicle routing strategies have the desirable property that an intruder cannot predictably plan a path to avoid surveillance agents. The authors in [25], [16], [14] use Markov chains to design surveillance strategies. A novel convex optimization formulation is used to design strategies with minimum mean hitting time in [25].…”

Section: B Literature Reviewmentioning

confidence: 99%

Robotic Surveillance Based on the Meeting Time of Random Walks

Duan¹,

George²,

Patel³

et al. 2019

Preprint

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This paper analyzes the meeting time between a pair of pursuer and evader performing random walks on digraphs. The existing bounds on the meeting time usually work only for certain classes of walks and cannot be used to formulate optimization problems and design robotic strategies. First, by analyzing multiple random walks on a common graph as a single random walk on the Kronecker product graph, we provide the first closed-form expression for the expected meeting time in terms of the transition matrices of the moving agents. This novel expression leads to necessary and sufficient conditions for the meeting time to be finite and to insightful graph-theoretic interpretations. Second, based on the closedform expression, we setup and study the minimization problem for the expected capture time for a pursuer/evader pair. We report theoretical and numerical results on basic case studies to show the effectiveness of the design.

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“…Markov jump system (MJS), as a special member of hybrid systems, has attracted extensive research attention owing to its powerful depiction of practical systems with abrupt changing parameters or characteristics. Typical applications have been reported in the literatures, such as biological systems [1], [2], economic systems [3], [4], robotic systems [5], [6] and so on [7]- [10]. As such, A great number of fundamental stability, filtering and synchronization problems of MJS have been solved with remarkable results [11]- [13].…”

Section: Introductionmentioning

confidence: 99%

Mode-Dependent Event-Triggered Fault Detection for Nonlinear Semi-Markov Jump Systems With Quantization: Application to Robotic Manipulator

Wang

2021

IEEE Access

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This paper is studied with fault detection issue for nonlinear semi-Markov jump systems. In particular, the mode-dependent mechanism of event-triggered transmission is developed for improving communication efficiency. Furthermore, the mode-dependent quantization method is utilized to cope with the limited network bandwidth. These strategies are chosen for more effective utilization of system mode information with less conservatism. Mode-dependent filter type fault detectors are constructed and sufficient conditions are established by Lyapunov-Krasovskii functionals, such that the filter error system can achieve the desired dissipative performance. In the end, the designed fault detection method is verified through a practical example of robotic manipulator.INDEX TERMS Mode-dependent quantization, mode-dependent event-triggered, fault detection, semi-Markov jump system, robotic manipulator.

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Markov Chains With Maximum Entropy for Robotic Surveillance

Cited by 28 publications

References 25 publications

Markov Chains With Maximum Return Time Entropy for Robotic Surveillance

Markov Chains With Maximum Return Time Entropy for Robotic Surveillance

Robotic Surveillance Based on the Meeting Time of Random Walks

Mode-Dependent Event-Triggered Fault Detection for Nonlinear Semi-Markov Jump Systems With Quantization: Application to Robotic Manipulator

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