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Hide-and-Seek with Directional Sensing *

IFAC Proceedings Volumes 2011年第1期44卷 9343-9348页

作者： Alessandro Borri Shaunak D. Bopardikar Joao P. Hespanha Maria D. Di Benedetto Department of Electrical Engineering University of L'Aquila Italy Center for Control Dynamical Systems and Computation University of California at Santa Barbara CA 93106 USA

Abstract We consider a game played between a hider, who hides a static object in one of several possible positions in a bounded planar region, and a searcher, who wishes to reach the object by querying sensors placed in the plane. The searcher is a mobile agent, and whenever it physically visits a sensor, the sensor returns a random direction, corresponding to a half-plane in which the hidden object is located. We first present a novel search heuristic and characterize bounds on the expected distance covered before reaching the object. Next, we model this game as a large-dimensional zero-sum dynamic game and we apply a recently introduced randomized sampling technique that provides a probabilistic level of security to the hider. We observe that, when the randomized sampling approach is only allowed to select a very small number of samples, the cost of the heuristic is comparable to the security level provided by the randomized procedure. However, as we allow the number of samples to increase, the randomized procedure provides a higher probabilistic security level.

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Sampling-based roadmap methods for a visual reconnaissance UAV

Sampling-based roadmap methods for a visual reconnaissance U...

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AIAA Guidance, Navigation, and control Conference

作者： Obermeyer, Karl J. Oberlin, Paul Darbha, Swaroop University of California at Santa Barbara Santa Barbara CA 93106 United States Texas A and M University College Station TX 77843 United States Center for Control Dynamical Systems and Computation United States Department of Mechanical Engineering United States

ISBN: (纸本)9781600869624

This article considers a path planning problem for a single fixed-wing aircraft performing a reconnaissance mission using EO (Electro-Optical) camera(s). A mathematical formulation of the general aircraft visual reconnaissance problem for static ground targets in terrain is given and it is shown, under simplifying assumptions, that it can be reduced to what we call the PVDTSP (Polygon-Visiting Dubins Traveling Salesman Problem), a variation of the famous TSP (Traveling Salesman Problem). Two algorithms are developed to solve the PVDTSP. They fall into the class of algorithms known as sampling-based roadmap methods because they operate by sampling a finite set of points from a continuous state space in order to reduce a continuous motion planning problem to planning on a finite discrete graph. The first method is resolution complete, which means it provably converges to a nonisolated global optimum as the number of samples grows. The second method achieves slightly shorter computation times by using approximate dynamic programming, but consequently is only guaranteed to converge to a nonisolated global optimum modulo target order. Numerical experiments indicate that, for up to about 20 targets, both methods deliver good solutions suitably quickly for online purposes. Additionally, both algorithms allow trade-off of computation time for solution quality and are shown extensible to handle wind, airspace constraints, any vehicle dynamics, and open-path (vs. closed-tour) problems. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

关键词： Unmanned aerial vehicles (UAV)

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control under Clock Offsets and Actuator Saturation

Control under Clock Offsets and Actuator Saturation

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IEEE Annual Conference on Decision and control

作者： Masashi Wakaiki Kunihisa Okano Joao P. Hespanha Center for Control Dynamical-systems and Computation (CCDC) University of California Santa Barbara CA 93106-9560 USA

ISBN: (纸本)9781479978878

This paper studies the stability analysis and the stabilization problem for systems with asynchronous sensors and controllers, and actuators subject to saturation. We consider systems with parameter uncertainties caused by clock offsets. By using a polytopic overapproximation, we investigate how large clock offsets affect stability. In addition, we employ a sector characterization approach to address actuator saturation. We see from a numerical study that the range of allowable clock offset bounds drops if the saturation limit becomes smaller than a certain value.

关键词： clock skew parameter uncertainty actuators Timing devices offsets Saturated Stability analysis Standing Orders controllers

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Exponential Stability of Parametric Optimization-Based controllers via Lur’e Contractivity

arXiv

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arXiv 2024年

作者： Davydov, Alexander Bullo, Francesco The Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106 United States

In this letter, we investigate sufficient conditions for the exponential stability of LTI systems driven by controllers derived from parametric optimization problems. Our primary focus is on parametric projection controllers, namely parametric programs whose objective function is the squared distance to a nominal controller. Leveraging the virtual system method of analysis and a novel contractivity result for Lur’e systems, we establish a sufficient LMI condition for the exponential stability of an LTI system with a parametric projection-based controller. Separately, we prove additional results for single-integrator systems. Finally, we apply our results to state-dependent saturated control systems and control barrier function-based control and provide numerical simulations. Copyright © 2024, The Authors. All rights reserved.

关键词： controllers

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When showing your hand pays off: Announcing strategic intentions in Colonel Blotto games

arXiv

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arXiv 2020年

作者： Chandan, Rahul Paarporn, Keith Marden, Jason R. Department of Electrical and Computer Engineering Center of Control Dynamical Systems and Computation UC SantaBarbara United States

— In competitive adversarial environments, it is often advantageous to obfuscate one’s strategies or capabilities. However, revealing one’s strategic intentions may shift the dynamics of the competition in complex ways. Can it ever be advantageous to reveal strategic intentions to an opponent? In this paper, we consider three-stage Colonel Blotto games in which one player can choose whether or not to pre-commit resources to a single battlefield before play begins. This pre-commitment is public knowledge. In response, the opponent can either secure the battlefield by matching the pre-commitment with its own forces, or withdraw. In a two-player setting, we show that a weaker player never has an incentive to pre-commit any amount of resources to a battlefield regardless of how valuable it is. We then consider a three-player setting in which two players fight against a common adversary on separate fronts. Only one of the two players facing the adversary has the option of pre-committing. We find there are instances where this player benefits from pre-committing. The analysis indicates that under non-cooperative team settings and no possibility of forming alliances, there can be incentives to publicly announce one’s strategic intentions to an adversary. Copyright © 2020, The Authors. All rights reserved.

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Target assignment for robotic networks: Asymptotic performance under limited communication

Target assignment for robotic networks: Asymptotic performan...

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American control Conference (ACC)

作者： Stephen L. Smith Francesco Bullo Department of Mechanical Engineering Center for Control Dynamical Systems and Computation University of California Santa Barbara CA USA

We are given an equal number of mobile robotic agents, and distinct target locations. Each agent has simple integrator dynamics, a limited communication range, and knowledge of the position of every target. We address the problem of designing a distributed algorithm that allows the group of agents to divide the targets among themselves and, simultaneously, leads each agent to reach its unique target. We do not require connectivity of the communication graph at any time. We introduce a novel assignment-based algorithm with the following features: initial assignments and robot motions follow a greedy rule, and distributed refinements of the assignment exploit an implicit circular ordering of the targets. We prove correctness of the algorithm, and give worst-case asymptotic bounds on the time to complete the assignment as the environment grows with the number of agents. We show that among a certain class of distributed algorithms, our algorithm is asymptotically optimal. The analysis utilizes results on the Euclidean traveling salesperson problem.

关键词： Mobile communication Distributed algorithms Mobile robots Communication system control Algorithm design and analysis Polynomials Concurrent computing Approximation algorithms Robot kinematics Cost function

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L2-induced gain analysis of switched linear systems via finitely parametrized storage functions

L2-induced gain analysis of switched linear systems via fini...

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作者： Hirata, Kenji Hespanha, João P. Department of Mechanical Engineering Nagaoka University of Technology Nagaoka 940 2188 Japan Department of Electrical and Computer Engineering Center for Control Dynamical Systemsand Computation University of California Santa Barbara CA 93106 United States

ISBN: (纸本)9781424474264

This paper addresses the computation of the L2-induced gain for switched linear systems. The main contribution of the paper is to completely characterize the induced gain of a switched system though a differential inequalities on a finitely parametrized common storage function, one equation for each system being switched. The motivation for computing the induced gain of a switched system is the application of robust stability tools to the analysis of hybrid systems. © 2010 AACC.

关键词： Hybrid systems

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Dynamic Vehicle Routing with Moving Demands - Part II: High speed demands or low arrival rates

Dynamic Vehicle Routing with Moving Demands - Part II: High ...

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2009 American control Conference (ACC 2009)

作者： Stephen L. Smith Shaunak D. Bopardikar Francesco Bullo Joao P. Hespanha Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara CA 93106 USA

ISBN: (纸本)9781424445233

In the companion paper we introduced a vehicle routing problem in which service demands arrive stochastically on a line segment. Upon arrival, the demands translate perpendicular to the line with a fixed speed. A vehicle, with speed greater than that of the demands, seeks to provide service by reaching each mobile demand. In this paper we study a first-come-first-served (FCFS) policy in which the service vehicle serves demands in the order in which they arrive. When the demand arrival rate is very low, we show that the FCFS policy can be used to minimize the expected time, or the worst-case time, to service a demand. We determine necessary and sufficient conditions on the arrival rate of the demands (as a function of the problem parameters) for the stability of the FCFS policy. When the demands are much slower than the service vehicle, the necessary and sufficient conditions become equal. We also show that in the limiting regime when the demands move nearly as fast as the service vehicle;(i) the demand arrival rate must tend to zero;(ii) every stabilizing policy must service the demands in the order in which they arrive, and;(iii) the FCFS policy minimizes the expected time to service a demand.

关键词： arrival rate Vehicle routing Policies demand service Line sections Sufficient conditions High speed

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Direct Numerical Solution of Algebraic Lyapunov Equations For Large-Scale systems Using Quantized Tensor Trains

Direct Numerical Solution of Algebraic Lyapunov Equations Fo...

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IEEE Annual Conference on Decision and control

作者： Michael Nip Joao P. Hespanha Mustafa Khammash Center for Control Dynamical Systems and Computation University of California Santa Barbara California USA 93106 Center for Control Dynamical Systems and Computation University of California Santa Barbara California USA 93106 Department of Biosystems Science and Engineering ETH-Zurich 4058 Basel Switzerland

ISBN: (纸本)9781467357159

We present a novel method for solving high-dimensional algebraic Lyapunov equations exploiting the recently proposed Quantized Tensor Train (QTT) numerical linear algebra. A key feature of the approach is that given a prescribed error tolerance, it automatically calculates the optimal lowest rank approximation of the solution in the Frobenius norm. The low rank nature of the approximation potentially enables a sublinear scaling of the computational complexity with the number of states of the dynamical system. The resulting solutions appear in a new matrix tensor format which we call the Vectorized-QTT-Matrix format. We show the effectiveness of our method by calculating the controllability Gramians for discretized reaction-diffusion equations. We introduce an algorithm for the new tensor format of the solution for calculating the matrix-by-vector product and combine it with the celebrated Lanczos algorithm to compute the dominant eigenvalues/eigenvectors of the matrix.

关键词： large-scale systems Tensor TRAIN Algebra NUMERICAL SOLUTION

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On Opinion Dynamics in Heterogeneous Networks

On Opinion Dynamics in Heterogeneous Networks

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2011 American control Conference (ACC)

作者： Anahita Mirtabatabaei Francesco Bullo Center for Control Dynamical Systems and Computation University of California슠Santa Barbara Santa Barbara CA USA

This paper studies the opinion dynamics model recently introduced by Hegselmann and Krause: each agent in a group maintains a real number describing its opinion;and each agent updates its opinion by averaging all other opinions that are within some given confidence range. The confidence ranges are distinct for each agent. This heterogeneity and state-dependent topology leads to poorly-understood complex dynamic behavior. We classify the agents via their interconnection topology and, accordingly, compute the equilibria of the system. We conjecture that any trajectory of this model eventually converges to a steady state under fixed topology. To establish this conjecture, we derive two novel sufficient conditions: both conditions guarantee convergence and constant topology for infinite time, while one condition also guarantees monotonicity of the convergence. In the evolution under fixed topology for infinite time, we define leader groups that determine the followers' rate and direction of convergence.

关键词： Convergence Topology Trajectory Network topology computational modeling Steady-state Mathematical model

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