arXiv subjects

Shaunak D. Bopardikar

Publications and source records attributed to Shaunak D. Bopardikar.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Hiding with Partial Information of the Seeker's Route

We consider a hide-and-seek game between a Hider and a Seeker over a finite set of locations. The Hider chooses one location to conceal a stationary treasure, while the Seeker visits the locations sequentially along a route. As the search progresses, the Hider observes a prefix of the Seeker's route. After observing this information, the Hider has the option to relocate the treasure at most once to another unvisited location by paying a switching cost. We study two seeker models. In the first, the Seeker is unaware of the fact that the Hider can relocate. In the second, the Seeker select its route while accounting for the possibility that the Hider observes its path and reallocates. For the restricted case, we define the value-of-information created by the reveal and derive upper bounds in terms of the switching cost using a worst-case evaluation over routes. We also show that seeker awareness reduces the game value, with the difference between the restricted and feedback models bounded by the entry-wise gap between the corresponding payoff matrices. Numerical examples show how this benefit decreases as the switching cost increases and as the reveal occurs later along the route.

eess.SY↗

arXiv2026

Games Over Observation Spaces in Multi-Agent Capture the Flag

We consider a multi-agent Capture the Flag (CtF) scenario in a graph-based environment, where a team of attackers seeks to reach designated flag vertices while a defending team attempts to intercept them. In our setting, both teams operate using decentralized heuristic policies. While the attacking team may choose its heuristic from a diverse library of policies, the defense is restricted to playing a single fixed policy. To overcome this limitation, a centralized defense oracle strategically restricts the portion of the graph visible to each of its agents in order to elicit a wider range of emergent behaviors from its fixed policy. We formalize this interaction as a two-player zero-sum game, where the attacker reasons over its library of heuristics and the defense reasons over the combinatorial space of visibility profiles. To solve this intractably large game, we propose a Double Oracle algorithm to find approximate empirical equilibria, and we empirically validate that observation manipulation can improve the defense's performance.

cs.GT↗

arXiv2026

Encirclement Guaranteed Finite-Time Capture against Unknown Evader Strategies

We consider a pursuit-evasion scenario involving a group of pursuers and a single evader in a two-dimensional unbounded environment. The pursuers aim to capture the evader in finite time while ensuring the evader remains enclosed within the convex hull of their positions until capture, without knowledge of the evader's heading angle. Prior works have addressed the problem of encirclement and capture separately in different contexts. In this paper, we present a class of strategies for the pursuers that guarantee capture in finite time while maintaining encirclement, irrespective of the evader's strategy. Furthermore, we derive an upper bound on the time to capture. Numerical results highlight the effectiveness of the proposed framework against a range of evader strategies.

eess.SY↗

arXiv2025

Vector Cost Behavioral Planning for Autonomous Robotic Systems with Contemporary Validation Strategies

The vector cost bimatrix game is a method for multi-objective decision making that enables autonomous robotic systems to optimize for multiple goals at once while avoiding worst-case scenarios in neglected objectives. We expand this approach to arbitrary numbers of objectives and compare its performance to scalar weighted sum methods during competitive motion planning. Explainable Artificial Intelligence (XAI) software is used to aid in the analysis of high dimensional decision-making data. State-space Exploration of Multidimensional Boundaries using Adherence Strategies (SEMBAS) is applied to explore performance modes in the parameter space as a sensitivity study for the baseline and proposed frameworks. While some works have explored aspects of game theoretic planning and intelligent systems validation separately, we combine each of these into a novel and comprehensive simulation pipeline. This integration demonstrates a dramatic improvement of the vector cost method over scalarization and offers an interpretable and generalizable framework for robotic behavioral planning. Code available at https://github.com/toazbenj/race_simulation. The video companion to this work is available at https://tinyurl.com/vectorcostvideo.

cs.RO↗

arXiv2025

FlipDyn with Control: Resource Takeover Games with Dynamics

We introduce FlipDyn with control, a finite-horizon zero-sum resource takeover game, where a defender and an adversary decide when to takeover and how to control a common resource. At each discrete-time step, the players can take over or retain control, incurring state and control-dependent costs. The system is modeled as a hybrid dynamical system, with a discrete \texttt{FlipDyn} state determining control authority. Our contributions are: (i) For arbitrary non-negative costs, we derive the saddle-point value of the \texttt{FlipDyn} game and the corresponding Nash equilibria (NE) takeover strategies. (ii) For linear dynamical systems with quadratic costs, we establish sufficient conditions under which the game admits an NE. (iii) For scalar linear dynamical systems with quadratic costs, we derive parameterized NE takeover strategies and saddle-point values independent of the continuous state. (iv) For higher-dimensional linear dynamical systems with quadratic costs, we derive approximate NE takeover strategies and control policies, and compute bounds on the saddle-point values. We validate our results through a numerical study on adversarial control of a linear system.

eess.SY↗

arXiv2025

Mutual Support by Sensor-Attacker Team for a Passive Target

We introduce a pursuit game played between a team of a sensor and an attacker and a mobile target in the unbounded Euclidean plane. The target is faster than the sensor, but slower than the attacker. The sensor's objective is to keep the target within a sensing radius so that the attacker can capture the target, whereas the target seeks to escape by reaching beyond the sensing radius from the sensor without getting captured by the attacker. We assume that as long as the target is within the sensing radius from the sensor, the sensor-attacker team is able to measure the target's instantaneous position and velocity. We pose and solve this problem as a \emph{game of kind} in which the target uses an open-loop strategy (passive target). Aside from the novel formulation, our contributions are four-fold. First, we present optimal strategies for both the sensor and the attacker, according to their respective objectives. Specifically, we design a sensor strategy that maximizes the duration for which the target remains within its sensing range, while the attacker uses proportional navigation to capture the target. Second, we characterize the \emph{sensable region} -- the region in the plane in which the target remains within the sensing radius of the sensor during the game -- and show that capture is guaranteed {if and only if} the Apollonius circle between the attacker and the target is fully contained within this region. Third, we {derive a lower bound} on the target's speed below which capture is guaranteed, and an upper bound on the target speed above which there exists an escape strategy for the target, from an arbitrary initial orientation between the agents. Fourth, for a given initial orientation between the agents, we present a sharper upper bound on the target speed above which there exists an escape strategy for the target.

eess.SY↗

arXiv2025

Deception in Asymmetric Information Homicidal Chauffeur Game

The classic Homicidal Chauffeur game is a pursuit-evasion game played in an unbounded planar environment between a pursuer constrained to move with fixed speed on curves with bounded curvature, and a slower evader with fixed speed but with simple kinematics. We introduce a new variant of this game with asymmetric information in which the evader has the ability to choose its speed among a finite set of choices that is unknown to the pursuer a priori. Therefore the pursuer is required to estimate the evader's maximum speed based on the observations so far. This formulation leads to the question of whether the evader can exploit this asymmetry by moving deceptively by first picking a slower speed to move with and then switching to a faster speed when a specified relative configuration is attained to increase the capture time as compared to moving with the maximum speed at all times. Our contributions are as follows. First, we derive optimal feedback Nash equilibrium strategies for the complete information case of this game in which the evader is allowed to vary its speed in a given interval. Second, for the version with asymmetric information, we characterize regions of initial player locations in the game space from which the evader does not have any advantage in using deceptive strategies. Finally, we provide numerical evidence of regions in the game space from which the evader can increase the capture time by moving deceptively.

eess.SY↗

arXiv2025

Vector Cost Bimatrix Games with Applications to Autonomous Racing

We formulate a vector cost alternative to the scalarization method for weighting and combining multi-objective costs. The algorithm produces solutions to bimatrix games that are simultaneously pure, unique Nash equilibria and Pareto optimal with guarantees for avoiding worst case outcomes. We achieve this by enforcing exact potential game constraints to guide cost adjustments towards equilibrium, while minimizing the deviation from the original cost structure. The magnitude of this adjustment serves as a metric for differentiating between Pareto optimal solutions. We implement this approach in a racing competition between agents with heterogeneous cost structures, resulting in fewer collision incidents with a minimal decrease in performance. Code is available at https://github.com/toazbenj/race_simulation.

cs.GT↗

arXiv2025

Competitive Perimeter Defense in Tree Environments

We consider a perimeter defense problem in a rooted full tree graph environment in which a single defending vehicle seeks to defend a set of specified vertices, termed as the perimeter from mobile intruders that enter the environment through the tree's leaves. We adopt the technique of competitive analysis to characterize the performance of an online algorithm for the defending vehicle. We first derive fundamental limits on the performance of any online algorithm relative to that of an optimal offline algorithm. Specifically, we give three fundamental conditions for finite, 2, and 3/2 competitive ratios in terms of the environment parameters. We then design and analyze three classes of online algorithms that have provably finite competitiveness under varying environmental parameter regimes. Finally, we give a numerical visualization of these regimes to better show the comparative strengths and weaknesses of each algorithm.

eess.SY↗

arXiv2024

FlipDyn in Graphs: Resource Takeover Games in Graphs

We present \texttt{FlipDyn-G}, a dynamic game model extending the \texttt{FlipDyn} framework to a graph-based setting, where each node represents a dynamical system. This model captures the interactions between a defender and an adversary who strategically take over nodes in a graph to minimize (resp. maximize) a finite horizon additive cost. At any time, the \texttt{FlipDyn} state is represented as the current node, and each player can transition the \texttt{FlipDyn} state to a depending based on the connectivity from the current node. Such transitions are driven by the node dynamics, state, and node-dependent costs. This model results in a hybrid dynamical system where the discrete state (\texttt{FlipDyn} state) governs the continuous state evolution and the corresponding state cost. Our objective is to compute the Nash equilibrium of this finite horizon zero-sum game on a graph. Our contributions are two-fold. First, we model and characterize the \texttt{FlipDyn-G} game for general dynamical systems, along with the corresponding Nash equilibrium (NE) takeover strategies. Second, for scalar linear discrete-time dynamical systems with quadratic costs, we derive the NE takeover strategies and saddle-point values independent of the continuous state of the system. Additionally, for a finite state birth-death Markov chain (represented as a graph) under scalar linear dynamical systems, we derive analytical expressions for the NE takeover strategies and saddle-point values. We illustrate our findings through numerical studies involving epidemic models and linear dynamical systems with adversarial interactions.

cs.GT↗

arXiv2024

Game Theory in Distributed Systems Security: Foundations, Challenges, and Future Directions

Many of our critical infrastructure systems and personal computing systems have a distributed computing systems structure. The incentives to attack them have been growing rapidly as has their attack surface due to increasing levels of connectedness. Therefore, we feel it is time to bring in rigorous reasoning to secure such systems. The distributed system security and the game theory technical communities can come together to effectively address this challenge. In this article, we lay out the foundations from each that we can build upon to achieve our goals. Next, we describe a set of research challenges for the community, organized into three categories -- analytical, systems, and integration challenges, each with "short term" time horizon (2-3 years) and "long term" (5-10 years) items. This article was conceived of through a community discussion at the 2022 NSF SaTC PI meeting.

cs.CR↗

arXiv2024

Shortest Trajectory of a Dubins Vehicle with a Controllable Laser

We formulate a novel planar motion planning problem for a Dubins-Laser system that consists of a Dubins vehicle with an attached controllable laser. The vehicle moves with unit speed and the laser, having a finite range, can rotate in a clockwise or anti-clockwise direction with a bounded angular rate. From an arbitrary initial position and orientation, the objective is to steer the system so that a given static target is within the range of the laser and the laser is oriented at it in minimum time. We characterize multiple properties of the optimal trajectory and establish that the optimal trajectory for the Dubins-laser system is one out of a total of 16 candidates. Finally, we provide numerical insights that illustrate the properties characterized in this work.

eess.SY↗

arXiv2024

Matrix Concentration Inequalities for Sensor Selection

In this work, we address the problem of sensor selection for state estimation via Kalman filtering. We consider a linear time-invariant (LTI) dynamical system subject to process and measurement noise, where the sensors we use to perform state estimation are randomly drawn according to a sampling with replacement policy. Since our selection of sensors is randomly chosen, the estimation error covariance of the Kalman filter is also a stochastic quantity. Fortunately, concentration inequalities (CIs) for the estimation error covariance allow us to gauge the estimation performance we intend to achieve when our sensors are randomly drawn with replacement. To obtain a non-trivial improvement on existing CIs for the estimation error covariance, we first present novel matrix CIs for a sum of independent and identically-distributed (i.i.d.) and positive semi-definite (p.s.d.) random matrices, whose support is finite. Next, we show that our guarantees generalize an existing matrix CI. Also, we show that our generalized guarantees require significantly fewer number of sampled sensors to be applicable. Lastly, we show through a numerical study that our guarantees significantly outperform existing ones in terms of their ability to bound (in the semi-definite sense) the steady-state estimation error covariance of the Kalman filter.

eess.SY↗

arXiv2023

On Multi-Fidelity Impedance Tuning for Human-Robot Cooperative Manipulation

We examine how a human-robot interaction (HRI) system may be designed when input-output data from previous experiments are available. In particular, we consider how to select an optimal impedance in the assistance design for a cooperative manipulation task with a new operator. Due to the variability between individuals, the design parameters that best suit one operator of the robot may not be the best parameters for another one. However, by incorporating historical data using a linear auto-regressive (AR-1) Gaussian process, the search for a new operator's optimal parameters can be accelerated. We lay out a framework for optimizing the human-robot cooperative manipulation that only requires input-output data. We establish how the AR-1 model improves the bound on the regret and numerically simulate a human-robot cooperative manipulation task to show the regret improvement. Further, we show how our approach's input-output nature provides robustness against modeling error through an additional numerical study.

cs.RO↗

arXiv2023

A Multi-Fidelity Bayesian Approach to Safe Controller Design

Safely controlling unknown dynamical systems is one of the biggest challenges in the field of control. Oftentimes, an approximate model of a system's dynamics exists which provides beneficial information for the selection of controls. However, differences between the approximate and true systems present challenges as well as safety concerns. We propose an algorithm called SAFE-SLOPE to safely evaluate points from a Gaussian process model of a function when its Lipschitz constant is unknown. We establish theoretical guarantees for the performance of SAFE-SLOPE and quantify how multi-fidelity modeling improves the algorithm's performance. Finally, we demonstrate how SAFE-SLOPE achieves lower cumulative regret than a naive sampling method by applying it to find the control gains of a linear time-invariant system.

eess.SY↗

arXiv2023

A Concentration-Based Approach for Optimizing the Estimation Performance in Stochastic Sensor Selection

In this work, we consider a sensor selection drawn at random by a sampling with replacement policy for a linear time-invariant dynamical system subject to process and measurement noise. We employ the Kalman filter to estimate the state of the system. However, the statistical properties of the filter are not deterministic due to the stochastic selection of sensors. As a consequence, we derive concentration inequalities to bound the estimation error covariance of the Kalman filter in the semi-definite sense. Concentration inequalities provide a framework for deriving semi-definite bounds that hold in a probabilistic sense. Our main contributions are three-fold. First, we develop algorithmic tools to aid in the implementation of a matrix concentration inequality. Second, we derive concentration-based bounds for three types of stochastic selections. Third, we propose a polynomial-time procedure for finding a sampling distribution that indirectly minimizes the maximum eigenvalue of the estimation error covariance. Our proposed sampling policy is also shown to empirically outperform three other sampling policies: uniform, deterministic greedy, and randomized greedy.

eess.SY↗

arXiv2023

Perimeter Defense using a Turret with Finite Range and Service Times

We consider a perimeter defense problem in a planar conical environment comprising a single turret that has a finite range and non-zero service time. The turret seeks to defend a concentric perimeter against $N\geq 2$ intruders. Upon release, each intruder moves radially towards the perimeter with a fixed speed. To capture an intruder, the turret's angle must be aligned with that of the intruder's angle and must spend a specified service time at that orientation. We address offline and online versions of this optimization problem. Specifically, in the offline version, we establish that in general parameter regimes, this problem is equivalent to solving a Travelling Repairperson Problem with Time Windows (TRP-TW). We then identify specific parameter regimes in which there is a polynomial time algorithm that maximizes the number of intruders captured. In the online version, we present a competitive analysis technique in which we establish a fundamental guarantee on the existence of at best $(N-1)$-competitive algorithms. We also design two online algorithms that are provably $1$ and $2$-competitive in specific parameter regimes.

eess.SY↗

arXiv2022

FlipDyn: A game of resource takeovers in dynamical systems

We introduce a game in which two players with opposing objectives seek to repeatedly takeover a common resource. The resource is modeled as a discrete time dynamical system over which a player can gain control after spending a state-dependent amount of energy at each time step. We use a FlipIT-inspired deterministic model that decides which player is in control at every time step. A player's policy is the probability with which the player should spend energy to gain control at each time step. Our main results are three-fold. First, we present analytic expressions for the cost-to-go as a function of the hybrid state of the system, i.e., the physical state of the dynamical system and the binary \texttt{FlipDyn} state for any general system with arbitrary costs. These expressions are exact when the physical state is also discrete and has finite cardinality. Second, for a continuous physical state with linear dynamics and quadratic costs, we derive expressions for Nash equilibrium (NE). For scalar physical states, we show that the NE depends only on the parameters of the value function and costs, and is independent of the state. Third, we derive an approximate value function for higher dimensional linear systems with quadratic costs. Finally, we illustrate our results through a numerical study on the problem of controlling a linear system in a given environment in the presence of an adversary.

cs.GT↗