arXiv subjects

Vaibhav Katewa

Publications and source records attributed to Vaibhav Katewa.

18 recordsLinked to original sources

arXiv2026

Multi-Sensor Alignment for Weather Simulations

Perception tasks for autonomous vehicles need to work satisfactorily in adverse weather conditions. Due to lack of real-world weather datasets, weather simulations are a promising alternative. To ensure simulations closely mirror real-world weather data, it's crucial that they represent the same weather characteristics, including severity and particle positioning, across different sensors. To achieve this, we propose the Reference Dataset Alignment Method (ReDAM) for weather intensity alignment in fog and Unified-weather-edit (inspired by Weather-edit[1]) for particle positioning alignment in rain and snow. We validate both alignment methods using statistical and geometrical tests, respectively. We find that 3D detection models for non-aligned versions tend to be overly optimistic as compared to aligned versions. We also show the aligned-multi-sensor simulation's effectiveness for achieving robustness for 3D object detection task by finetuning existing sensor fusion models on it.

cs.AI↗

arXiv2025

Exploiting Adjacent Similarity in Multi-Armed Bandit Tasks via Transfer of Reward Samples

We consider a sequential multi-task problem, where each task is modeled as the stochastic multi-armed bandit with K arms. We assume the bandit tasks are adjacently similar in the sense that the difference between the mean rewards of the arms for any two consecutive tasks is bounded by a parameter. We propose two algorithms (one assumes the parameter is known while the other does not) based on UCB to transfer reward samples from preceding tasks to improve the overall regret across all tasks. Our analysis shows that transferring samples reduces the regret as compared to the case of no transfer. We provide empirical results for our algorithms, which show performance improvement over the standard UCB algorithm without transfer and a naive transfer algorithm.

cs.LG↗

arXiv2024

Transfer in Sequential Multi-armed Bandits via Reward Samples

We consider a sequential stochastic multi-armed bandit problem where the agent interacts with bandit over multiple episodes. The reward distribution of the arms remain constant throughout an episode but can change over different episodes. We propose an algorithm based on UCB to transfer the reward samples from the previous episodes and improve the cumulative regret performance over all the episodes. We provide regret analysis and empirical results for our algorithm, which show significant improvement over the standard UCB algorithm without transfer.

cs.LG↗

arXiv2024

Approximate Stability Radius Analysis and Design in Linear Systems

The robustness of the stability properties of dynamical systems in the presence of unknown/adversarial perturbations to system parameters is a desirable property. In this paper, we present methods to efficiently compute and improve the approximate stability radius of linear time-invariant systems. We propose two methods to derive closed-form expressions of approximate stability radius, and use these to re-design the system matrix to increase the stability radius. Our numerical studies show that the approximations work well and are able to improve the robustness of the stability of the system.

eess.SY↗

arXiv2023

Control Barrier Functions in UGVs for Kinematic Obstacle Avoidance: A Collision Cone Approach

In this paper, we propose a new class of Control Barrier Functions (CBFs) for Unmanned Ground Vehicles (UGVs) that help avoid collisions with kinematic (non-zero velocity) obstacles. While the current forms of CBFs have been successful in guaranteeing safety/collision avoidance with static obstacles, extensions for the dynamic case have seen limited success. Moreover, with the UGV models like the unicycle or the bicycle, applications of existing CBFs have been conservative in terms of control, i.e., steering/thrust control has not been possible under certain scenarios. Drawing inspiration from the classical use of collision cones for obstacle avoidance in trajectory planning, we introduce its novel CBF formulation with theoretical guarantees on safety for both the unicycle and bicycle models. The main idea is to ensure that the velocity of the obstacle w.r.t. the vehicle is always pointing away from the vehicle. Accordingly, we construct a constraint that ensures that the velocity vector always avoids a cone of vectors pointing at the vehicle. The efficacy of this new control methodology is later verified by Pybullet simulations on TurtleBot3 and F1Tenth.

cs.RO↗

arXiv2023

Minimum-norm Sparse Perturbations for Opacity in Linear Systems

Opacity is a notion that describes an eavesdropper's inability to estimate a system's 'secret' states by observing the system's outputs. In this paper, we propose algorithms to compute the minimum sparse perturbation to be added to a system to make its initial states opaque. For these perturbations, we consider two sparsity constraints - structured and affine. We develop an algorithm to compute the global minimum-norm perturbation for the structured case. For the affine case, we use the global minimum solution of the structured case as initial point to compute a local minimum. Empirically, this local minimum is very close to the global minimum. We demonstrate our results via a running example.

eess.SY↗

arXiv2022

Behavioral Feedback for Optimal LQG Control

In this work, we revisit the Linear Quadratic Gaussian (LQG) optimal control problem from a behavioral perspective. Motivated by the suitability of behavioral models for data-driven control, we begin with a reformulation of the LQG problem in the space of input-output behaviors and obtain a complete characterization of the optimal solutions. In particular, we show that the optimal LQG controller can be expressed as a static behavioral-feedback gain, thereby eliminating the need for dynamic state estimation characteristic of state space methods. The static form of the optimal LQG gain also makes it amenable to its computation by gradient descent, which we investigate via numerical experiments. Furthermore, we highlight the advantage of this approach in the data-driven control setting of learning the optimal LQG controller from expert demonstrations.

eess.SY↗

arXiv2022

On Connections between Opacity and Security in Linear Systems

Opacity and attack detectability are important properties for any system as they allow the states to remain private and malicious attacks to be detected, respectively. In this paper, we show that a fundamental trade-off exists between these properties for a linear dynamical system, in the sense that if an opaque system is subjected to attacks, all attacks cannot be detected. We first characterize the opacity conditions for the system in terms of its weakly unobservable subspace (WUS) and show that the number of opaque states is proportional to the size of the WUS. Further, we establish conditions under which increasing the opaque sets also increases the set of undetectable attacks. This highlights a fundamental trade-off between security and privacy. We demonstrate application of our results on a remotely controlled automotive system.

eess.SY↗

arXiv2021

Robust Adversarial Classification via Abstaining

In this work, we consider a binary classification problem and cast it into a binary hypothesis testing framework, where the observations can be perturbed by an adversary. To improve the adversarial robustness of a classifier, we include an abstain option, where the classifier abstains from making a decision when it has low confidence about the prediction. We propose metrics to quantify the nominal performance of a classifier with an abstain option and its robustness against adversarial perturbations. We show that there exist a tradeoff between the two metrics regardless of what method is used to choose the abstain region. Our results imply that the robustness of a classifier with an abstain option can only be improved at the expense of its nominal performance. Further, we provide necessary conditions to design the abstain region for a 1- dimensional binary classification problem. We validate our theoretical results on the MNIST dataset, where we numerically show that the tradeoff between performance and robustness also exist for the general multi-class classification problems.

cs.LG↗

arXiv2020

Network Theoretic Analysis of Maximum a Posteriori Detectors for Optimal Input Detection

This paper considers maximum-a-posteriori (MAP) and linear discriminant based MAP detectors to detect changes in the mean and covariance of a stochastic input, driving specific network nodes, using noisy measurements from sensors non-collocated with the input nodes. We explicitly characterize both detectors' performance in terms of the network edge weights and input and sensor nodes' location. In the asymptotic measurement regime, when the input and measurement noise are jointly Gaussian, we show that the detectors' performance can be studied using the input to output gain of the system's transfer function matrix. Using this result, we obtain conditions for which the detection performance associated with the sensors on a given network cut is better (or worse) than that of the sensors associated with the subnetwork induced by the cut and not containing the input nodes. Our results also provide structural insights into the sensor placement from a detection-theoretic viewpoint. We validate our theoretical findings via multiple numerical examples.

math.OC↗

arXiv2020

Minimum-gain Pole Placement with Sparse Static Feedback

The minimum-gain eigenvalue assignment/pole placement problem (MGEAP) is a classical problem in LTI systems with static state feedback. In this paper, we study the MGEAP when the state feedback has arbitrary sparsity constraints. We formulate the sparse MGEAP problem as an equality-constrained optimization problem and present an analytical characterization of its locally optimal solution in terms of eigenvector matrices of the closed loop system. This result is used to provide a geometric interpretation of the solution of the non-sparse MGEAP, thereby providing additional insights for this classical problem. Further, we develop an iterative projected gradient descent algorithm to obtain local solutions for the sparse MGEAP using a parametrization based on the Sylvester equation. We present a heuristic algorithm to compute the projections, which also provides a novel method to solve the sparse EAP. Also, a relaxed version of the sparse MGEAP is presented and an algorithm is developed to obtain approximately sparse local solutions to the MGEAP. Finally, numerical studies are presented to compare the properties of the algorithms, which suggest that the proposed projection algorithm converges in most cases.

math.OC↗

arXiv2020

On a Security vs Privacy Trade-off in Interconnected Dynamical Systems

We study a security problem for interconnected systems, where each subsystem aims to detect local attacks using local measurements and information exchanged with neighboring subsystems. The subsystems also wish to maintain the privacy of their states and, therefore, use privacy mechanisms that share limited or noisy information with other subsystems. We quantify the privacy level based on the estimation error of a subsystem's state and propose a novel framework to compare different mechanisms based on their privacy guarantees. We develop a local attack detection scheme without assuming the knowledge of the global dynamics, which uses local and shared information to detect attacks with provable guarantees. Additionally, we quantify a trade-off between security and privacy of the local subsystems. Interestingly, we show that, for some instances of the attack, the subsystems can achieve a better detection performance by being more private. We provide an explanation for this counter-intuitive behavior and illustrate our results through numerical examples.

eess.SY↗

arXiv2020

Accuracy Prevents Robustness in Perception-based Control

In this paper we prove the existence of a fundamental trade-off between accuracy and robustness in perception-based control, where control decisions rely solely on data-driven, and often incompletely trained, perception maps. In particular, we consider a control problem where the state of the system is estimated from measurements extracted from a high-dimensional sensor, such as a camera. We assume that a map between the camera's readings and the state of the system has been learned from a set of training data of finite size, from which the noise statistics are also estimated. We show that algorithms that maximize the estimation accuracy (as measured by the mean squared error) using the learned perception map tend to perform poorly in practice, where the sensor's statistics often differ from the learned ones. Conversely, increasing the variability and size of the training data leads to robust performance, however limiting the estimation accuracy, and thus the control performance, in nominal conditions. Ultimately, our work proves the existence and the implications of a fundamental trade-off between accuracy and robustness in perception-based control, which, more generally, affects a large class of machine learning and data-driven algorithms.

math.OC↗

arXiv2019

On the Robustness of Data-Driven Controllers for Linear Systems

This paper proposes a new framework and several results to quantify the performance of data-driven state-feedback controllers for linear systems against targeted perturbations of the training data. We focus on the case where subsets of the training data are randomly corrupted by an adversary, and derive lower and upper bounds for the stability of the closed-loop system with compromised controller as a function of the perturbation statistics, size of the training data, sensitivity of the data-driven algorithm to perturbation of the training data, and properties of the nominal closed-loop system. Our stability and convergence bounds are probabilistic in nature, and rely on a first-order approximation of the data-driven procedure that designs the state-feedback controller, which can be computed directly using the training data. We illustrate our findings via multiple numerical studies.

eess.SY↗

arXiv2019

Data-Driven Minimum-Energy Controls for Linear Systems

In this paper we study the problem of computing minimum-energy controls for linear systems from experimental data. The design of open-loop minimum-energy control inputs to steer a linear system between two different states in finite time is a classic problem in control theory, whose solution can be computed in closed form using the system matrices and its controllability Gramian. Yet, the computation of these inputs is known to be ill-conditioned, especially when the system is large, the control horizon long, and the system model uncertain. Due to these limitations, open-loop minimum-energy controls and the associated state trajectories have remained primarily of theoretical value. Surprisingly, in this paper we show that open-loop minimum-energy controls can be learned exactly from experimental data, with a finite number of control experiments over the same time horizon, without knowledge or estimation of the system model, and with an algorithm that is significantly more reliable than the direct model-based computation. These findings promote a new philosophy of controlling large, uncertain, linear systems where data is abundantly available.

math.OC↗

arXiv2019

Centralized Versus Decentralized Detection of Attacks in Stochastic Interconnected Systems

We consider a security problem for interconnected systems governed by linear, discrete, time-invariant, stochastic dynamics, where the objective is to detect exogenous attacks by processing the measurements at different locations. We consider two classes of detectors, namely centralized and decentralized detectors, which differ primarily in their knowledge of the system model. In particular, a decentralized detector has a model of the dynamics of the isolated subsystems, but is unaware of the interconnection signals that are exchanged among subsystems. Instead, a centralized detector has a model of the entire dynamical system. We characterize the performance of the two detectors and show that, depending on the system and attack parameters, each of the detectors can outperform the other. In particular, it may be possible for the decentralized detector to outperform its centralized counterpart, despite having less information about the system dynamics, and this surprising property is due to the nature of the considered attack detection problem. To complement our results on the detection of attacks, we propose and solve an optimization problem to design attacks that maximally degrade the system performance while maintaining a pre-specified degree of detectability. Finally, we validate our findings via numerical studies on an electric power system.

math.OC↗

arXiv2019

A Fundamental Performance Limitation for Adversarial Classification

Despite the widespread use of machine learning algorithms to solve problems of technological, economic, and social relevance, provable guarantees on the performance of these data-driven algorithms are critically lacking, especially when the data originates from unreliable sources and is transmitted over unprotected and easily accessible channels. In this paper we take an important step to bridge this gap and formally show that, in a quest to optimize their accuracy, binary classification algorithms -- including those based on machine-learning techniques -- inevitably become more sensitive to adversarial manipulation of the data. Further, for a given class of algorithms with the same complexity (i.e., number of classification boundaries), the fundamental tradeoff curve between accuracy and sensitivity depends solely on the statistics of the data, and cannot be improved by tuning the algorithm.

cs.LG↗

arXiv2018

On the Real Stability Radius of Sparse Systems

In this paper, we study robust stability of sparse LTI systems using the stability radius (SR) as a robustness measure. We consider real perturbations with an arbitrary and pre-specified sparsity pattern of the system matrix and measure their size using the Frobenius norm. We formulate the SR problem as an equality-constrained minimization problem. Using the Lagrangian method for optimization, we characterize the optimality conditions of the SR problem, thereby revealing the relation between an optimal perturbation and the eigenvectors of an optimally perturbed system. Further, we use the Sylvester equation based parametrization to develop a penalty based gradient/Newton descent algorithm which converges to the local minima of the optimization problem. Finally, we illustrate how our framework provides structural insights into the robust stability of sparse networks.

eess.SY↗