Kunal Garg

Kunal Garg, Dimitra Panagou

This paper presents a method for control synthesis under spatio-temporal constraints. First, we consider the problem of reaching a set $S$ in a user-defined or prescribed time $T$. We define a new class of control Lyapunov functions, called prescribed-time control Lyapunov functions (PT CLF), and present sufficient conditions on the existence of a controller for this problem in terms of PT CLF. Then, we formulate a quadratic program (QP) to compute a control input that satisfies these sufficient conditions. Next, we consider control synthesis under spatio-temporal objectives given as: the closed-loop trajectories remain in a given set $S_s$ at all times; and, remain in a specific set $S_i$ during the time interval $[t_i, t_{i+1})$ for $i = 0, 1, \cdots, N$; and, reach the set $S_{i+1}$ on or before $t = t_{i+1}$. We show that such spatio-temporal specifications can be translated into temporal logic formulas. We present sufficient conditions on the existence of a control input in terms of PT CLF and control barrier functions. Then, we present a QP to compute the control input efficiently, and show its feasibility under the assumptions of existence of a PT CLF. To the best of authors' knowledge, this is the first paper proposing a QP based method for the aforementioned problem of satisfying spatio-temporal specifications for nonlinear control-affine dynamics with input constraints. We also discuss the limitations of the proposed methods and directions of future work to overcome these limitations. We present numerical examples to corroborate our proposed methods.

Kunal Garg, Ehsan Arabi, Dimitra Panagou

In this paper, we present a control framework for a general class of control-affine nonlinear systems under spatiotemporal and input constraints. Specifically, the proposed control architecture addresses the problem of reaching a given final set $S$ in a prescribed (user-defined) time with bounded control inputs. To this end, a time transformation technique is utilized to transform the system subject to temporal constraints into an equivalent form without temporal constraints. The transformation is defined so that asymptotic convergence in the transformed time scale results into prescribed-time convergence in the original time scale. To incorporate input constraints, we characterize a set of initial conditions $D_M$ such that starting from this set, the closed-loop trajectories reach the set $S$ within the prescribed time. We further show that starting from outside the set $D_M$, the system trajectories reach the set $D_M$ in a finite time that depends upon the initial conditions and the control input bounds. We use a novel parameter $μ$ in the controller, that controls the convergence-rate of the closed-loop trajectories and dictates the size of the set $D_M$. Finally, we present a numerical example to showcase the efficacy of our proposed method.

James Usevitch, Kunal Garg, Dimitra Panagou

In this paper we consider the problem of a multi-agent system achieving a formation in the presence of misbehaving or adversarial agents. We introduce a novel continuous time resilient controller to guarantee that normally behaving agents can converge to a formation with respect to a set of leaders. The controller employs a norm-based filtering mechanism, and unlike most prior algorithms, also incorporates input bounds. In addition, the controller is shown to guarantee convergence in finite time. A sufficient condition for the controller to guarantee convergence is shown to be a graph theoretical structure which we denote as Resilient Directed Acyclic Graph (RDAG). Further, we employ our filtering mechanism on a discrete time system which is shown to have exponential convergence. Our results are demonstrated through simulations.

Kunal Garg, Dimitra Panagou

This paper presents novel controllers that yield finite-time stability for linear systems. We first present a sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finite-time controllers based on vector fields and barrier functions to demonstrate the utility of this geometric condition. We also consider the general class of linear controllable systems, and present a continuous feedback control law to stabilize the system in finite time. Finally, we present simulation results for each of these cases, showing the efficacy of the designed control laws.

Kunal Garg, Dongkun Han, Dimitra Panagou

This paper presents a robust distributed coordination protocol that achieves generation of collision-free trajectories for multiple unicycle agents in the presence of stochastic uncertainties. We build upon our earlier work on semi-cooperative coordination and we redesign the coordination controllers so that the agents counteract a class of state (wind) disturbances and measurement noise. Safety and convergence is proved analytically, while simulation results demonstrate the efficacy of the proposed solution.

Kunal Garg, Dimitra Panagou

This paper presents a novel hybrid control protocol for de-conflicting multiple vehicles with constraints on control inputs. We consider turning rate and linear speed constraints to represent fixed-wing or car-like vehicles. A set of state-feedback controllers along with a state-dependent switching logic are synthesized in a hybrid system to generate collision-free trajectories that converge to the desired destinations of the vehicles. The switching law is designed so that the safety can be guaranteed while no Zeno behavior can occur. A novel temporary goal assignment technique is also designed to guarantee convergence. We analyze the individual modes for safety and the closed-loop hybrid system for convergence. The theoretical developments are demonstrated via simulation results.

Kunal Garg, Mayank Baranwal

This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems viewpoint of an optimization algorithm, accelerated convergence to a saddle point can be obtained. Instead of requiring the objective function to be strongly-convex--strongly-concave (as necessitated for accelerated convergence of several saddle-point algorithms), uniform fixed-time convergence is guaranteed for functions satisfying only the two-sided Polyak-Łojasiewicz (PL) inequality. A large number of practical problems, including the robust least squares estimation, are known to satisfy the two-sided PL inequality. The proposed method achieves arbitrarily fast convergence compared to any other state-of-the-art method with linear or even super-linear convergence, as also corroborated in numerical case studies.

Kunal Garg, Mayank Baranwal

Distributed optimization has gained significant attention in recent years, primarily fueled by the availability of a large amount of data and privacy-preserving requirements. This paper presents a fixed-time convergent optimization algorithm for solving a potentially non-convex optimization problem using a first-order multi-agent system. Each agent in the network can access only its private objective function, while local information exchange is permitted between the neighbors. The proposed optimization algorithm combines a fixed-time convergent distributed parameter estimation scheme with a fixed-time distributed consensus scheme as its solution methodology. The results are presented under the assumption that the team objective function is strongly convex, as opposed to the common assumptions in the literature requiring each of the local objective functions to be strongly convex. The results extend to the class of possibly non-convex team objective functions satisfying only the Polyak-Łojasiewicz (PL) inequality. It is also shown that the proposed continuous-time scheme, when discretized using Euler's method, leads to consistent discretization, i.e., the fixed-time convergence behavior is preserved under discretization. Numerical examples comprising large-scale distributed linear regression and training of neural networks corroborate our theoretical analysis.

Kunal Garg

In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and fixed-time convergence, thereby relaxing the requirement of existence a differentiable, positive definite Lyapunov function. Based on these findings, we show that a dynamical system whose equilibrium point is globally asymptotically stable can be modified through scaling so that the resulting dynamical system has a fixed-time stable equilibrium point. The results in this paper expand our understanding of various convergence rates and strengthen the hypothesis that all the convergence rates are interconnected through a suitable transformation.

Kunal Garg, Xi Yu

Coordinated operations of multi-robot systems (MRS) require agents to maintain communication connections to accomplish team objectives. However, maintaining the connections imposes costs in terms of restricted robot mobility, resulting in suboptimal team performance. In this work, we consider a realistic MRS framework in which agents are subject to unknown dynamical disturbances and experience communication delays. Most existing works on connectivity maintenance use consensus-based frameworks for graph reconfiguration, where decision-making time scales with the number of nodes and requires multiple rounds of communication, making them ineffective under communication delays. To address this, we propose a novel leader-based decision-making algorithm that uses a central node for efficient real-time reconfiguration, reducing decision-making time to depend on the graph diameter rather than the number of nodes and requiring only one round of information transfer through the network. We propose a novel method for estimating robot locations within the MRS that actively accounts for unknown disturbances and the communication delays. Using these position estimates, the central node selects a set of edges to delete while allowing the formation of new edges, aiming to keep the diameter of the new graph within a threshold. We provide numerous simulation results to showcase the efficacy of the proposed method.

Kunal Garg, Songyuan Zhang, Jacob Arkin et al.

Connected multi-agent robotic systems (MRS) are prone to deadlocks in an obstacle environment where the robots can get stuck away from their desired locations under a smooth low-level control policy. Without an external intervention, often in terms of a high-level command, a low-level control policy cannot resolve such deadlocks. Utilizing the generalizability and low data requirements of foundation models, this paper explores the possibility of using text-based models, i.e., large language models (LLMs), and text-and-image-based models, i.e., vision-language models (VLMs), as high-level planners for deadlock resolution. We propose a hierarchical control framework where a foundation model-based high-level planner helps to resolve deadlocks by assigning a leader to the MRS along with a set of waypoints for the MRS leader. Then, a low-level distributed control policy based on graph neural networks is executed to safely follow these waypoints, thereby evading the deadlock. We conduct extensive experiments on various MRS environments using the best available pre-trained LLMs and VLMs. We compare their performance with a graph-based planner in terms of effectiveness in helping the MRS reach their target locations and computational time. Our results illustrate that, compared to grid-based planners, the foundation models perform better in terms of the goal-reaching rate and computational time for complex environments, which helps us conclude that foundation models can assist MRS operating in complex obstacle-cluttered environments to resolve deadlocks efficiently.

Teo Susnjak, Cole Palffy, Tatiana Zimina et al.

The scientific discourse surrounding Chronic Lyme Disease (CLD) and Post-Treatment Lyme Disease Syndrome (PTLDS) has evolved over the past twenty-five years into a complex and polarised debate, shaped by shifting research priorities, institutional influences, and competing explanatory models. This study presents the first large-scale, systematic examination of this discourse using an innovative hybrid AI-driven methodology, combining large language models with structured human validation to analyse thousands of scholarly abstracts spanning 25 years. By integrating Large Language Models (LLMs) with expert oversight, we developed a quantitative framework for tracking epistemic shifts in contested medical fields, with applications to other content analysis domains. Our analysis revealed a progressive transition from infection-based models of Lyme disease to immune-mediated explanations for persistent symptoms. This study offers new empirical insights into the structural and epistemic forces shaping Lyme disease research, providing a scalable and replicable methodology for analysing discourse, while underscoring the value of AI-assisted methodologies in social science and medical research.

Param Budhraja, Mayank Baranwal, Kunal Garg et al.

Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for achieving acceleration, based on the recently introduced notion of fixed-time stability of dynamical systems. The method presents itself as a generalization of simple gradient-based methods suitably scaled to achieve convergence to the optimizer in a fixed-time, independent of the initialization. We achieve this by first leveraging a continuous-time framework for designing fixed-time stable dynamical systems, and later providing a consistent discretization strategy, such that the equivalent discrete-time algorithm tracks the optimizer in a practically fixed number of iterations. We also provide a theoretical analysis of the convergence behavior of the proposed gradient flows, and their robustness to additive disturbances for a range of functions obeying strong convexity, strict convexity, and possibly nonconvexity but satisfying the Polyak-Łojasiewicz inequality. We also show that the regret bound on the convergence rate is constant by virtue of the fixed-time convergence. The hyperparameters have intuitive interpretations and can be tuned to fit the requirements on the desired convergence rates. We validate the accelerated convergence properties of the proposed schemes on a range of numerical examples against the state-of-the-art optimization algorithms. Our work provides insights on developing novel optimization algorithms via discretization of continuous-time flows.