arXiv subjects

Pavankumar Tallapragada

Publications and source records attributed to Pavankumar Tallapragada.

At least 19 recordsLinked to original sources

arXiv2026

Guaranteed cost structured control in infinite-horizon linear-quadratic cooperative differential games

In this paper, we consider the infinite-horizon linear-quadratic cooperative differential games with output feedback information structure. We first show that computing Pareto optimal controls under output feedback is difficult even for low-dimensional games. To address this, we introduce the concept of feedback guaranteed cost structured control (GCSC). At a feedback GCSC, the total weighted team cost remains below a prescribed threshold while satisfying the structural constraint. We derive monotonicity properties of the feedback GCSC set and the admissible weight set, respectively. Further, we show that Pareto optimal controls (if they exist) belong to the class of feedback GCSCs. We provide performance measures of the Pareto optimal controls and the proposed GCSC relative to the output feedback optimal control. We also establish verification and synthesis conditions for a feedback GCSC using linear matrix inequalities, where the synthesis formulation is convex and requires no semi-definite programming relaxation. Finally, we illustrate the effectiveness of the proposed approach through numerical examples, including a microgrid tracking synchronization case study.

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arXiv2026

A Network Formation Game for Katz Centrality Maximization: A Resource Allocation Perspective

In this paper, we study a network formation game in which agents seek to maximize their influence by allocating constrained resources to choose connections with other agents. In particular, we use Katz centrality to model agents' influence in the network. Allocations are restricted to neighbors in a given unweighted network encoding topological constraints. The allocations by an agent correspond to the weights of its outgoing edges. Such allocation by all agents thereby induces a network. This models a strategic-form game in which agents' utilities are given by their Katz centralities. We characterize the Nash equilibrium networks of this game and analyze their properties. We propose a sequential best-response dynamics (BRD) to model the network formation process. We show that it converges to the set of Nash equilibria under very mild assumptions. For complete underlying topologies, we show that Katz centralities are proportional to agents' budgets at Nash equilibria. For general underlying topologies in which each agent has a self-loop, we show that hierarchical networks form at Nash equilibria. Finally, simulations illustrate our findings.

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arXiv2025

Multi-Topic Projected Opinion Dynamics for Resource Allocation

We propose a model of opinion formation on resource allocation among multiple topics by multiple agents, who are subject to hard budget constraints. We define a utility function for each agent and then derive a projected dynamical system model of opinion evolution assuming that each agent myopically seeks to maximize its utility subject to its constraints. Inter-agent coupling arises from an undirected social network, while inter-topic coupling arises from resource constraints. We show that opinions always converge to the equilibrium set. For special networks with very weak antagonistic relations, the opinions converge to a unique equilibrium point. We further show that the underlying opinion formation game is a potential game. We relate the equilibria of the dynamics and the Nash equilibria of the game and characterize the unique Nash equilibrium for networks with no antagonistic relations. Finally, simulations illustrate our findings.

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arXiv2024

A Control Lyapunov Function Approach to Event-Triggered Parameterized Control for Discrete-Time Linear Systems

This paper proposes an event-triggered parameterized control method using a control Lyapunov function approach for discrete time linear systems with external disturbances. In this control method, each control input to the plant is a linear combination of a fixed set of linearly independent scalar functions. The controller updates the coefficients of the parameterized control input in an event-triggered manner so as to minimize a quadratic cost function subject to quadratic constraints and communicates the same to the actuator. We design an event-triggering rule that guarantees global uniform ultimate boundedness of trajectories of the closed loop system and non-trivial inter-event times. We illustrate our results through numerical examples and we also compare the performance of the proposed control method with other existing control methods in the literature.

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arXiv2024

Opinion Dynamics for Utility Maximizing Agents: Exploring the Impact of the Resource Penalty

We propose a continuous-time nonlinear model of opinion dynamics with utility-maximizing agents connected via a social influence network. A distinguishing feature of the proposed model is the inclusion of an opinion-dependent resource-penalty term in the utilities, which limits the agents from holding opinions of large magnitude. This model is applicable in scenarios where the opinions pertain to the usage of resources, such as money, time, computational resources etc. Each agent myopically seeks to maximize its utility by revising its opinion in the gradient ascent direction of its utility function, thus leading to the proposed opinion dynamics. We show that, for any arbitrary social influence network, opinions are ultimately bounded. For networks with weak antagonistic relations, we show that there exists a globally exponentially stable equilibrium using contraction theory. We establish conditions for the existence of consensus equilibrium and analyze the relative dominance of the agents at consensus. We also conduct a game-theoretic analysis of the underlying opinion formation game, including on Nash equilibria and on prices of anarchy in terms of satisfaction ratios. Additionally, we also investigate the oscillatory behavior of opinions in a two-agent scenario. Finally, simulations illustrate our findings.

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arXiv2024

Event-Triggered Parameterized Control of Nonlinear Systems

This paper deals with event-triggered parameterized control (ETPC) of nonlinear systems with external disturbances. In this control method, between two successive events, each control input to the plant is a linear combination of a set of linearly independent scalar functions. At each event, the controller updates the coefficients of the parameterized control input so as to minimize the error in approximating a continuous time control signal and communicates the same to the actuator. We design an event-triggering rule (ETR) that guarantees global uniform ultimate boundedness of trajectories of the closed loop system. We also ensure the absence of Zeno behavior by showing the existence of a uniform positive lower bound on the inter-event times (IETs). We illustrate our results through numerical examples.

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arXiv2023

Event-Triggered Polynomial Control for Trajectory Tracking by Unicycle Robots

This paper proposes an event-triggered polynomial control method for trajectory tracking by unicycle robots. In this method, each control input between two consecutive events is a polynomial and its coefficients are chosen to minimize the error in approximating a continuous-time control signal. We design an event-triggering rule that guarantees uniform ultimate boundedness of the tracking error and non-Zeno behavior of inter-event times. We illustrate our results through a suite of numerical simulations and experiments, which indicate that the number of events generated by the proposed controller is significantly less compared to that by a time-triggered controller or a event-triggered controller based on zero-order hold while guaranteeing similar tracking performance.

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arXiv2023

Reinforcement Learning Aided Sequential Optimization for Unsignalized Intersection Management of Robot Traffic

We consider the problem of optimal unsignalized intersection management, wherein we seek to obtain safe and optimal trajectories, for a set of robots that arrive randomly and continually. This problem involves repeatedly solving a mixed integer program (with robot acceleration trajectories as decision variables) with different parameters, for which the computation time using a naive optimization algorithm scales exponentially with the number of robots and lanes. Hence, such an approach is not suitable for real-time implementation. In this paper, we propose a solution framework that combines learning and sequential optimization. In particular, we propose an algorithm for learning a shared policy that given the traffic state information, determines the crossing order of the robots. Then, we optimize the trajectories of the robots sequentially according to that crossing order. This approach inherently guarantees safety at all times. We validate the performance of this approach using extensive simulations and compare our approach against $5$ different heuristics from the literature in $9$ different simulation settings. Our approach, on average, significantly outperforms the heuristics from the literature in various metrics like objective function, weighted average of crossing times and computation time. For example, in some scenarios, we have observed that our approach offers up to $150\%$ improvement in objective value over the first come first serve heuristic. Even on untrained scenarios, our approach shows a consistent improvement (in objective value) of more than $30\%$ over all heuristics under consideration. We also show through simulations that the computation time for our approach scales linearly with the number of robots (assuming all other factors are constant). Learnt policies are implemented on physical robots with slightly modified framework to address real-world challenges.

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arXiv2022

Analysis of Inter-Event Times in Linear Systems under Region-Based Self-Triggered Control

This paper analyzes the evolution of inter-event times (IETs) in linear systems under region-based self-triggered control (RBSTC). In this control method, the state space is partitioned into a finite number of conic regions and each region is associated with a fixed IET. In this framework, studying the steady state behavior of the IETs is equivalent to studying the existence of a conic subregion that is positively invariant under the map that gives the evolution of the state from one event to the next. We provide necessary conditions and sufficient conditions for the existence of a positively invariant subregion (PIS). We also provide necessary and sufficient conditions for a PIS to be asymptotically stable. Indirectly, they provide necessary and sufficient conditions for local convergence of IETs to a constant or to a given periodic sequence. We illustrate the proposed method of analysis and results through numerical simulations.

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arXiv2022

Asymptotic Behavior of Inter-Event Times in Planar Systems under Event-Triggered Control

This paper analyzes the asymptotic behavior of inter-event times in planar linear systems, under event-triggered control with a general class of scale-invariant event triggering rules. In this setting, the inter-event time is a function of the angle of the state at an event. This viewpoint allows us to analyze the inter-event times by studying the fixed points of the angle map, which represents the evolution of the angle of the state from one event to the next. We provide a sufficient condition for the convergence or non-convergence of inter-event times to a steady state value under a scale-invariant event-triggering rule. Following up on this, we further analyze the inter-event time behavior in the special case of threshold based event-triggering rule and we provide various conditions for convergence or non-convergence of inter-event times to a constant. We also analyze the asymptotic average inter-event time as a function of the angle of the initial state of the system. With the help of ergodic theory, we provide a sufficient condition for the asymptotic average inter-event time to be a constant for all non-zero initial states of the system. Then, we consider a special case where the angle map is an orientation-preserving homeomorphism. Using rotation theory, we comment on the asymptotic behavior of the inter-event times, including on whether the inter-event times converge to a periodic sequence. We illustrate the proposed results through numerical simulations.

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arXiv2021

Data-Driven Distributed Intersection Management for Connected and Automated Vehicles

This work addresses the problem of autonomous traffic management at an isolated intersection for connected and automated vehicles. We decompose the trajectory of each vehicle into two phases: the provisional phase and the coordinated phase. A vehicle, upon entering the region of interest, initially operates in the provisional phase, during which the vehicle optimizes its trajectory but is constrained from entering the intersection. Periodically, all the vehicles in their provisional phase switch to their coordinated phase, which is obtained by coordinated optimization of the sequence of the vehicles' intersection usage as well as their trajectories. For the coordinated phase, we propose a data driven solution, in which the intersection usage sequence is obtained through a data-driven online classification and the trajectories are computed sequentially. This approach also allows for the incorporation of macro information such as traffic arrival rates into the solution. The overall algorithm is provably safe and can be implemented in a distributed manner. Finally, we compare the proposed algorithm against traditional methods of intersection management and against some existing literature through simulations. Through simulations, we also demonstrate that the computation time per vehicle remains constant for the proposed algorithm over a wide range of traffic arrival rates.

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arXiv2021

Event-triggered Control for Nonlinear Systems with Center Manifolds

In this work, we consider the problem of event-triggered implementation of control laws designed for the local stabilization of nonlinear systems with center manifolds. We propose event-triggering conditions which are derived from a local input-to-state stability characterization of such systems. The triggering conditions ensure local ultimate boundedness of the trajectories and the existence of a uniform positive lower bound for the inter-event times. The ultimate bound can be made arbitrarily small, but by allowing for smaller inter-event times. Under certain assumptions on the controller structure, local asymptotic stability of the origin is also guaranteed. Two sets of triggering conditions are proposed, that cater to the cases where the exact center manifold and only an approximation of the center manifold is computable. The closed-loop system exhibits some desirable properties when the exact knowledge of the center manifold is employed in checking the triggering conditions. Three illustrative examples that explore different scenarios are presented and the applicability of the proposed methods is demonstrated. The third example concerns the event-triggered implementation of a position stabilizing controller for the open-loop unstable Mobile Inverted Pendulum (MIP) robot.

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arXiv2021

One-Shot Coordination of First and Last Mode Transportation

In this paper, we consider coordinated control of feeder vehicles for first and last mode transportation. The model is macroscopic with volumes of demands and supplies along with flows of vehicles. We propose a one-shot problem for transportation of demand to or from a hub within a fixed time window, assuming the knowledge of the demand and supply configurations. We present a unified optimization framework that is applicable for both operator profit maximization and social welfare maximization. The latter goal is useful for applications such as disaster response. The decision variables in the optimization problem are routing and allocations of the vehicles for different services. With K.K.T. analysis we propose an offline method for reducing the problem size. Further, we also analyze the problem of maximizing profits by optimally locating the supply for a given total supply and present a closed form expression of the maximum profits that can be earned over all supply configurations for a given demand configuration. We also show an equivalence between optimal supply location in the first mode problem and the last mode problem. We present a model for pricing based on the cost and travel time of the best alternate transportation and present necessary conditions for the feeder service to be viable. We illustrate the results through simulations and also compare the proposed model with a traditional vehicle routing problem. Through simulations, we also compare with the microscopic version of the problem with the decision variables being integers. We demonstrate that the route reduction algorithm proposed for the macroscopic formulation is still useful for computing nearly optimal solutions to the microscopic problem with much improved computational efficiency.

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arXiv2020

Dynamics of a Stratified Population of Optimum Seeking Agents on a Network -- Part I: Modeling and Convergence Analysis

In this work, we consider a population composed of a continuum of agents that seek to maximize a payoff function by moving on a network. The nodes in the network may represent physical locations or abstract choices. The population is stratified and hence agents opting for the same choice may not get the same payoff. In particular, we assume payoff functions that model diminishing returns, that is, agents in "newer" strata of a node receive a smaller payoff compared to "older" strata. In this first part of two-part work, we model the population dynamics under three choice revision policies, each having varying levels of coordination -- i. no coordination and the agents are selfish, ii. coordination among agents in each node and iii. coordination across the entire population. To model the case with selfish agents, we generalize the Smith dynamics to our setting, where we have a stratified population and network constraints. To model nodal coordination, we allow the fraction of population in a node, as a whole, to take the `best response' to the state of the population in the node's neighborhood. For the case of population-wide coordination, we explore a dynamics where the population evolves according to centralized gradient ascent of the social utility, though constrained by the network. In each case, we show that the dynamics has existence and uniqueness of solutions and also show that the solutions from any initial condition asymptotically converge to the set of Nash equilibria.

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arXiv2020

Dynamics of a Stratified Population of Optimum Seeking Agents on a Network -- Part II: Steady State Analysis

In this second part of our work, we study the steady state of the population and the social utility for the three dynamics SSD, NBRD and NRPM; which were introduced in the first part. We provide sufficient conditions on the network based on a maximum payoff density parameter of each node under which there exists a unique Nash equilibrium. We then utilize positive correlation properties of the dynamics to reduce the flow graph in order to provide an upper bound on the steady state social utility. Finally we extend the idea behind the sufficient condition for the existence of a unique Nash equilibrium to partition the graph appropriately in order to provide a lower bound on the steady state social utility. We also illustrate interesting cases as well as our results using simulations.

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arXiv2019

Control Under Action-Dependent Markov Packet Drops: An Event-Triggered Approach

In this paper, we consider the problem of second moment stabilization of a scalar linear plant with process noise. We assume that the sensor must communicate with the controller over an unreliable channel, whose state evolves according to a Markov chain, with the transition matrix on a timestep depending on whether there is a transmission or not on that timestep. Under such a setting, we propose an event-triggered transmission policy which meets the objective of exponential convergence of the second moment of the plant state to an ultimate bound. Furthermore, we provide upper bounds on the transmission fraction of the proposed policy. The guarantees on performance and transmission fraction are verified using simulations.

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arXiv2017

Event-Triggered Stabilization of Nonlinear Systems with Time-Varying Sensing and Actuation Delay

This paper studies the problem of stabilization of a nonlinear system with time-varying delays in both sensing and actuation using event-triggered control. Our proposed strategy seeks to opportunistically minimize the number of control updates while guaranteeing stabilization and builds on predictor feedback to compensate for arbitrarily large known time-varying delays. We establish, using a Lyapunov approach, the global asymptotic stability of the closed-loop system as long as the open-loop system is globally input-to-state stabilizable in the absence of time delays and sampling. We further prove that the proposed event-triggered law has inter-event times that are uniformly lower bounded and hence does not exhibit Zeno behavior. For the particular case of a stabilizable linear system, we show global exponential stability of the closed-loop system and analyze the trade-off between the rate of exponential convergence and a bound on the sampling frequency. We illustrate these results in simulation and also examine the properties of the proposed event-triggered strategy beyond the class of systems for which stabilization can be guaranteed.

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arXiv2017

Time-triggering versus event-triggering control over communication channels

Time-triggered and event-triggered control strategies for stabilization of an unstable plant over a rate-limited communication channel subject to unknown, bounded delay are studied and compared. Event triggering carries implicit information, revealing the state of the plant. However, the delay in the communication channel causes information loss, as it makes the state information out of date. There is a critical delay value, when the loss of information due to the communication delay perfectly compensates the implicit information carried by the triggering events. This occurs when the maximum delay equals the inverse of the entropy rate of the plant. In this context, extensions of our previous results for event triggering strategies are presented for vector systems and are compared with the data-rate theorem for time-triggered control, that is extended here to a setting with unknown delay.

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