Pavankumar Tallapragada

Pavankumar Tallapragada, Nikhil Chopra

In this paper we study an event based control algorithm for trajectory tracking in nonlinear systems. The desired trajectory is modelled as the solution of a reference system with an exogenous input and it is assumed that the desired trajectory and the exogenous input to the reference system are uniformly bounded. Given a continuous-time control law that guarantees global uniform asymptotic tracking of the desired trajectory, our algorithm provides an event based controller that not only guarantees uniform ultimate boundedness of the tracking error, but also ensures non-accumulation of inter-execution times. In the case that the derivative of the exogenous input to the reference system is also uniformly bounded, an arbitrarily small ultimate bound can be designed. If the exogenous input to the reference system is piecewise continuous and not differentiable everywhere then the achievable ultimate bound is constrained and the result is local, though with a known region of attraction. The main ideas in the paper are illustrated through simulations of trajectory tracking by a nonlinear system.

Mohammad Javad Khojasteh, Pavankumar Tallapragada, Jorge Cortés et al.

We study event-triggered control for stabilization of unstable linear plants over rate-limited communication channels subject to unknown, bounded delay. On one hand, the timing of event triggering carries implicit information about the state of the plant. On the other hand, the delay in the communication channel causes information loss, as it makes the state information available at the controller out of date. Combining these two effects, we show a phase transition behavior in the transmission rate required for stabilization using a given event-triggering strategy. For small values of the delay, the timing information carried by the triggering events is substantial, and the system can be stabilized with any positive rate. When the delay exceeds a critical threshold, the timing information alone is not enough to achieve stabilization and the required rate grows. When the loss of information due to the communication delay perfectly compensates the implicit information carried by the triggering events, the delay equals the inverse of the entropy rate of the plant, and we obtain the same rate requirement prescribed by the data-rate theorem. When the delay is larger than this threshold, the required rate becomes larger than that required by the data-rate theorem. We also provide an explicit construction yielding a sufficient rate for stabilization, and generalize our results to vector systems. The results do not rely on any a priori probabilistic model of the delay or the initial conditions.

Pavankumar Tallapragada, Nikhil Chopra

This paper considers nonlinear systems with full state feedback, a central controller and distributed sensors not co-located with the central controller. We present a methodology for designing decentralized asynchronous event-triggers, which utilize only locally available information, for determining the time instants of transmission from the sensors to the central controller. The proposed design guarantees a positive lower bound for the inter-transmission times of each sensor, while ensuring asymptotic stability of the origin of the system with an arbitrary, but priorly fixed, compact region of attraction. In the special case of Linear Time Invariant (LTI) systems, global asymptotic stability is guaranteed and scale invariance of inter-transmission times is preserved. A modified design method is also proposed for nonlinear systems, with the addition of event-triggered communication from the controller to the sensors, that promises to significantly increase the average sensor inter-transmission times compared to the case where the controller does not transmit data to the sensors. The proposed designs are illustrated through simulations of a linear and a nonlinear example.

Erfan Nozari, Pavankumar Tallapragada, Jorge Cortés

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.

Pavankumar Tallapragada, Jorge Cortés

This paper considers the problem of coordinating the vehicular traffic at an intersection and on the branches leading to it for minimizing a combination of total travel time and energy consumption. We propose a provably safe hierarchical-distributed solution to balance computational complexity and optimality of the system operation. In our design, a central intersection manager communicates with vehicles heading towards the intersection, groups them into clusters (termed bubbles) as they appear, and determines an optimal schedule of passage through the intersection for each bubble. The vehicles in each bubble receive their schedule and implement local distributed control to ensure system-wide inter-vehicular safety while respecting speed and acceleration limits, conforming to the assigned schedule, and seeking to optimize their individual trajectories. Our analysis rigorously establishes that the different aspects of the hierarchical design operate in concert and that the safety guarantees provided by the proposed design are satisfied. We illustrate its execution in a suite of simulations and compare its performance to traditional signal-based coordination over a wide range of system parameters.

Mohammad Javad Khojasteh, Pavankumar Tallapragada, Jorge Cortes et al.

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.

Balaji R, Prashil Wankhede, Pavankumar Tallapragada · microsoft-research

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.

Aniruddha Roy, Pavankumar Tallapragada

In this paper, we consider infinite-horizon linear-quadratic cooperative differential games with output feedback information structure. We first demonstrate that, under output feedback information structure, computing Pareto optimal controls can be difficult even for simple low-dimensional differential games. To address this issue, this paper introduces the concept of feedback guaranteed cost structured control (GCSC). The feedback GCSC concept is inspired from suboptimal control. At a feedback GCSC, the total weighted team cost remains below a prescribed threshold while satisfying the structural constraints. We derive fundamental properties of the feedback GCSC and the admissible weight set, including their monotonicity properties. In particular, we show that if Pareto optimal controls exist, they belong to the class of feedback GCSCs. We also quantify the suboptimalty of Pareto optimal controls (if they exist) and the proposed GCSC with respect to output feedback optimal control. Furthermore, we provide the conditions for verification and the synthesis of a feedback GCSC. Finally, we illustrate the effectiveness of the proposed approach through numerical examples, including a case study on tracking synchronization in a microgrid.

Pavankumar Tallapragada, Massimo Franceschetti, Jorge Cortes

This paper deals with the stabilization of linear systems with process noise under packet drops between the sensor and the controller. Our aim is to ensure exponential convergence of the second moment of the plant state to a given bound in finite time. Motivated by considerations about the efficient use of the available resources, we adopt an event-triggering approach to design the transmission policy. In our design, the sensor's decision to transmit or not the state to the controller is based on an online evaluation of the future satisfaction of the control objective. The resulting event-triggering policy is hence specifically tailored to the control objective. We formally establish that the proposed event-triggering policy meets the desired objective and quantify its efficiency by providing an upper bound on the fraction of expected number of transmissions in an infinite time interval. Simulations for scalar and vector systems illustrate the results.

Pavankumar Tallapragada, Jorge Cortes

This paper studies an optimal control problem for a string of vehicles with safety requirements and finite-time specifications on the approach time to a target region. Our problem formulation is motivated by scenarios involving autonomous vehicles circulating on arterial roads with intelligent management at traffic intersections. We propose a provably correct distributed control algorithm that ensures that the vehicles satisfy the finite-time specifications under speed limits, acceleration saturation, and safety requirements. The safety specifications are such that collisions can be avoided even in cases of communication failure. We also discuss how the proposed distributed algorithm can be integrated with an intelligent intersection manager to provide information about the feasible approach times of the vehicle string and a guaranteed bound of its time of occupancy of the intersection. Our simulation study illustrates the algorithm and its properties regarding approach time, occupancy time, and fuel and time cost.

Pavankumar Tallapragada, Massimo Franceschetti, Jorge Cortes

This paper studies event-triggered stabilization of linear time-invariant systems over time-varying rate-limited communication channels. We explicitly account for the possibility of channel blackouts, i.e., intervals of time when the communication channel is unavailable for feedback. Assuming prior knowledge of the channel evolution, we study the data capacity, which is the maximum total number of bits that could be communicated over a given time interval, and provide an efficient real-time algorithm to lower bound it for a deterministic time-slotted model of channel evolution. Building on these results, we design an event-triggering strategy that guarantees Zeno-free, exponential stabilization at a desired convergence rate even in the presence of intermittent channel blackouts. The contributions are the notion of channel blackouts, the effective event-triggered control despite their occurrence, and the analysis and quantification of the data capacity for a class of time-varying continuous-time channels. Various simulations illustrate the results.

Pavankumar Tallapragada, Jorge Cortes

This paper addresses the problem of exponential practical stabilization of linear time-invariant systems with disturbances using event-triggered control and bounded communication bit rate. We consider both the case of instantaneous communication with finite precision data at each transmission and the case of non-instantaneous communication with bounded communication rate. Given a prescribed rate of convergence, the proposed event-triggered control implementations opportunistically determine the transmission instants and the finite precision data to be transmitted on each transmission. We show that our design exponentially practically stabilizes the origin while guaranteeing a uniform positive lower bound on the inter-transmission and inter-reception times, ensuring that the number of bits transmitted on each transmission is upper bounded uniformly in time, and allowing for the possibility of transmitting fewer bits at any given time if more bits than prescribed were transmitted earlier. We also characterize the necessary and sufficient average data rate for exponential practical stabilization. Several simulations illustrate the results.