arXiv subjects

Shirantha Welikala

Publications and source records attributed to Shirantha Welikala.

29 records · Page 2Linked to original sources

arXiv2022

Centralized and Decentralized Techniques for Analysis and Synthesis of Non-Linear Networked Systems

In this paper, we develop centralized and decentralized techniques for analyzing and synthesizing networked systems comprised of interconnected sets of non-linear subsystems - only using the subsystem dissipativity properties. In particular, this paper extends a recent work that proposed dissipativity based centralized analysis techniques for non-linear networked systems as linear matrix inequality (LMI) problems. First, we consider four networked system configurations (NSCs) of interest and provide centralized stability/dissipativity \emph{analysis} techniques for them as LMI problems. Second, we show that the centralized interconnection topology \emph{synthesis} techniques for these NSCs can also be developed as LMI problems. This enables synthesizing the interconnection topology among the subsystems so that specific stability/dissipativity measures of the networked system are optimized. Next, we show that the proposed analysis and synthesis techniques can be implemented in a decentralized and compositional manner (i.e., subsystems can be added/removed conveniently). Finally, we include several numerical results to demonstrate our contributions.

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arXiv2022

A Decentralized Analysis and Control Synthesis Approach for Networked Systems with Arbitrary Interconnections

This paper considers the problem of decentralized analysis and control synthesis to verify and ensure properties like stability and dissipativity of a large-scale networked system comprised of linear subsystems interconnected in an arbitrary topology. In particular, we design systematic networked system analysis and control synthesis processes that can be executed in a decentralized manner at the subsystem level with minimal information sharing among the subsystems. Compared to our most recent work on the same topic, we consider a substantially more generalized problem setup in this paper and develop decentralized processes to verify and ensure a broader range of networked system properties. We show that for such decentralized processes: optimizing the used subsystem indexing scheme can substantially reduce the required inter-subsystem information-sharing sessions, and in some network topologies, information sharing among only neighboring subsystems is sufficient (distributed!). Moreover, the proposed networked system analysis and control synthesis processes are compositional/resilient to subsystem removals, which enable them to conveniently and efficiently handle situations where new subsystems are being added/removed to/from an existing network. We also provide significant insights into our decentralized approach so that it can be quickly adopted to verify and ensure properties beyond the stability and dissipativity of networked systems. Towards developing such decentralized techniques, we have also derived new centralized solutions for dissipative observer and dynamic output feedback controller design problems. Subsequently, we also specialize all the derived results for discrete-time networked systems. We conclude this paper by providing several simulation results demonstrating the proposed novel decentralized analysis and control synthesis processes and dissipativity-based results.

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arXiv2022

On-line Estimation of Stability and Passivity Metrics

We consider the problem of on-line evaluation of critical characteristic parameters such as the L_2-gain (L2G), input feedforward passivity index (IFP) and output feedback passivity index (OFP) of non-linear systems using their input-output data. Typically, having an accurate measure of such "system indices" enables the application of systematic control design techniques. Moreover, if such system indices can efficiently be evaluated on-line, they can be exploited to device intelligent controller reconfiguration and fault-tolerant control techniques. However, the existing estimation methods of such system indices (i.e., L2G, IFP and OFP) are predominantly off-line, computationally inefficient, and require a large amount of actual or synthetically generated input-output trajectory data under some specific initial/terminal conditions. On the other hand, the existing on-line estimation methods take an averaging-based approach, which may be sub-optimal, computationally inefficient and susceptible to estimate saturation. In this paper, to overcome these challenges (in the on-line estimation of system indices), we establish and exploit several interesting theoretical results on a particular class of fractional function optimization problems. For comparison purposes, the details of an existing averaging-based approach are provided for the same on-line estimation problem. Finally, several numerical examples are discussed to demonstrate the proposed on-line estimation approach and to highlight our contributions.

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arXiv2022

Robust Approximate Simulation for Hierarchical Control of Piecewise Affine Systems under Bounded Disturbances

Piecewise affine (PWA) systems are widely applied in many practical cases such as the control of nonlinear systems and hybrid dynamics. However, most of the existing PWA control methods have poor scalability with respect to the number of modes and system dimensions and may not be robust to the disturbances in performance. In this paper, we present a robust approximate simulation based control method for PWA systems under bounded external disturbances. First, a lower-dimensional linear system (abstraction) and an associated interface are designed to enable the output of the PWA system (concrete system) to track the output of the abstraction. Then, a Lyapunov-like simulation function is designed to show the boundedness of the output errors between the two systems. Furthermore, the results obtained for linear abstraction are extended to the case that a simpler PWA system is the abstraction. To illustrate the effectiveness of the proposed approach, simulation results are provided for two design examples.

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arXiv2022

Minimax Multi-Agent Persistent Monitoring of a Network System

We investigate the problem of optimally observing a finite set of targets using a mobile agent over an infinite time horizon. The agent is tasked to move in a network-constrained structure to gather information so as to minimize the worst-case uncertainty about the internal states of the targets. To do this, the agent has to decide its sequence of target-visits and the corresponding dwell-times at each visited target. For a given visiting sequence, we prove that in an optimal dwelling time allocation the peak uncertainty is the same among all the targets. This allows us to formulate the optimization of dwelling times as a resource allocation problem and to solve it using a novel efficient algorithm. Next, we optimize the visiting sequence using a greedy exploration process, using heuristics inspired by others developed in the context of the traveling salesman problem. Numerical results are included to illustrate the contributions.

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arXiv2021

Event-Driven Receding Horizon Control for Distributed Estimation in Network Systems

We consider the problem of estimating the states of a distributed network of nodes (targets) through a team of cooperating agents (sensors) persistently visiting the nodes so that an overall measure of estimation error covariance evaluated over a finite period is minimized. We formulate this as a multi-agent persistent monitoring problem where the goal is to control each agent's trajectory defined as a sequence of target visits and the corresponding dwell times spent making observations at each visited target. A distributed on-line agent controller is developed where each agent solves a sequence of receding horizon control problems (RHCPs) in an event-driven manner. A novel objective function is proposed for these RHCPs so as to optimize the effectiveness of this distributed estimation process and its unimodality property is established under some assumptions. Moreover, a machine learning solution is proposed to improve the computational efficiency of this distributed estimation process by exploiting the history of each agent's trajectory. Finally, extensive numerical results are provided indicating significant improvements compared to other state-of-the-art agent controllers.

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arXiv2021

Event-Driven Receding Horizon Control of Energy-Aware Dynamic Agents For Distributed Persistent Monitoring

This paper addresses the persistent monitoring problem defined on a network where a set of nodes (targets) needs to be monitored by a team of dynamic energy-aware agents. The objective is to control the agents' motion to jointly optimize the overall agent energy consumption and a measure of overall node state uncertainty, evaluated over a finite period of interest. To achieve these objectives, we extend an established event-driven Receding Horizon Control (RHC) solution by adding an optimal controller to account for agent motion dynamics and associated energy consumption. The resulting RHC solution is computationally efficient, distributed and on-line. Finally, numerical results are provided highlighting improvements compared to an existing RHC solution that uses energy-agnostic first-order agents.

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arXiv2020

Asymptotic Analysis for Greedy Initialization of Threshold-Based Distributed Optimization of Persistent Monitoring on Graphs

This paper considers the optimal multi-agent persistent monitoring problem defined for a team of agents on a set of nodes (targets) interconnected according to a fixed network topology. The aim is to control this team so as to minimize a measure of overall node state uncertainty evaluated over a finite time interval. A class of distributed threshold-based parametric controllers has been proposed in prior work to control agent dwell times at nodes and next-node destinations by enforcing thresholds on the respective node states. Under such a Threshold Control Policy (TCP), an on-line gradient technique was used to determine optimal threshold values. However, due to the non-convexity of the problem, this approach often leads to a poor local optima highly dependent on the initial thresholds used. To overcome this initialization challenge, we develop a computationally efficient off-line greedy technique based on the asymptotic analysis of the network system. This analysis is then used to generate a high-performing set of initial thresholds. Extensive numerical results show that such initial thresholds are almost immediately (locally) optimal or quickly lead to optimal values. In all cases, they perform significantly better than the locally optimal solutions known to date.

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arXiv2020

Event-Driven Receding Horizon Control For Distributed Persistent Monitoring in Network Systems

We address the multi-agent persistent monitoring problem defined on a set of nodes (targets) interconnected over a network topology. A measure of mean overall node state uncertainty evaluated over a finite period is to be minimized by controlling the motion of a cooperating team of agents. To address this problem, we propose an event-driven receding horizon control approach that is computationally efficient, distributed and on-line. The proposed controller differs from the existing on-line gradient-based parametric controllers and off-line greedy cycle search methods that often lead to either low-performing local optima or computationally intensive centralized solutions. A critical novel element in this controller is that it automatically optimizes its planning horizon length, thus making it parameter-free. We show that explicit globally optimal solutions can be obtained for every distributed optimization problem encountered at each event where the receding horizon controller is invoked. Numerical results are provided showing improvements compared to state of the art distributed on-line parametric control solutions.

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arXiv2020

Distributed Non-convex Optimization of Multi-agent Systems Using Boosting Functions to Escape Local Optima: Theory and Applications

We address the problem of multiple local optima arising due to non-convex objective functions in cooperative multi-agent optimization problems. To escape such local optima, we propose a systematic approach based on the concept of boosting functions. The underlying idea is to temporarily transform the gradient at a local optimum into a boosted gradient with a non-zero magnitude. We develop a Distributed Boosting Scheme (DBS) based on a gradient-based optimization algorithm using a novel optimal variable step size mechanism so as to guarantee convergence. Even though our motivation is based on the coverage control problem setting, our analysis applies to a broad class of multi-agent problems. Simulation results are provided to compare the performance of different boosting functions families and to demonstrate the effectiveness of the boosting function approach in attaining improved (still generally local) optima.

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arXiv2020

Optimal Composition of Heterogeneous Multi-Agent Teams for Coverage Problems with Performance Bound Guarantees

We consider the problem of determining the optimal composition of a heterogeneous multi-agent team for coverage problems by including costs associated with different agents and subject to an upper bound on the maximal allowable number of agents. We formulate a resource allocation problem without introducing additional non-convexities to the original problem. We develop a distributed Projected Gradient Ascent (PGA) algorithm to solve the optimal team composition problem. To deal with non-convexity, we initialize the algorithm using a greedy method and exploit the submodularity and curvature properties of the coverage objective function to derive novel tighter performance bound guarantees on the optimization problem solution. Numerical examples are included to validate the effectiveness of this approach in diverse mission space configurations and different heterogeneous multi-agent collections. Comparative results obtained using a commercial mixed-integer nonlinear programming problem solver demonstrate both the accuracy and computational efficiency of the distributed PGA algorithm.

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