Age Optimal Information Gathering and Dissemination on Graphs

We consider the problem of timely exchange of updates between a central station and a set of ground terminals $V$, via a mobile agent that traverses across the ground terminals along a mobility graph $G = (V, E)$. We design the trajectory of the mobile agent to minimize peak and average age of information (AoI), two newly proposed metrics for measuring timeliness of information. We consider randomized trajectories, in which the mobile agent travels from terminal $i$ to terminal $j$ with probability $P_{i,j}$. For the information gathering problem, we show that a randomized trajectory is peak age optimal and factor-$8\mathcal{H}$ average age optimal, where $\mathcal{H}$ is the mixing time of the randomized trajectory on the mobility graph $G$. We also show that the average age minimization problem is NP-hard. For the information dissemination problem, we prove that the same randomized trajectory is factor-$O(\mathcal{H})$ peak and average age optimal. Moreover, we propose an age-based trajectory, which utilizes information about current age at terminals, and show that it is factor-$2$ average age optimal in a symmetric setting

Optimal Event-Driven Multi-Agent Persistent Monitoring of a Finite Set of Targets

We consider the problem of controlling the movement of multiple cooperating agents so as to minimize an uncertainty metric associated with a finite number of targets. In a one-dimensional mission space, we adopt an optimal control framework and show that the solution is reduced to a simpler parametric optimization problem: determining a sequence of locations where each agent may dwell for a finite amount of time and then switch direction. This amounts to a hybrid system which we analyze using Infinitesimal Perturbation Analysis (IPA) to obtain a complete on-line solution through an event-driven gradient-based algorithm which is also robust with respect to the uncertainty model used. The resulting controller depends on observing the events required to excite the gradient-based algorithm, which cannot be guaranteed. We solve this problem by proposing a new metric for the objective function which creates a potential field guaranteeing that gradient values are non-zero. This approach is compared to an alternative graph-based task scheduling algorithm for determining an optimal sequence of target visits. Simulation examples are included to demonstrate the proposed methods.Comment: 12 pages full version, IEEE Conference on Decision and Control, 201

Multi-agent persistent monitoring of a finite set of targets

The general problem of multi-agent persistent monitoring finds applications in a variety of domains ranging from meter to kilometer-scale systems, such as surveillance or environmental monitoring, down to nano-scale systems such as tracking biological macromolecules for studying basic biology and disease. The problem can be cast as moving the agents between targets, acquiring information from or in some fashion controlling the states of the targets. Under this formulation, at least two questions need to be addressed. The first is the design of motion trajectories for the agents as they move among the spatially distributed targets and jointly optimize a given cost function that describes some desired application. The second is the design of the controller that an agent will use at a target to steer the target's state as desired. The first question can be viewed in at least two ways: first, as an optimal control problem with the domain of the targets described as a continuous space, and second as a discrete scheduling task. In this work we focus on the second approach, which formulates the target dynamics as a hybrid automaton, and the geometry of the targets as a graph. We show how to find solutions by translating the scheduling problem into a search for the optimal route. With a route specifying the visiting sequence in place, we derive the optimal time the agent spends at each target analytically. The second question, namely that of steering the target's state, can be formulated from the perspective of the target, rather than the agent. The mobile nature of the agents leads to intermittencontrol, such that the controller is assumed to be disconnected when no agent is at the target. The design of the visiting schedule of agents to one target can affect the reachability (controllability) of this target's control system and the design of any specific controller. Existing test techniques for reachability are combined with the idea of lifting to provide conditions on systems such that reachability is maintained in the presence of periodic disconnections from the controller. While considering an intermittently connected control with constraints on the control authority and in the presence of a disturbance, the concept of 'degree of controllability' is introduced. The degree is measured by a region of states that can be brought back to the origin in a given finite time. The size of this region is estimated to evaluate the performance of a given sequence

Cooperative control for multi-agent persistent monitoring problems

In persistent monitoring tasks, cooperating mobile agents are used to monitor a dynamically changing environment that cannot be fully covered by a stationary team of agents. The exploration process leads to the discovery of various "points of interest" (targets) to be perpetually monitored. Through an optimal control approach, the first part of this dissertation shows that in a one-dimensional mission space the solution can be reduced to a simpler parametric problem. The behavior of agents under optimal control is described by a hybrid system which can be analyzed using Infinitesimal Perturbation Analysis (IPA) to obtain an on-line solution. IPA allows the modeling of virtually arbitrary stochastic effects in target uncertainty and its event-driven nature renders the solution scalable in the number of events rather than the state space. The second part of this work extends the results of the one-dimensional persistent monitoring problem to a two-dimensional space with constrained agent mobility. Under a general graph setting, the properties of the one-dimensional optimal control solution are largely inherited. The solution involves the design of agent trajectories defined by both the sequence of nodes to be visited and the amount of time spent at each node. A class of distributed threshold-based parametric controllers is proposed to reduce the computational complexity. These parameters are optimized through an event-driven IPA gradient-based algorithm and yield optimal controllers within this family of threshold-based policies. The performance of the threshold-based parametric controller is close to that of the optimal controller derived through dynamic programming and its computational complexity is smaller by orders of magnitude. Although effective, the aforementioned optimal controls are established on the assumption that agents are all connected via a centralized controller which is energy-consuming and unreliable in adversarial environments. The third part of this work extends the previous controls by developing decentralized controllers which distribute functionality to the agents so that each one acts upon local information and sparse communication with neighbors. The complexity of decentralization for persistent monitoring problems is significant given agent mobility and the overall time-varying graph topology. Conditions are identified and a decentralized framework is proposed under which the centralized solution can be exactly recovered in a decentralized event-driven manner based on local information -- except for one event requiring communication from a non-neighbor agent