Randy Cogill

A Constant Factor Approximation Algorithm for Event-Based Sampling

We consider a control system in which sensor data is transmitted from the plant to a receiver over a communication channel, and the receiver uses the data to estimate the state of the plant. Using a feedback policy to choose when to transmit data, the goal is to schedule transmissions to balance a trade-off between communication rate and estimation error. Computing an optimal policy for this problem is generally computationally intensive. Here we provide a simple algorithm for computing a suboptimal policy for scheduling state transmissions which incurs a cost within a factor of six of the optimal achievable cost.

Event-based control using quadratic approximate value functions

In this paper we consider several problems involving control with limited actuation and sampling rates. Event-based control has emerged as an attractive approach for addressing the problems of control system design under rate limitations. In event-based control, a system is actuated or a control signal is changed only when certain events occur. For example, a control signal might be applied only when some measure of deviation of the system state from equilibrium is exceeded. Thus, control action is only applied when it is needed, keeping control performance satisfactory while reducing the rate that the system must be sensed and actuated.

Convexity of optimal control over networks with delays and arbitrary topology

We consider the design of optimal controllers for a networked system (or a spatio-temporal system), where the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. We show that if a simple condition holds, then the optimal control problem may be recast as a convex optimisation problem. This is shown to unify and broadly generalise the class of such systems amenable to convex synthesis. When we consider the special case of spatially invariant systems, this again broadly generalises the known class of tractable problems.

A Simple Condition for the Convexity of Optimal Control over Networks with Delays

We consider the problem of multiple subsystems, each with its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. We wish to synthesize controllers to minimize a closed-loop norm for the entire system. We show that if the transmission delays satisfy the triangle inequality, then the simple condition that the transmission delay between any two subsystems is less than the propagation delay between those subsystems allows for the optimal control problem to be recast as a convex optimization problem.

Stable Throughput for Multicast With Random Linear Coding

This paper compares scheduling and coding strategies for a multicast version of a classic downlink problem. We consider scheduling strategies where, in each time slot, a scheduler observes the lengths of all queues and the connectivities of all links and can transmit the head-of-the-line packet from a single queue. We juxtapose this to a coding strategy that is simply a form of classical random linear coding. We show that there are configurations for which the stable throughput region of the scheduling strategy is a strict subset of the corresponding throughput region of the coding strategy. This analysis is performed for both time-invariant and time-varying channels. The analysis is also performed both with and without accounting for the impact on throughput of including coding overhead symbols in each encoded packet. Additionally, we compare coding strategies that only code within individual queues against a coding strategy that codes across separate queues. The strategy that codes across queues simply sends packets from all queues to all receivers. As a result, this strategy sends many packets to unnecessary recipients. We show, surprisingly, that there are cases where the strategy that codes across queues can achieve the same throughput region achievable by coding within individual queues.

Brief paper: Structured semidefinite programs for the control of symmetric systems

In this paper we show how the symmetry present in many linear systems can be exploited to significantly reduce the computational effort required for controller synthesis. This approach may be applied when controller design specifications are expressible via semidefinite programming. In particular, when the overall system description is invariant under unitary coordinate transformations of the state space matrices, synthesis semidefinite programs can be decomposed into a collection of smaller semidefinite programs.

Suboptimality Bounds in Stochastic Control: A Queueing Example

In this paper we consider Markov decision processes with average cost criteria, and discuss an approach for characterizing the performance loss associated with using a suboptimal control policy. Because there are often difficulties associated with computing and implementing optimal control policies, heuristic control policies are often used in practice. For such a policy, we would like to be able to compute guaranteed bounds on its performance, specifically its performance relative to an optimal policy. In other words, our goal is to produce a systematic approach for evaluating how far a specific policy is from optimality. This approach is demonstrated on a simple queuing system with a single server and multiple job classes. We use the general methods developed in the first part of the paper to show that for any non-idling policy, suboptimality of the resulting average queue length is bounded by a factor which only involves service rates

Stability analysis of random linear coding across multicast sessions

We consider a problem of managing separate multicast sessions from a single transmitter. Each of K sessions has an associated packet stream, and a single transmitter must transmit these packet streams to a group of receivers. The multicast sessions are separate in the sense that each receiver only wants packets from one of the K streams. We will compare the maximum stable arrival rates that can be supported with and without using random linear coding across the K sessions. Intuitively, it seems that coding across sessions is not beneficial. Coding across sessions appears to introduce unnecessary additional delay since each receiver does not receive its next packet until it can decode the head-of-line packets from all K streams. However, we show that in many cases the maximum stable arrival rate that can be supported when coding across sessions is significantly greater than maximum stable arrival rate that can be supported when not coding across sessions. We provide a sufficient condition that indicates when coding across sessions is preferable. This condition is expressed in terms of the number of sessions, the number of receivers per session, and the reliability of the channels connecting the transmitter to the receivers.

An Approximation Algorithm for the Discrete Team Decision Problem

In this paper we study a discrete version of the classical team decision problem. It has been shown previously that the general discrete team decision problem is NP-hard. Here we present an efficient approximation algorithm for this problem. For the maximization version of this problem with nonnegative rewards, this algorithm computes decision rules which are guaranteed to be within a fixed bound of optimal.

Charlottesville bike route planner

In this paper we discuss the design of a web-based tool that will help bicyclists determine safe and efficient routes. Specifically, we will discuss the selection of the appropriate metrics for ranking bicycle routes, together with our approach for collecting data on these metrics. The web based route planner that we have designed uses a weighted combination of five different metrics to determine routes that optimize a tradeoff among various safety factors and distance.