Samuel Coogan

Scaling the size of a formation using relative position feedback

We consider a multiagent coordination problem where the objective is to steer a team of mobile agents into a formation of variable size. We assume the shape description of the formation is known to all agents, but the desired size scaling of the formation is known only to a subset of agents. We present two strategies that allow the agents to maneuver to the desired scaled formation using only local relative position information. These strategies can be implemented using information gathered via local sensors and no interagent communication. We compare the two methods through several examples with simulations.

A learning based approach to control synthesis of Markov decision processes for linear temporal logic specifications

We propose to synthesize a control policy for a Markov decision process (MDP) such that the resulting traces of the MDP satisfy a linear temporal logic (LTL) property. We construct a product MDP that incorporates a deterministic Rabin automaton generated from the desired LTL property. The reward function of the product MDP is defined from the acceptance condition of the Rabin automaton. This construction allows us to apply techniques from learning theory to the problem of synthesis for LTL specifications even when the transition probabilities are not known a priori. We prove that our method is guaranteed to find a controller that satisfies the LTL property with probability one if such a policy exists, and we suggest empirically that our method produces reasonable control strategies even when the LTL property cannot be satisfied with probability one.

Energy management via pricing in LQ dynamic games

This paper investigates the use of pricing mechanisms as a means to achieve a desired feedback control strategy among selfish agents in the context of HVAC resource allocation in buildings. We pose the problem of resource allocation as a linear-quadratic game with many dynamically coupled zone occupants(agents) and an uncoupled social planner. The social planner influences the game by choosing the quadratic dependence on control actions for each agents cost function. We propose a neighborhood-based simplification of the dynamic game that results in a more realistic and scalable framework than is considered in standard dynamic game theory. In addition, we construct the pricing design problem as a convex feasibility problem and apply our method to an eight zone building model.

Efficient finite abstraction of mixed monotone systems

We present an efficient computational procedure for finite abstraction of discrete-time mixed monotone systems by considering a rectangular partition of the state space. Mixed monotone systems are decomposable into increasing and decreasing components, and significantly generalize the well known class of monotone systems. We tightly overapproximate the one-step reachable set from a box of initial conditions by computing a decomposition function at only two points, regardless of the dimension of the state space. We apply our results to verify the dynamical behavior of a model for insect population dynamics and to synthesize a signaling strategy for a traffic network.

Dynamical properties of a compartmental model for traffic networks

In this paper, we propose a traffic network flow model particularly suitable for qualitative analysis as a dynamical system. Flows at a junction are determined by downstream supply of capacity (lack of congestion) as well as upstream demand of traffic wishing to flow through the junction. This approach is rooted in the celebrated Cell Transmission Model for freeway traffic flow, and we analyze resulting equilibrium flows and convergence properties.

Traffic Network Control From Temporal Logic Specifications

We propose a framework for generating a signal control policy for a traffic network of signalized intersections to accomplish control objectives expressible using linear temporal logic. By applying techniques from model checking and formal methods, we obtain a correct-by-construction controller that is guaranteed to satisfy complex specifications. To apply these tools, we identify and exploit structural properties particular to traffic networks that allow for efficient computation of a finite-state abstraction. In particular, traffic networks exhibit a componentwise monotonicity property which enables reaching set computations that scale linearly with the dimension of the continuous state space.

A Compartmental Model for Traffic Networks and Its Dynamical Behavior

We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as well as upstream demand of traffic wishing to flow through the junction. This approach is rooted in the celebrated Cell Transmission Model for freeway traffic flow. Unlike related results which rely on certain system cooperativity properties, our model generally does not possess these properties. We show that the lack of cooperativity is in fact a useful feature that allows traffic control methods, such as ramp metering, to be effective. Finally, we leverage the results of the technical note to develop a linear program for optimal ramp metering.

Freeway traffic control from linear temporal logic specifications

We propose a methodology for synthesizing ramp metering control strategies for freeway networks from linear temporal logic specifications. Such specifications allow very rich control objectives constructed from temporal operators such as “always” and “eventually” combined with Boolean operators and encompass e.g. safety, reachability, and liveness conditions. We use the cell transmission model of traffic flow on freeway networks to obtain a piecewise affine model of the traffic network, and we apply recent results on control of such systems from temporal logic specifications to synthesize ramp metering strategies that are correct by construction. We demonstrate our approach on several examples.

Stability of traffic flow networks with a polytree topology

We consider global stability of a flow network model for vehicular traffic. Standard approaches which rely on monotonicity of flow networks for stability analysis do not immediately apply to traffic networks with diverging junctions. In this paper, we show that the network model nonetheless exhibits a mixed monotonicity property. Mixed monotonicity allows us to prove global asymptotic stability by embedding the system in a larger system that is monotone.

Controlling a network of signalized intersections from temporal logical specifications

We propose a framework for generating a control policy for a traffic network of signalized intersections to accomplish control objectives expressed in linear temporal logic. Traffic management indeed calls for a rich class of objectives and offers a novel domain for these formal methods tools. We show that traffic networks possess structural properties that allow significant reduction in the time required to compute a finite state abstraction. We further extend our approach to a probabilistic framework by modeling the traffic dynamics as a Markov Decision Process.