Nuno C. Martins

Waseem A. Malik, Nuno C. Martins, Ananthram Swami

We consider the centralized detection of an intruder, whose location is modeled as uniform across a specified set of points, using an optimally placed team of sensors. These sensors make conditionally independent observations. The local detectors at the sensors are also assumed to be identical, with detection probability $(P_{_{D}})$ and false alarm probability $(P_{_{F}})$. We formulate the problem as an N-ary hypothesis testing problem, jointly optimizing the sensor placement and detection policies at the fusion center. We prove that uniform sensor placement is never strictly optimal when the number of sensors $(M)$ equals the number of placement points $(N)$. We prove that for $N_{2} > N_{1} > M$, where $N_{1},N_{2}$ are number of placement points, the framework utilizing $M$ sensors and $N_{1}$ placement points has the same optimal placement structure as the one utilizing $M$ sensors and $N_{2}$ placement points. For $M\leq 5$ and for fixed $P_{_{D}}$, increasing $P_{_{F}}$ leads to optimal placements that are higher in the majorization-based placement scale. Similarly for $M\leq 5$ and for fixed $P_{_{F}}$, increasing $P_{_{D}}$ leads to optimal placements that are higher in the majorization-based placement scale. For $M>5$, this result does not necessarily hold and we provide a simple counterexample. It is conjectured that the set of optimal placements for a given $(M,N)$ can always be placed on a majorization-based placement scale.

Serban Sabau, Nuno C. Martins

Consider that a linear time-invariant (LTI) plant is given and that we wish to design a stabilizing controller for it. Admissible controllers are LTI and must comply with a pre-selected sparsity pattern. The sparsity pattern is assumed to be quadratically invariant (QI) with respect to the plant, which, from prior results, guarantees that there is a convex parametrization of all admissible stabilizing controllers provided that an initial admissible stable stabilizing controller is provided. This paper addresses the previously unsolved problem of determining necessary and sufficient conditions for the existence of an admissible stabilizing controller. The main idea is to cast the existence of such a controller as the feasibility of an exact model-matching problem with stability restrictions, which can be tackled using existing methods. Furthermore, we show that, when it exists, the solution of the model-matching problem can be used to compute an admissible stabilizing controller. This method also leads to a convex parametrization that may be viewed as an extension of Youla's classical approach so as to incorporate sparsity constraints. Applications of this parametrization on the design of norm-optimal controllers via convex methods are also explored. An illustrative example is provided, and a special case is discussed for which the exact model matching problem has a unique and easily computable solution.

Eduardo Arvelo, Nuno C. Martins

This paper focuses on the design of time-invariant memoryless control policies for fully observed controlled Markov chains, with a finite state space. Safety constraints are imposed through a pre-selected set of forbidden states. A state is qualified as safe if it is not a forbidden state and the probability of it transitioning to a forbidden state is zero. The main objective is to obtain control policies whose closed loop generates the maximal set of safe recurrent states, which may include multiple recurrent classes. A design method is proposed that relies on a finitely parametrized convex program inspired on entropy maximization principles. A numerical example is provided and the adoption of additional constraints is discussed.

David Ward, Nuno C. Martins

Consider a discrete-time remote estimation system formed by an encoder, a transmission policy, a channel, and a remote estimator. The encoder assesses a random process that the remote estimator seeks to estimate based on information sent to it by the encoder via the channel. The channel is affected by Bernoulli drops. The instantaneous probability of a drop is governed by a finite state machine (FSM). The state of the FSM is denoted as the channel state. At each time step, the encoder decides whether to attempt a transmission through the packet-drop link. The sequence of encoder decisions is the input to the FSM. This paper seeks to design an encoder, transmission policy and remote estimator that minimize a finite-horizon mean squared error cost. We present two structural results. The first result in which we assume that the process to be estimated is white and Gaussian, we show that there is an optimal transmission policy governed by a threshold on the estimation error. The second result characterizes optimal symmetric transmission policies for the case when the measured process is the state of a scalar linear time-invariant plant driven by white Gaussian noise. Use-dependent packet-drop channels can be used to quantify the effect of transmission on channel quality when the encoder is powered by energy harvesting. An application to a mixed initiative system in which a human operator performs visual search tasks is also presented.

Eduardo Arvelo, Nuno C. Martins

We propose a receding horizon control strategy that readily handles systems that exhibit interval-wise total energy constraints on the input control sequence. The approach is based on a variable optimization horizon length and contractive final state constraint sets. The optimization horizon, which recedes by N steps every N steps, is the key to accommodate the interval-wise total energy constraints. The varying optimization horizon along with the contractive constraints are used to achieve analytic asymptotic stability of the system under the proposed scheme. The strategy is demonstrated by simulation examples.

Semih Kara, Yasin Sonmez, Can Kizilkale et al.

Growing EV adoption can worsen traffic conditions if chargers are sited without regard to their impact on congestion. We study how to strategically place EV chargers to reduce congestion using two equilibrium models: one based on congestion games and one based on an atomic queueing simulation. We apply both models within a scalable greedy station-placement algorithm. Experiments show that this greedy scheme yields optimal or near-optimal congestion outcomes in realistic networks, even though global optimality is not guaranteed as we show with a counterexample. We also show that the queueing-based approach yields more realistic results than the congestion-game model, and we present a unified methodology that calibrates congestion delays from queue simulation and solves equilibrium in link-space.

Eduardo Arvelo, Eric Kim, Nuno C. Martins

This paper deals with the design of time-invariant memoryless control policies for robots that move in a finite two- dimensional lattice and are tasked with persistent surveillance of an area in which there are forbidden regions. We model each robot as a controlled Markov chain whose state comprises its position in the lattice and the direction of motion. The goal is to find the minimum number of robots and an associated time-invariant memoryless control policy that guarantees that the largest number of states are persistently surveilled without ever visiting a forbidden state. We propose a design method that relies on a finitely parametrized convex program inspired by entropy maximization principles. Numerical examples are provided.