Bundle-based pruning in the max-plus curse of dimensionality free method

Recently a new class of techniques termed the max-plus curse of dimensionality-free methods have been developed to solve nonlinear optimal control problems. In these methods the discretization in state space is avoided by using a max-plus basis expansion of the value function. This requires storing only the coefficients of the basis functions used for representation. However, the number of basis functions grows exponentially with respect to the number of time steps of propagation to the time horizon of the control problem. This so called "curse of complexity" can be managed by applying a pruning procedure which selects the subset of basis functions that contribute most to the approximation of the value function. The pruning procedures described thus far in the literature rely on the solution of a sequence of high dimensional optimization problems which can become computationally expensive. In this paper we show that if the max-plus basis functions are linear and the region of interest in state space is convex, the pruning problem can be efficiently solved by the bundle method. This approach combining the bundle method and semidefinite formulations is applied to the quantum gate synthesis problem, in which the state space is the special unitary group (which is non-convex). This is based on the observation that the convexification of the unitary group leads to an exact relaxation. The results are studied and validated via examples

Gaze Guidance, Task-Based Eye Movement Prediction, and Real-World Task Inference using Eye Tracking

The ability to predict and guide viewer attention has important applications in computer graphics, image understanding, object detection, visual search and training. Human eye movements provide insight into the cognitive processes involved in task performance and there has been extensive research on what factors guide viewer attention in a scene. It has been shown, for example, that saliency in the image, scene context, and task at hand play significant roles in guiding attention. This dissertation presents and discusses research on visual attention with specific focus on the use of subtle visual cues to guide viewer gaze and the development of algorithms to predict the distribution of gaze about a scene. Specific contributions of this work include: a framework for gaze guidance to enable problem solving and spatial learning, a novel algorithm for task-based eye movement prediction, and a system for real-world task inference using eye tracking. A gaze guidance approach is presented that combines eye tracking with subtle image-space modulations to guide viewer gaze about a scene. Several experiments were conducted using this approach to examine its impact on short-term spatial information recall, task sequencing, training, and password recollection. A model of human visual attention prediction that uses saliency maps, scene feature maps and task-based eye movements to predict regions of interest was also developed. This model was used to automatically select target regions for active gaze guidance to improve search task performance. Finally, we develop a framework for inferring real-world tasks using image features and eye movement data. Overall, this dissertation naturally leads to an overarching framework, that combines all three contributions to provide a continuous feedback system to improve performance on repeated visual search tasks. This research has important applications in data visualization, problem solving, training, and online education

Efficient Desynchronization of Thermostatically Controlled Loads

This paper considers demand side management in smart power grid systems containing significant numbers of thermostatically controlled loads such as air conditioning systems, heat pumps, etc. Recent studies have shown that the overall power consumption of such systems can be regulated up and down centrally by broadcasting small setpoint change commands without significantly impacting consumer comfort. However, sudden simultaneous setpoint changes induce undesirable power consumption oscillations due to sudden synchronization of the on/off cycles of the individual units. In this paper, we present a novel algorithm for counter-acting these unwanted oscillations, which requires neither central management of the individual units nor communication between units. We present a formal proof of convergence of homogeneous populations to desynchronized status, as well as simulations that indicate that the algorithm is able to effectively dampen power consumption oscillations for both homogeneous and heterogeneous populations of thermostatically controlled loads.Comment: 6 pages, 8 Figure

Maximizing concave piecewise affine functions on the unitary group

International audienceWe show that a convex relaxation, introduced by Sridharan, McEneaney, Gu and James to approximate the value function of an optimal controlproblem arising from quantum gate synthesis, is exact. This relaxation appliesto the maximization of a class of concave piecewise affine functions over theunitary grou