Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Ant-Inspired Density Estimation via Random Walks

Many ant species employ distributed population density estimation in applications ranging from quorum sensing [Pra05], to task allocation [Gor99], to appraisal of enemy colony strength [Ada90]. It has been shown that ants estimate density by tracking encounter rates -- the higher the population density, the more often the ants bump into each other [Pra05,GPT93]. We study distributed density estimation from a theoretical perspective. We prove that a group of anonymous agents randomly walking on a grid are able to estimate their density within a small multiplicative error in few steps by measuring their rates of encounter with other agents. Despite dependencies inherent in the fact that nearby agents may collide repeatedly (and, worse, cannot recognize when this happens), our bound nearly matches what would be required to estimate density by independently sampling grid locations. From a biological perspective, our work helps shed light on how ants and other social insects can obtain relatively accurate density estimates via encounter rates. From a technical perspective, our analysis provides new tools for understanding complex dependencies in the collision probabilities of multiple random walks. We bound the strength of these dependencies using $local\ mixing\ properties$ of the underlying graph. Our results extend beyond the grid to more general graphs and we discuss applications to size estimation for social networks and density estimation for robot swarms

Strategies for Scaleable Communication and Coordination in Multi-Agent (UAV) Systems

A system is considered in which agents (UAVs) must cooperatively discover interest-points (i.e., burning trees, geographical features) evolving over a grid. The objective is to locate as many interest-points as possible in the shortest possible time frame. There are two main problems: a control problem, where agents must collectively determine the optimal action, and a communication problem, where agents must share their local states and infer a common global state. Both problems become intractable when the number of agents is large. This survey/concept paper curates a broad selection of work in the literature pointing to a possible solution; a unified control/communication architecture within the framework of reinforcement learning. Two components of this architecture are locally interactive structure in the state-space, and hierarchical multi-level clustering for system-wide communication. The former mitigates the complexity of the control problem and the latter adapts to fundamental throughput constraints in wireless networks. The challenges of applying reinforcement learning to multi-agent systems are discussed. The role of clustering is explored in multi-agent communication. Research directions are suggested to unify these components