Dissipative Deep Neural Dynamical Systems

In this paper, we provide sufficient conditions for dissipativity and local asymptotic stability of discrete-time dynamical systems parametrized by deep neural networks. We leverage the representation of neural networks as pointwise affine maps, thus exposing their local linear operators and making them accessible to classical system analytic and design methods. This allows us to "crack open the black box" of the neural dynamical system's behavior by evaluating their dissipativity, and estimating their stationary points and state-space partitioning. We relate the norms of these local linear operators to the energy stored in the dissipative system with supply rates represented by their aggregate bias terms. Empirically, we analyze the variance in dynamical behavior and eigenvalue spectra of these local linear operators with varying weight factorizations, activation functions, bias terms, and depths.Comment: Under review at IEEE Open Journal of Control System

Data-guided Estimation and Tracking Methods for Unmanned Aerial Vehicles

Thesis (Ph.D.)--University of Washington, 2019Autonomous aerial robots provide new possibilities to study interesting phenomena and offer a unique vantage point for many surveillance and tracking tasks. Tracking a rogue or an unknown target is an important task in which an agent typically adopts a reactive strategy to the changes reflected in the target observations. As these aerial vehicles increasingly share airspace with fixed wing commercial airplanes, it has become critical to establish reliable, high quality tracking strategies. This work seeks to leverage the concepts of modern control theory, statistics and reinforcement learning to enhance traditional tracking control design strategies to achieve improved tracking performance. A data-guided approach is proposed which shows that embedding observation data in to the control loop improves tracking performance for certain classes of target systems. A comparative study of model-based and model-free approaches for tracking is presented in which an agent, guided by vision-based sensors, directly learns an optimal policy to track the unknown reference trajectory. In addition, a distributed framework is developed in which multiple agents perform consensus on the learned parameters to improve tracking accuracy. Numerical simulations are presented to validate this data-guided tracking scheme for a single agent and a network of agents