Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems

We consider the initial-boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system discontinuously switches between a finite set of modes. The switching system is fairly general in that the system matrix functions as well as the boundary conditions may switch in time. We show how the stability mechanism developed for classical solutions of hyperbolic initial boundary value problems can be generalized to the case in which weaker solutions become necessary due to arbitrary switching. We also provide an explicit dwell-time bound for guaranteeing exponential stability of the switching system when, for each mode, the system is exponentially stable. Our stability conditions only depend on the system parameters and boundary data. These conditions easily generalize to switching systems in the nondiagonal form under a simple commutativity assumption. We present tutorial examples to illustrate the instabilities that can result from switching

A Proof of Kirchhoff's First Law for Hyperbolic Conservation Laws on Networks

Networks are essential models in many applications such as information technology, chemistry, power systems, transportation, neuroscience, and social sciences. In light of such broad applicability, a general theory of dynamical systems on networks may capture shared concepts, and provide a setting for deriving abstract properties. To this end, we develop a calculus for networks modeled as abstract metric spaces and derive an analog of Kirchhoff's first law for hyperbolic conservation laws. In dynamical systems on networks, Kirchhoff's first law connects the study of abstract global objects, and that of a computationally-beneficial edgewise-Euclidean perspective by stating its equivalence. In particular, our results show that hyperbolic conservation laws on networks can be stated without explicit Kirchhoff-type boundary conditions.Comment: 20 pages, 6 figure

Environmental Sensing by Wearable Device for Indoor Activity and Location Estimation

We present results from a set of experiments in this pilot study to investigate the causal influence of user activity on various environmental parameters monitored by occupant carried multi-purpose sensors. Hypotheses with respect to each type of measurements are verified, including temperature, humidity, and light level collected during eight typical activities: sitting in lab / cubicle, indoor walking / running, resting after physical activity, climbing stairs, taking elevators, and outdoor walking. Our main contribution is the development of features for activity and location recognition based on environmental measurements, which exploit location- and activity-specific characteristics and capture the trends resulted from the underlying physiological process. The features are statistically shown to have good separability and are also information-rich. Fusing environmental sensing together with acceleration is shown to achieve classification accuracy as high as 99.13%. For building applications, this study motivates a sensor fusion paradigm for learning individualized activity, location, and environmental preferences for energy management and user comfort.Comment: submitted to the 40th Annual Conference of the IEEE Industrial Electronics Society (IECON