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Publication Hierarchical Trajectory Generation for a Class of Nonlinear Systems(2003-12-09) Tabuada, Paulo; Pappas, George JTrajectory generation and motion planning for nonlinear control systems is an important and difficult problem. In this paper, we provide a constructive method for hierarchical trajectory generation and hierarchical motion planning. The approach is based on the recent notion of φ-related control systems. Given a control affine system satisfying certain assumptions, we project the trajectory planning problem onto a φ-related control system of smaller dimension. Trajectories designed for the smaller, abstracted system are guaranteed, by construction, to be feasible for the original system. Constructive procedures are provided for refining trajectories of the coarser system to the more detailed system.Publication Finite Bisimulations of Controllable Linear Systems(2003-12-09) Tabuada, Paulo; Pappas, George JFinite abstractions of infinite state models have been critical in enabling and applying formal and algorithmic verification methods to continuous and hybrid systems. This has triggered the study and characterization of classes of continuous dynamics which can be abstracted by finite transition systems. In this paper, we focus on synthesis rather than analysis. In this spirit, we show that given any discrete-time, linear control system satisfying a generic controllability property, and any finite set of observations restricted to the boolean algebra of Brunovsky sets, a finite bisimulation always exists and can be effectively computed.Publication Geometric Programming Relaxations for Linear System Reachability(2004-06-30) Yazarel, Hakan; Pappas, George JOne of the main obstacles in the safety analysis of continuous and hybrid systems has been the computation of the reachable set for continuous systems in high dimensions. In this paper, we present a novel method that exploits the structure of linear dynamical systems, and the monotonicity of the exponential function in order to obtain safety certificates of continuous linear systems. By over-approximating the sets of initial and final states, the safety verification problem is expressed as a series of geometric programs which can be further transformed into linear programs. This provides the ability to verify the safety properties of high dimensional linear systems with realistic computation times. In addition, our optimization based formulation computes time intervals over which the system is safe and unsafe.Publication From Discrete Specifications to Hybrid Control(2003-12-09) Tabuada, Paulo; Pappas, George JA great challenge for modern systems theory is the design of controllers for continuous systems but with logical specifications. In this paper, we are interested in developing algorithmic methods which given a discrete time controllable linear system and a discrete specification (in the form of a finite transition system or a temporal logic formula), automatically design controllers resulting in desired, closed-loop behavior. This can be achieved using a natural approach involving three steps. In the first step, given a controllable linear system and discrete specification, we extract a finite transition system model which is equivalent (bisimilar) to the continuous system. The second step solves the controller synthesis problem for finite transition systems using well known and well developed algorithms. The third step, which is the focus of this paper, refines the discrete controller of the finite transition system, to a (necessarily) hybrid controller for the original continuous system. The hybrid controller composed with the continuous plant results in a closed-loop hybrid system that, by construction, satisfies the desired, discrete specification.Publication Sensor Network Devolution and Breakdown in Survivor Connectivity(2004-06-27) Kunniyur, Srisankar S; Venkatesh, Santosh SAs batteries fail in wireless sensor networks there is an inevitable devolution of the network characterised by a breakdown in connectivity between the surviving nodes of the network. A sharp limit theorem characterising the time at which this phenomena makes an appearance is derived.Publication Congestion Controllers for High Bandwidth Connections with Fiber Error Rates(2004-06-20) Kavak, Egemen; Kunniyur, Srisankar SThe inefficiency of a TCP connection in the presence of high bandwidth links due to the constant multiplicative decrease factor has been well documented in recent literature. In this paper we look at the effect of fiber error rates on the throughput of a TCP connection. We propose a congestion controller that removes the ill-effects of fiber error rates on TCP throughput by lower bounding the marking probability. We show that this congestion controller can achieve extremely high utilizations in high bandwidth links. We also discuss the TCP friendliness of this congestion controller and present simulation results that validate our analysis.Publication Predicting TCP Throughput From Non-invasive Network Sampling(2002-06-23) Goyal, Mukul; Guérin, Roch A; Rajan, RajuIn this paper, we wish to derive analytic models that predict the performance of TCP flows between specified end-points using routinely observed network characteristics such as loss and delay. The ultimate goal of our approach is to convert network observables into representative user and application relevant performance metrics.The main contributions of this paper are in studying which network performance data sources are most reflective of session characteristics, and then in thoroughly investigating a new TCP model based on [1] that uses non-invasive network samples to predict the throughput of representative TCP flows between given end-points.Publication Aggressive maneuvering of a thrust vectored flying wing: A receding horizon approach(2000-12-12) Hauser, John; Jadbabaie, AliThis paper deals with the control of a thrust vectored flying wing known as the ducted fan, developed at California Institute of Technology. The experiment was developed to serve as a testbed for nonlinear control design. In an earlier paper, the authors reported simulation results based on a simplified (no aerodynamics involved) planar model of the ducted fan around hover position. In this paper we report on the modeling and simulation of the ducted fan in forward flight, where aerodynamic forces and moments can no longer be ignored. A receding horizon scheme is developed to generate trajectories for the forward flight model. Using a more simplified version of the model, some aggressive trajectories are generated. These trajectories are then used as a reference in the receding horizon scheme, and morphed into the trajectories of the full model. Simulation results depict the capabilities of the ducted fan as well as this methodology in performing aggressive maneuvers.Publication A kernel view of the dimensionality reduction of manifolds(2004-07-24) Ham, Ji Hun; Lee, Daniel D; Mika, Sebastian; Schölkopf, BernhardWe interpret several well-known algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithms can be described as kernel PCA on specially constructed Gram matrices, and illustrate the similarities and differences between the algorithms with representative examples.Publication Metamaterials with Negative Permittivity and Permeability: Background, Salient Features, and New Trends(2003-06-08) Engheta, NaderHere we first present a brief background and the history of complex media, in particular the materials with negative permittivity and permeability, and then we discuss some of the salient electromagnetic features of these metamaterials. This is followed by description of some of the ideas regarding potential future applications of these metamaterials in devices and components, along with physical remarks and intuitive justification.