5,150 research outputs found

    Koopman operator-based model reduction for switched-system control of PDEs

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    We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables. A numerical approximation of the Koopman operator therefore yields a linear system for the observation of an autonomous dynamical system. In our approach, by introducing a finite number of constant controls, the dynamic control system is transformed into a set of autonomous systems and the corresponding optimal control problem into a switching time optimization problem. This allows us to replace each of these systems by a K-ROM which can be solved orders of magnitude faster. By this approach, a nonlinear infinite-dimensional control problem is transformed into a low-dimensional linear problem. In situations where the Koopman operator can be computed exactly using Extended Dynamic Mode Decomposition (EDMD), the proposed approach yields optimal control inputs. Furthermore, a recent convergence result for EDMD suggests that the approach can be applied to more complex dynamics as well. To illustrate the results, we consider the 1D Burgers equation and the 2D Navier--Stokes equations. The numerical experiments show remarkable performance concerning both solution times and accuracy.Comment: arXiv admin note: text overlap with arXiv:1801.0641

    Hybrid Optimal Theory and Predictive Control for Power Management in Hybrid Electric Vehicle

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    This paper presents a nonlinear-model based hybrid optimal control technique to compute a suboptimal power-split strategy for power/energy management in a parallel hybrid electric vehicle (PHEV). The power-split strategy is obtained as model predictive control solution to the power management control problem (PMCP) of the PHEV, i.e., to decide upon the power distribution among the internal combustion engine, an electric drive, and other subsystems. A hierarchical control structure of the hybrid vehicle, i.e., supervisory level and local or subsystem level is assumed in this study. The PMCP consists of a dynamical nonlinear model, and a performance index, both of which are formulated for power flows at the supervisory level. The model is described as a bi-modal switched system, consistent with the operating mode of the electric ED. The performance index prescribing the desired behavior penalizes vehicle tracking errors, fuel consumption, and frictional losses, as well as sustaining the battery state of charge (SOC). The power-split strategy is obtained by first creating the embedded optimal control problem (EOCP) from the original bi-modal switched system model with the performance index. Direct collocation is applied to transform the problem into a nonlinear programming problem. A nonlinear predictive control technique (NMPC) in conjunction with a sequential quadratic programming solver is used to compute suboptimal numerical solutions to the PMCP. Methods for approximating the numerical solution to the EOCP with trajectories of the original bi-modal PHEV are also presented in this paper. The usefulness of the approach is illustrated via simulation results on several case studies

    Automatic object detection and tracking in video

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    One ability of the human visual system is the ability to identify and track moving objects. Examples of this can easily be seen in any sporting event. Humans are able to find an object in motion and track its current path and even predict a trajectory based on its current motion. Computer vision systems exist that are able to track an object in video, but usually these systems need to be instructed what the object to track is. As a way to further the work done by these computer vision systems, I present two additions to the work in the form of Adaptive Thresholding, a way to dynamically discover a threshold value of difference images, and a new method of blob tracking to further improve the accuracy of tracking blobs in video

    Calibrating CHIME, A New Radio Interferometer to Probe Dark Energy

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    The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is a transit interferometer currently being built at the Dominion Radio Astrophysical Observatory (DRAO) in Penticton, BC, Canada. We will use CHIME to map neutral hydrogen in the frequency range 400 -- 800\,MHz over half of the sky, producing a measurement of baryon acoustic oscillations (BAO) at redshifts between 0.8 -- 2.5 to probe dark energy. We have deployed a pathfinder version of CHIME that will yield constraints on the BAO power spectrum and provide a test-bed for our calibration scheme. I will discuss the CHIME calibration requirements and describe instrumentation we are developing to meet these requirements

    Selected topics in video coding and computer vision

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    Video applications ranging from multimedia communication to computer vision have been extensively studied in the past decades. However, the emergence of new applications continues to raise questions that are only partially answered by existing techniques. This thesis studies three selected topics related to video: intra prediction in block-based video coding, pedestrian detection and tracking in infrared imagery, and multi-view video alignment.;In the state-of-art video coding standard H.264/AVC, intra prediction is defined on the hierarchical quad-tree based block partitioning structure which fails to exploit the geometric constraint of edges. We propose a geometry-adaptive block partitioning structure and a new intra prediction algorithm named geometry-adaptive intra prediction (GAIP). A new texture prediction algorithm named geometry-adaptive intra displacement prediction (GAIDP) is also developed by extending the original intra displacement prediction (IDP) algorithm with the geometry-adaptive block partitions. Simulations on various test sequences demonstrate that intra coding performance of H.264/AVC can be significantly improved by incorporating the proposed geometry adaptive algorithms.;In recent years, due to the decreasing cost of thermal sensors, pedestrian detection and tracking in infrared imagery has become a topic of interest for night vision and all weather surveillance applications. We propose a novel approach for detecting and tracking pedestrians in infrared imagery based on a layered representation of infrared images. Pedestrians are detected from the foreground layer by a Principle Component Analysis (PCA) based scheme using the appearance cue. To facilitate the task of pedestrian tracking, we formulate the problem of shot segmentation and present a graph matching-based tracking algorithm. Simulations with both OSU Infrared Image Database and WVU Infrared Video Database are reported to demonstrate the accuracy and robustness of our algorithms.;Multi-view video alignment is a process to facilitate the fusion of non-synchronized multi-view video sequences for various applications including automatic video based surveillance and video metrology. In this thesis, we propose an accurate multi-view video alignment algorithm that iteratively aligns two sequences in space and time. To achieve an accurate sub-frame temporal alignment, we generalize the existing phase-correlation algorithm to 3-D case. We also present a novel method to obtain the ground-truth of the temporal alignment by using supplementary audio signals sampled at a much higher rate. The accuracy of our algorithm is verified by simulations using real-world sequences

    Optimization-based Estimation and Control Algorithms for Quadcopter Applications

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    Optimization-based Estimation and Control Algorithms for Quadcopter Applications

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    Time-Delay Switch Attack on Networked Control Systems, Effects and Countermeasures

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    In recent years, the security of networked control systems (NCSs) has been an important challenge for many researchers. Although the security schemes for networked control systems have advanced in the past several years, there have been many acknowledged cyber attacks. As a result, this dissertation proposes the use of a novel time-delay switch (TDS) attack by introducing time delays into the dynamics of NCSs. Such an attack has devastating effects on NCSs if prevention techniques and countermeasures are not considered in the design of these systems. To overcome the stability issue caused by TDS attacks, this dissertation proposes a new detector to track TDS attacks in real time. This method relies on an estimator that will estimate and track time delays introduced by a hacker. Once a detector obtains the maximum tolerable time delay of a plant’s optimal controller (for which the plant remains secure and stable), it issues an alarm signal and directs the system to its alarm state. In the alarm state, the plant operates under the control of an emergency controller that can be local or networked to the plant and remains in this stable mode until the networked control system state is restored. In another effort, this dissertation evaluates different control methods to find out which one is more stable when under a TDS attack than others. Also, a novel, simple and effective controller is proposed to thwart TDS attacks on the sensing loop (SL). The modified controller controls the system under a TDS attack. Also, the time-delay estimator will track time delays introduced by a hacker using a modified model reference-based control with an indirect supervisor and a modified least mean square (LMS) minimization technique. Furthermore, here, the demonstration proves that the cryptographic solutions are ineffective in the recovery from TDS attacks. A cryptography-free TDS recovery (CF-TDSR) communication protocol enhancement is introduced to leverage the adaptive channel redundancy techniques, along with a novel state estimator to detect and assist in the recovery of the destabilizing effects of TDS attacks. The conclusion shows how the CF-TDSR ensures the control stability of linear time invariant systems

    Trajectory optimization and guidance law development for national aerospace plane applications

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    The work completed to date is comprised of the following: a simple vehicle model representative of the aerospace plane concept in the hypersonic flight regime, fuel-optimal climb profiles for the unconstrained and dynamic pressure constrained cases generated using a reduced order dynamic model, an analytic switching condition for transition to rocket powered flight as orbital velocity is approached, simple feedback guidance laws for both the unconstrained and dynamic pressure constrained cases derived via singular perturbation theory and a nonlinear transformation technique, and numerical simulation results for ascent to orbit in the dynamic pressure constrained case
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