Analysis, estimation and control for perturbed and singular systems for systems subject to discrete events.

"The principle investigator for this effort is Professor Alan S. Willsky, and Professor George C. Verghese is co-principal investigator."--P. [3].Includes bibliographical references (p. [20]-[25]).Final technical report for grant AFOSR-88-0032.Supported by the AFOSR. AFOSR-88-003

On Stability and Stabilization of Hybrid Systems

The thesis addresses the stability, input-to-state stability (ISS), and stabilization problems for deterministic and stochastic hybrid systems with and without time delay. The stabilization problem is achieved by reliable, state feedback controllers, i.e., controllers experience possible faulty in actuators and/or sensors. The contribution of this thesis is presented in three main parts. Firstly, a class of switched systems with time-varying norm-bounded parametric uncertainties in the system states and an external time-varying, bounded input is addressed. The problems of ISS and stabilization by a robust reliable $H_{\infty}$ control are established by using multiple Lyapunov function technique along with the average dwell-time approach. Then, these results are further extended to include time delay in the system states, and delay systems subject to impulsive effects. In the latter two results, Razumikhin technique in which Lyapunov function, but not functional, is used to investigate the qualitative properties. Secondly, the problem of designing a decentralized, robust reliable control for deterministic impulsive large-scale systems with admissible uncertainties in the system states to guarantee exponential stability is investigated. Then, reliable observers are also considered to estimate the states of the same system. Furthermore, a time-delayed large-scale impulsive system undergoing stochastic noise is addressed and the problems of stability and stabilization are investigated. The stabilization is achieved by two approaches, namely a set of decentralized reliable controllers, and impulses. Thirdly, a class of switched singularly perturbed systems (or systems with different time scales) is also considered. Due to the dominant behaviour of the slow subsystem, the stabilization of the full system is achieved through the slow subsystem. This approach results in reducing some unnecessary sufficient conditions on the fast subsystem. In fact, the singular system is viewed as a large-scale system that is decomposed into isolated, low order subsystems, slow and fast, and the rest is treated as interconnection. Multiple Lyapunov functions and average dwell-time switching signal approach are used to establish the stability and stabilization. Moreover, switched singularly perturbed systems with time-delay in the slow system are considered

Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

Issued as Progress report, and Final report, Project no. E-21-67

Health Monitoring of Nonlinear Systems with Application to Gas Turbine Engines

Health monitoring and prognosis of nonlinear systems is mainly concerned with system health tracking and its evolution prediction to future time horizons. Estimation and prediction schemes constitute as principal components of any health monitoring framework. In this thesis, the main focus is on development of novel health monitoring techniques for nonlinear dynamical systems by utilizing model-based and hybrid prognosis and health monitoring approaches. First, given the fact that particle filters (PF) are known as a powerful tool for performing state and parameter estimation of nonlinear dynamical systems, a novel dual estimation methodology is developed for both time-varying parameters and states of a nonlinear stochastic system based on the prediction error (PE) concept and the particle filtering scheme. Estimation of system parameters along with the states generate an updated model that can be used for a long-term prediction problem. Next, an improved particle filtering-based methodology is developed to address the prediction step within the developed health monitoring framework. In this method, an observation forecasting scheme is developed to extend the system observation profiles (as time-series) to future time horizons. Particles are then propagated to future time instants according to a resampling algorithm in the prediction step. The uncertainty in the long-term prediction of the system states and parameters are managed by utilizing dynamic linear models (DLM) for development of an observation forecasting scheme. A novel hybrid architecture is then proposed to develop prognosis and health monitoring methodologies for nonlinear systems by integration of model-based and computationally intelligent-based techniques. Our proposed hybrid health monitoring methodology is constructed based on a framework that is not dependent on the structure of the neural network model utilized in the implementation of the observation forecasting scheme. Moreover, changing the neural network model structure in this framework does not significantly affect the prediction accuracy of the entire health prediction algorithm. Finally, a method for formulation of health monitoring problems of dynamical systems through a two-time scale decomposition is introduced. For this methodology the system dynamical equations as well as the affected damage model, are investigated in the two-time scale system health estimation and prediction steps. A two-time scale filtering approach is developed based on the ensemble Kalman filtering (EnKF) methodology by taking advantage of the model reduction concept. The performance of the proposed two-time scale ensemble Kalman filters is shown to be more accurate and less computationally intensive as compared to the well-known particle filtering approach for this class of nonlinear systems. All of our developed methods have been applied for health monitoring and prognosis of a gas turbine engine when it is affected by various degradation damages. Extensive comparative studies are also conducted to validate and demonstrate the advantages and capabilities of our proposed frameworks and methodologies

Stochastic stability research for complex power systems

Bibliography: p. 302-311."November 1980." "Midterm report ... ."U.S. Dept. of Energy Contract ET-76-A-01-2295Tobias A. Trygar

Numerical Computation, Data Analysis and Software in Mathematics and Engineering

The present book contains 14 articles that were accepted for publication in the Special Issue “Numerical Computation, Data Analysis and Software in Mathematics and Engineering” of the MDPI journal Mathematics. The topics of these articles include the aspects of the meshless method, numerical simulation, mathematical models, deep learning and data analysis. Meshless methods, such as the improved element-free Galerkin method, the dimension-splitting, interpolating, moving, least-squares method, the dimension-splitting, generalized, interpolating, element-free Galerkin method and the improved interpolating, complex variable, element-free Galerkin method, are presented. Some complicated problems, such as tge cold roll-forming process, ceramsite compound insulation block, crack propagation and heavy-haul railway tunnel with defects, are numerically analyzed. Mathematical models, such as the lattice hydrodynamic model, extended car-following model and smart helmet-based PLS-BPNN error compensation model, are proposed. The use of the deep learning approach to predict the mechanical properties of single-network hydrogel is presented, and data analysis for land leasing is discussed. This book will be interesting and useful for those working in the meshless method, numerical simulation, mathematical model, deep learning and data analysis fields

Design, Construction and Control of a Quadrotor Helicopter Using a New Multirate Technique

This thesis describes the design, development, analysis and control of an autonomous Quadrotor Uninhabited Aerial Vehicle (UAV) that is controlled using a novel approach for multirate sampled-data systems. This technique uses three feedback loops: one loop for attitude, another for velocity and a third loop for position, yielding a piece-wise affine system. Appropriate control actions are also computed at different rates. It is shown that this technique improve the system's stability under sampling rates that are significantly lower than the ones required with more classical approaches. The control strategy, that uses sensor data that is sampled at different rates in different nodes of a network, is also applied to a ground wheeled vehicle. Simulations and experiments show very smooth tracking of set-points and trajectories at a very low sampling frequency, which is the main advantage of the new technique