Delay-Adaptive Linear Control

2020 ◽  
Author(s):  
Yang Zhu ◽  
Miroslav Krstic
Keyword(s):  
Nonlinear Differential Equations ◽  
Stability Study ◽  
Delay Systems ◽  
Engineering Practice ◽  
Delay Compensation ◽  
Infinite Dimensional ◽  
Controlled Systems ◽  
Finite Dimensional ◽  
And Control ◽  
Parameter Values

Actuator and sensor delays are among the most common dynamic phenomena in engineering practice, and when disregarded, they render controlled systems unstable. Over the past sixty years, predictor feedback has been a key tool for compensating such delays, but conventional predictor feedback algorithms assume that the delays and other parameters of a given system are known. When incorrect parameter values are used in the predictor, the resulting controller may be as destabilizing as without the delay compensation. This book develops adaptive predictor feedback algorithms equipped with online estimators of unknown delays and other parameters. Such estimators are designed as nonlinear differential equations, which dynamically adjust the parameters of the predictor. The design and analysis of the adaptive predictors involves a Lyapunov stability study of systems whose dimension is infinite, because of the delays, and nonlinear, because of the parameter estimators. This book solves adaptive delay compensation problems for systems with single and multiple inputs/outputs, unknown and distinct delays in different input channels, unknown delay kernels, unknown plant parameters, unmeasurable finite-dimensional plant states, and unmeasurable infinite-dimensional actuator states. Presenting breakthroughs in adaptive control and control of delay systems, the book offers powerful new tools for the control engineer and the mathematician.

Modeling and Control of Acoustic Ducts

2000 ◽  
Vol 123 (1) ◽  
pp. 2-10 ◽  
Author(s):  
H. R. Pota ◽  
A. G. Kelkar
Keyword(s):  
Controller Design ◽  
Parametric Uncertainty ◽  
Theoretical Models ◽  
Unmodeled Dynamics ◽  
Modeling And Control ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Dimensional Models ◽  
And Control ◽  
Acoustic Ducts

This paper presents closed-form mathematical models for an acoustic duct with general boundary conditions. These infinite-dimensional models are derived using symbolic computations. A new method to obtain finite dimensional approximations of infinite-dimensional models using quartic functions is presented. The theoretical models are compared with the experimental data obtained for the KSU duct. The experimental results of a new robust broadband feedback controller, designed using passivity-based techniques, are presented. The controller design is shown to be robust to the unmodeled dynamics and parametric uncertainty.

Reduction of Dimensionality, Dynamic Programming, and Control Processes

1961 ◽  
Vol 83 (1) ◽  
pp. 82-84 ◽  
Author(s):  
Richard Bellman ◽  
Robert Kalaba
Keyword(s):  
Dynamic Programming ◽  
Time Lag ◽  
Successive Approximations ◽  
Time Lags ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Control Processes ◽  
Finite Dimensional ◽  
Finite Set ◽  
And Control

A major difficulty in the way of a successful systematic approach to the study of control processes by way of the theory of dynamic programming is the occurrence of processes having state vectors of high dimension. However difficult the problem is for systems ruled by a finite set of differential equations, it is several orders of magnitude more complex for systems of infinite dimensionality and for systems with time lags. By combining a technique presented earlier for dealing with finite dimensional systems and various methods of successive approximations and quasi-linearization, certain classes of control processes associated with infinite dimensional systems can be treated. The ideas are illustrated by discussing control of a system involving a time lag and control of a thermal system.

scholarly journals Computation of double Hopf points for delay differential equations

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Yingxiang Xu ◽  
Tingting Shi
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Delay Systems ◽  
System Of Equations ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Defining System ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Branch Switching

AbstractRelating to the crucial problem of branch switching, the calculation of codimension 2 bifurcation points is one of the major issues in numerical bifurcation analysis. In this paper, we focus on the double Hopf points for delay differential equations and analyze in detail the corresponding eigenspace, which enable us to obtain the finite dimensional defining system of equations of such points, instead of an infinite dimensional one that happens naturally for delay systems. We show that the double Hopf point, together with the corresponding eigenvalues, eigenvectors and the critical values of the bifurcation parameters, is a regular solution of the finite dimensional defining system of equations, and thus can be obtained numerically through applying the classical iterative methods. We show our theoretical findings by a numerical example.

Active Control of Mechanical Vibrations in a Circular Disk

1992 ◽  
Vol 114 (1) ◽  
pp. 104-112 ◽  
Author(s):  
C. Y. Kuo ◽  
C. C. Huang
Keyword(s):  
Mechanical Vibration ◽  
Circular Disk ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Sensors And Actuators ◽  
Mechanical Vibrations ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Finite Dimensional ◽  
And Control

Mechanical vibration is a common phenomenon observed in the operation of many machines and arises from the inertia effect of machine parts in motion. While many control system design methods for distributed parameter systems have already been proposed in the literature, generally they are either based on truncated models and, as a result, suffer from computational and “spillover” difficulties or require distributed parameter actuators which are rarely available in reality. Therefore, there is a definite need for the development of a class of controllers which can be realized by spatially discrete sensors and actuators and whose design specifically includes stabilization and control of all the higher frequency vibration modes. To address this need, we propose the design of linear compensators whose design is based on root locus arguments for infinite dimensional systems. Since the design is not based on finite dimensional models of the plant to be controlled, we expect it to perform well for those distributed parameter systems for which sufficiently accurate data on pole and zero locations can be obtained. In this paper we apply this approach to control mechanical vibrations in those physical systems which can be accurately modeled as a flexible circular disk. Computer simulation results indicate that all the predominant lower frequency vibrations can be efficiently eliminated by just a few pairs of colocated sensor and actuator.

scholarly journals An FDA-Based Approach for Clustering Elicited Expert Knowledge

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 184-204
Author(s):  
Carlos Barrera-Causil ◽  
Juan Carlos Correa ◽  
Andrew Zamecnik ◽  
Francisco Torres-Avilés ◽  
Fernando Marmolejo-Ramos
Keyword(s):  
Functional Data ◽  
Expert Knowledge ◽  
Probability Distributions ◽  
Knowledge Elicitation ◽  
Parallel Analysis ◽  
Data Sets ◽  
Dimensional Problem ◽  
Prior Distributions ◽  
Infinite Dimensional ◽  
Finite Dimensional

Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile discrepant elicited prior distributions. This paper proposes the parallel analysis of clusters of prior distributions through a hierarchical method for clustering distributions and that can be readily extended to functional data. The proposed method consists of (i) transforming the infinite-dimensional problem into a finite-dimensional one, (ii) using the Hellinger distance to compute the distances between curves and thus (iii) obtaining a hierarchical clustering structure. In a simulation study the proposed method was compared to k-means and agglomerative nesting algorithms and the results showed that the proposed method outperformed those algorithms. Finally, the proposed method is illustrated through an EKE experiment and other functional data sets.

scholarly journals The Farkas lemma of Shimizu, Aiyoshi and Katayama

1985 ◽  
Vol 31 (3) ◽  
pp. 445-450 ◽  
Author(s):  
Charles Swartz
Keyword(s):  
Convex Programming ◽  
Infinite Dimensional ◽  
Farkas Lemma ◽  
Finite Dimensional

Shimizu, Aiyoshi and Katayama have recently given a finite dimensional generalization of the classical Farkas Lemma. In this note we show that a result of Pshenichnyi on convex programming can be used to give a generalization of the result of Shimizu, Aiyoshi and Katayama to infinite dimensional spaces. A generalized Farkas Lemma of Glover is also obtained.

Sign in / Sign up

Export Citation Format

Share Document