# A mathematical formulation of the SCOLE control problem.

Publisher: National Aeronautics and Space Administration, Langley Research Center in Hampton, Virginia

Written in English

## Subjects:

- Differential equations.

## Edition Notes

Statement | A.V. Balakrishnan. |

Series | NASA contractor report -- 172581., NASA contractor report -- NASA CR-172581. |

Contributions | Langley Research Center. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL15276883M |

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## A mathematical formulation of the SCOLE control problem. by A. V. Balakrishnan Download PDF EPUB FB2

In particular, it is possible to solve in closed form the associated infinite-dimensional steady-state Riccati equations. The SCOLE model involves associated partial differential equations in a single space variable, but the compensator design theory developed is far more general since it is given in the abstract wave equation : A.

Balakrishnan. Get this from a library. A mathematical formulation of the SCOLE control problem. Part 1. [A V Balakrishnan; Langley Research Center.]. A mathematical formulation of the SCOLE control problem in terms of a continuous model described by partial differential equations with delta functions on the boundary is presented along with three techniques of solution.

The abstract wave equation approach leads immediately to a linear feedback law that can ensure (strong) : A. Balakrishnan. A mathematical formulation of the SCOLE control problem. Part II, Optimal compensator design.

INTRODUCTION The problem of modeling and control of large flexible spacecraft has been a subject of considerable research in recent years.

A mathematical formulation of the SCOLE control problem. book These spacecraft would consist of a rigid bus and several flexible appendages, such as long beams, solar panels, antenna etc. Flexibility of various components of the spacecraft introduces many unforeseen complexities in the process of system modeling and controller by: Space Shuttle Global Asymptotic Stability Compact Resolvent Picard Iteration Linear Feedback Control These keywords were added by machine and not by the authors.

This process is experimental and the keywords may be updated as the learning algorithm by: 2. Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume ) Abstract We establish strong stability for a class of nonlinear boundary feedback controllers using an abstract wave-equation formulation of a beam stabilization problem arising in the control of flexible structures in by: 1.

A mathematical formulation and efficient heuristics for the dynamic container relocation problem Article in Naval Research Logistics 61(2) March with Reads How we measure 'reads'. Control Problem Formulation Given the DPS as defined in (), it is desired to find a finite dimensional controller so that the output y(t) follows a desirable output trajectory Ym(t).Author: H.

Kaufman, M. Balas, D. Minnick, A. Musalem. Mathematical Modelling in Systems Biology: An Introduction Brian Ingalls What this book aims to achieve Mathematical modelling is becoming an increasingly valuable tool for molecular cell biology.

Con-sequently, it is important for life scientists to have a background in the relevant mathematical tech- Metabolic Control Analysis File Size: 5MB. Get this from a library. A mathematical formulation of the SCOLE control problem. Part II, Optimal compensator design. [A V Balakrishnan; Langley Research Center.].

A MATHEMATICAL FORMULATION OF TIlE SCOLE CONTROL PROBLEM, PART It: OPTIMAL COMPENSATOR DESIGN I. Introduction In this report we conclude the study initiated in Part I [I] and go on to consider optimal feedback control (compensator) design for stability augmentation, t_owing the mathema-tical formulation developed in Part 1.

This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years at the International School for Advanced Studies, Trieste, s: 2.

IEEE Trans. autom. Control AC, (). Balakrishnan, A mathematical formulation of the SCOLE control problem. NASA ReportLangley Research Center, Va (). Greensite, Analysis and Design of Sapce Vehicle Flight Control Systems. Spartan Books, New York ().

2 Mathematical formulation We consider a stochastic control problem with ﬁnite time horizon Ton a probability space (;F;P) with a ﬁltration F 0 ˆF 1 ˆˆF T = F. Throughout the paper we adopt the convention that any variable indexed by tis F t-measurable. We use s t2S tˆRmto denote the state variable, where S t is the set of potential states.

A mathematical problem and a Spacecraft Control Laboratory Experiment (SCOLE) used to evaluate control laws for flexible spacecraft. NASA/IEEE design challenge Article. Model reference controllers Lave been developed for distributed parameter systems (DPS) and applied to the SCCLE roll beam, mode.

equation. When the true partial eifferential. equation representation is used, the resulting control is finite dimensional but defined by an, infinite series which must be trurcatec for application.

when a large but finite dimensional approximation to the DPS is. In this article, a preliminary formulation of large space structures and their stabilization is considered.

The system consists of a (rigid) massive body and flexible configurations that consist of several beams, forming the space structure. The rigid body is located at the center of the space structure and may play the role of experimental modules.

A complete dynamics of the system has been. problems for which mathematical programming has had most impact; and indicate how other techniques can be integrated with mathematical-programming models.

The remainder of the chapter concentrates on mathematical programming itself in terms of problem formulation and implementation, including the role of the computer. DaeBuilder class The DaeBuilder class in CasADi is an auxiliary class intended to facilitate the modeling complex dynamical systems for later use with optimal control algorithms.

This class can be seen as a low-level alternative to a physical modeling language such as Modelica (cf. Section ), while still being higher level than working directly with CasADi symbolic expressions. A mathematical formulation of the SCOLE control problem. Part II, Optimal compensator design [microform] Applied network optimization / Christoph Mandl; Hypersonic vehicle trajectory optimization and control [microform]: final report, grant number--NAG 1 1.

The aim of this book is to present a rigorous phenomenological and mathematical formulation of sedimentation processes and to show how this theory can be applied to the design and control of continuous thickeners. The book is directed to stu dents and researchers in applied mathematics and engineering sciences, especially in metallurgical.

Mathematical modeling is a principled activity that has both principles behind it and methods that can be successfully applied.

The principles are over-arching or meta-principles phrased as questions about the intentions and purposes of mathematical modeling.

These meta-principles are. Mathematical Modelling in Systems Biology: An Introduction Brian Ingalls What this book aims to achieve Mathematical modelling is becoming an increasingly valuable tool for molecular cell biology. Con-sequently, it is important for life scientists to have a background in the relevant mathematical tech- Metabolic Control Analysis.