Tensor Product Model Transformation in Polytopic Model-Based Control: 1st Edition (Paperback) book cover

Tensor Product Model Transformation in Polytopic Model-Based Control

1st Edition

By Péter Baranyi, Yeung Yam, Péter Várlaki

CRC Press

262 pages | 73 B/W Illus.

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Description

Tensor Product Model Transformation in Polytopic Model-Based Control offers a new perspective of control system design. Instead of relying solely on the formulation of more effective LMIs, which is the widely adopted approach in existing LMI-related studies, this cutting-edge book calls for a systematic modification and reshaping of the polytopic convex hull to achieve enhanced performance. Varying the convexity of the resulting TP canonical form is a key new feature of the approach. The book concentrates on reducing analytical derivations in the design process, echoing the recent paradigm shift on the acceptance of numerical solution as a valid form of output to control system problems. The salient features of the book include:

  • Presents a new HOSVD-based canonical representation for (qLPV) models that enables trade-offs between approximation accuracy and computation complexity
  • Supports a conceptually new control design methodology by proposing TP model transformation that offers a straightforward way of manipulating different types of convexity to appear in polytopic representation
  • Introduces a numerical transformation that has the advantage of readily accommodating models described by non-conventional modeling and identification approaches, such as neural networks and fuzzy rules
  • Presents a number of practical examples to demonstrate the application of the approach to generate control system design for complex (qLPV) systems and multiple control objectives.

The authors’ approach is based on an extended version of singular value decomposition applicable to hyperdimensional tensors. Under the approach, trade-offs between approximation accuracy and computation complexity can be performed through the singular values to be retained in the process. The use of LMIs enables the incorporation of multiple performance objectives into the control design problem and assurance of a solution via convex optimization if feasible. Tensor Product Model Transformation in Polytopic Model-Based Control includes examples and incorporates MATLAB® Toolbox TPtool. It provides a reference guide for graduate students, researchers, engineers, and practitioners who are dealing with nonlinear systems control applications.

Reviews

"… well written and easily readable. … The examples and applications to 3 Degrees Of Freedom (DOFs) control schemes for helicopters, models for aeroelastic wing sections and models for controlling the behavior of suspension system in heavy trucks are the main strength of the book. … for control engineers with a solid mathematical formation as well as control theorists and even applied mathematicians."

zbMATH 1308 in 2015

"The book provides an introduction to a method that has potential to significantly advance the theory and practice of control system design. The modeling step is frequently the most time-consuming stage of practical control system design. The unifying TP representation of quasi LPV models described in this book has potential to make this stage more efficient as well as enabling many of the powerful LMI-based control design methods for LPV systems to be applied to practical problems."

—James Whidborne, Cranfield University, Bedfordshire, UK

Table of Contents

Introduction

Significant paradigm changes

Current computational methods and Applications

Role of the TP model transformation in control design

Part I: Tensor-product Model Transformation of Linear Parameter Varying Models

Higher Order Singular Value Decomposition of Tensors

Basic concept of tensor algebra

Higher Order Singular Value Decomposition (HOSVD)

Approximation trade-off by HOSVD

HOSVD-based canonical form of Linear Parameter-varying Models

Linear Parameter-Varying state-space model

HOSVD-based canonical form of LPV models

Numerical reconstruction of the HOSVD based canonical form

TP model transformation

Algorithm of the TP model transformation

Example of the TORA benchmark system

Computational relaxed TP model transformation

Column equivalence

Modified TP transformation

Evaluation of complexity reduction

Discretization complexity

Computational load of the HOSVD

Computational load of the tensor product

Numerical examples

A simple example

A more complex example

Convex TP model forms of Linear Parameter-varying Models

Convex TP model

Different types of convex TP models

Computation of different convex TP models

Methods for SN, NN and NO type matrices

Inverse, relaxed and normalized convex TP models (lNO, RNO)

The TORA benchmark example

Approximation and complexity trade-off by the TP model transformation

Approximation theory framework

No-where denseness

Examples

Part II: Control Design Examples

TP model transformation based design

Linear Matrix Inequality in system control design

Parallel Distributed Compensation based control design framework

Immediate link between the TP models and the PDC design framework

TP model transformation based control design methodology

Application to 2-D prototypical aeroelastic wing section with structural nonlinearity

Introduction to the prototypical aeroelastic wing section

Finite element convex TP model of the prototypical aeroelastic wing section

State-feedback control design

Observer based output-feedback control design

Application to 3 DOF helicopter with four propellers

Nomenclature

Equations of Motion of the RC Helicopter Dynamics

Finite element convex TP model of the -3-DOF RC helicopter

Control design of the3-DOF RC helicopter

Control results

Application to Parallel Double Inverted Pendulum

Nomenclature

Equations of Motion of the RC Helicopter Dynamics

Finite element convex TP model of the PDIP

Control design of the PDIP

Control results

About the Authors

Peter Beranyi, Ph.D, D. Sc, is head of the Computer and Automation Research Institute of the Hungarian Academy of Sciences and a professor at the Budapest University of Technology and Economics. He received his D.Sc in Informatics, his Ph.D. in Electrical Engineering, his M.Sc. in Education of Engineering Science, and his M.Sc. in Electrical Engineering at Budapest University of Technology and Economics. His research interest is on LPV- and LMI-based control design, modeling based on TP functions, fuzzy modeling, fuzzy rule interpolation, and calculation complexity reduction of various model types. He has written 48 journal papers for 262 publications.

Yeung Yam, is a professor in the Department of Mechanical and Automation Engineering at the Chinese University of Hong Kong. He obtained his B.Sc. from the Chinese University of Hong Kong, his M.Sc. from the University of Akron, Ohio, USA and his M.Sc., D.Sc. from the Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. He has published over 100 technical papers in various areas of research, including human skill acquisition and analysis, dynamics modeling, control, system identification, fuzzy approximation, and intelligent and autonomous systems.

Peter Valarki, is a professor at the Budapest University of Technology and Economics. He graduated in mechanical engineering in 1971 at the Faculty of Transportation Engineering at the Technical University of Budapest, now the Budapest University of Technology and Economics. He also earned his Ph.D., his C.Sc. and his D.Sc. He is a founding member of the Hungarian Academy of Engineering and the main topics of his research field are the stochastic control theory, statistical system identification, and computational intelligency. He is the co-author of 10 books and more than 250 other scientific and technical publications.

About the Series

Automation and Control Engineering

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Subject Categories

BISAC Subject Codes/Headings:
TEC007000
TECHNOLOGY & ENGINEERING / Electrical
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical