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TitleTensor Product Model Transformation in Polytopic Model-Based Control
File Size4.1 MB
Total Pages264
Table of Contents
                            Tensor Product Model Transformation in Polytopic Model-Based Control
Acronyms and Abbreviations
1 Introduction
	1.1 An overview
	1.2 TP model
	1.3 HOSVD-based computation
	1.4 Convex optimization via LMIs/PDC framework
	1.5 Model convexity and convex hull manipulation
	1.6 Significant paradigm changes
	1.7 Outline of the book
Part I: Tensor Product (TP) Model Formulation
2 TP Model
3 TP Model Transformation
	3.1 Introduction to HOSVD
	3.2 Transformation procedures
	3.3 The extracted model
	3.4 Addition of sampling grid lines
4 TP Canonical Model Form
	4.1 Definition
	4.2 Numerical reconstruction
	4.3 The TORA example
		4.3.1 Equations of motion
		4.3.2 TP canonical model
5 Approximation and Complexity Trade-Off
	5.1 TP model form of bounded order
	5.2 The nowhere dense property
	5.3 Trade-off examples
		5.3.1 A mass-spring-damper system
		5.3.2 A mass-spring-damper system with nonlinear term
	5.4 Trade-off study on the TORA example
6 TP Model Convexity Incorporation
	6.1 TP model convexity
	6.2 Incorporation of convexity conditions
		6.2.1 Incorporating the SN condition
		6.2.2 Incorporating the NN condition
		6.2.3 Incorporating the NO condition
		6.2.4 Incorporating the RNO condition
	6.3 Alternate method for INO and RNO conditions
		6.3.1 The partial algorithm
		6.3.2 The complete algorithm
	6.4 The TORA example
7 Introduction to the TPtool Toolbox
	7.1 Generating the TP canonical model
	7.2 Incorporating convexity conditions
8 Centralized Model Form
	8.1 The centralized model
		8.1.1 Mathematical properties
		8.1.2 Control properties
		8.1.3 Computational advantages
	8.2 Illustrating examples
9 Computational Relaxed TP Model Transformation
	9.1 SVD-based column equivalence
	9.2 Modified transformation algorithm
	9.3 Evaluation of computational reduction
		9.3.1 Discretization complexity
		9.3.2 HOSVD computation
		9.3.3 Tensor product computation
	9.4 Examples
		9.4.1 A simple numerical example
		9.4.2 The double inverted pendulum example
Part II: TP Model-Based Control System Design
10 Overview of TP Model-Based Design Strategy
11 LMI Theorems under the PDC Framework
	11.1 LMIs for control system design
		11.1.1 Definition of LMIs
		11.1.2 Constraints expressed via LMIs
		11.1.3 Generic problems for LMIs
	11.2 LMI optimization under the PDC framework
		11.2.1 Lyapunov stability criteria
		11.2.2 Control design for stability
		11.2.3 Multiobjective control optimization
		11.2.4 Simultaneous observer/controller design
	11.3 TP model-based control design procedures
	11.4 LMI-based control design for the TORA example
		11.4.1 Control specifications
		11.4.2 State feedback control design
		11.4.3 Observer-based output feedback control design
12 Convex Hull Manipulation
	12.1 Nonlinear sensitivity of control solutions
	12.2 Conservativeness of control solutions
Part III: Control Design Examples
13 Control Design with TPtool Toolbox
14 2-D Prototypical Aeroelastic Wing Section with Structural Nonlinearity
	14.1 Dynamics modeling
	14.2 The TP model
	14.3 State feedback control design
		14.3.1 Controller for asymptotic stabilization
		14.3.2 Controller for decay rate control
		14.3.3 Controller for constraint on the control value
		14.3.4 Comparison to other control solutions
	14.4 Observer-based output feedback control design
		14.4.1 An alternative TP model
		14.4.2 Control system design
		14.4.3 Control performance
	14.5 Convex hull manipulation
	14.6 Convex hull geometry
		14.6.1 Effects on LMI-based controller performance
		14.6.2 Effects on LMI-based observer performance
15 3-D Prototypical Aeroelastic Wing Section with Structural Nonlinearity
	15.1 Dynamics modeling
	15.2 The TP model
	15.3 LMI-based output feedback control design
		15.3.1 Controller 1: Asymptotic stabilization
		15.3.2 Controller 2: Constraint on the control value
		15.3.3 Control performance
16 3-DoF Helicopter with Four Propellers
	16.1 Dynamics Modeling
		16.1.1 A simplified model
		16.1.2 Modeling of uncertainty
	16.2 The TP model
	16.3 Control system design
	16.4 Control performance
17 Heavy Vehicle Rollover Prevention Problem
	17.1 Problem introduction
	17.2 A qLPV model for heavy vehicles
	17.3 The TP model
	17.4 Control system design and performance
Document Text Contents
Page 2

Tensor Product
Model Transformation

in Polytopic
Model-Based Control

K10948_FM.indd 1 7/19/13 9:17 AM

Page 132

Part II

TP Model-Based Control
System Design


Page 263


heavy vehicle rollover prevention problem, 214

substitution, 177

TPtool toolbox, control design with, 156


Web site, TPtool toolbox, 7, 83
Weighted interpolation problems, 126


Yaw-roll model, 209, 210, 213

Yaw-roll motion, 8

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