# Constrained Control of Uncertain, Time-Varying, Discrete-Time Systems

## An Interpolation-Based Approach

• Interpolating control methods detailed provide a computationally simpler alternative to the popular model predictive control especially for high-order and uncertain systems

• Reinforces the reader’s learning and understanding of the methods described using many worked examples for imitation and repetition

• Facilitates readers’ solution of their own application problems by providing a library of MATLAB® script files which can be used and adapted for the purpose

Book

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 451)

1. Front Matter
Pages I-XIV
2. Hoai-Nam Nguyen
Pages 1-3
3. ### Background

1. Front Matter
Pages 5-5
2. Hoai-Nam Nguyen
Pages 7-42
3. Hoai-Nam Nguyen
Pages 43-64
4. ### Interpolating Control

1. Front Matter
Pages 65-65
2. Hoai-Nam Nguyen
Pages 67-114
3. Hoai-Nam Nguyen
Pages 115-158
4. Hoai-Nam Nguyen
Pages 159-170
5. ### Applications

1. Front Matter
Pages 171-171
2. Hoai-Nam Nguyen
Pages 173-179
3. Hoai-Nam Nguyen
Pages 181-187
6. Back Matter
Pages 189-196

### Introduction

A comprehensive development of interpolating control, this monograph demonstrates the reduced computational complexity of a ground-breaking technique compared with the established model predictive control. The text deals with the regulation problem for linear, time-invariant, discrete-time uncertain dynamical systems having polyhedral state and control constraints, with and without disturbances, and under state or output feedback. For output feedback a non-minimal state-space representation is used with old inputs and outputs as state variables.

Constrained Control of Uncertain, Time-Varying, Discrete-time Systems details interpolating control in both its implicit and explicit forms. In the former at most two linear-programming or one quadratic-programming problem are solved on-line at each sampling instant to yield the value of the control variable. In the latter the control law is shown to be piecewise affine in the state, and so the state space is partitioned into polyhedral cells so that at each sampling interval the cell to which the measured state belongs must be determined. Interpolation is performed between vertex control, and a user-chosen control law in its maximal admissible set surrounding the origin.

Novel proofs of recursive feasibility and asymptotic stability of the vertex control law, and of the interpolating control law are given. Algorithms for implicit and explicit interpolating control are presented in such a way that the reader may easily realize them. Each chapter includes illustrative examples, and comparisons with model predictive control in which the disparity in computational complexity is shown to be particularly in favour of interpolating control for high-order systems, and systems with uncertainty. Furthermore, the performance of the two methods proves similar except in those cases when a solution cannot be found with model predictive control at all. The book concludes with two high dimensional examples and a benchmark robust model predictive control problem: the non-isothermal continuously-stirred-tank reactor.

For academic control researchers and students or for control engineers interested in implementing constrained control systems Constrained Control of Uncertain, Time-Varying, Discrete-time Systems will provide an attractive low-complexity control alternative for cases in which model predictive control is currently attempted.

### Keywords

Constrained Systems Interpolating Control Model Predictive Control Set Invariance Time-varying Systems Uncertain Linear Systems Vertex Control

#### Authors and affiliations

1. 1.Technion—Israel Institute of TechnologyHaifaIsrael

### Bibliographic information

• Book Title Constrained Control of Uncertain, Time-Varying, Discrete-Time Systems
• Book Subtitle An Interpolation-Based Approach
• Authors Hoai-Nam Nguyen
• Series Title Lecture Notes in Control and Information Sciences
• Series Abbreviated Title Lect. Notes Control
• DOI https://doi.org/10.1007/978-3-319-02827-9
• Copyright Information Springer International Publishing Switzerland 2014
• Publisher Name Springer, Cham
• eBook Packages Engineering Engineering (R0)
• Softcover ISBN 978-3-319-02826-2
• eBook ISBN 978-3-319-02827-9
• Series ISSN 0170-8643
• Series E-ISSN 1610-7411
• Edition Number 1
• Number of Pages XIV, 196
• Number of Illustrations 97 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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## Reviews

From the book reviews:

“The aim of this book is to propose an alternative approach to the model predictive control. The book consist of three parts: background, interpolating control and applications. … Each chapter includes interesting illustrative examples. The book is addressed to graduate students and scientists in control systems theory.” (Tadeusz Kaczorek, zbMATH, Vol. 1301, 2015)