Polynomial Methods in Optimal Control and Filtering
This book aims to demonstrate the power and breadth of polynomial methods in the control of engineering systems and the filtering of signals. Using commissioned contributions from renowned international specialists, the book progresses logically from the necessary background material (given at a tutorial level), through recent theoretical and practical developments, to detailed presentation of numerical algorithms.
Inspec keywords: control system synthesis; eigenstructure assignment; linear quadratic control; polynomial approximation; selfadjusting systems; H∞ control; matrix decomposition; linear systems; state feedback; adaptive control
Other keywords: LQ controller design; Jspectral factorisation; H∞ filtering; algebraic approach; selftuning control; optimal filtering; state feedback; eigenstructure assignment; control system design; polynomial method; linear system
Subjects: Control system analysis and synthesis methods; Optimal control; Selfadjusting control systems; Linear algebra (numerical analysis); General and management topics; Interpolation and function approximation (numerical analysis)
 Book DOI: 10.1049/PBCE049E
 Chapter DOI: 10.1049/PBCE049E
 ISBN: 9780863412950
 eISBN: 9781849193467
 Page count: 328
 Format: PDF

Front Matter
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1 The Algebraic Approach to Control System Design
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This chapter discusses algebraic approach to control system synthesis. The algebraic approach was the case of time varying linear systems. This approach is also needed to study infinitedimensional linear systems.

2 H_{2} Control Problems
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This chapter discusses H_{2} optimal controllers for multivariable plants. The basic regulator problem has been studied using a time domain approach in the statespace and a frequency domain approach using transfer function matrices and WienerHopf theory.

3 LQ Controller Design and Selftuning Control
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This chapter discusses LQ controller design and selftuning control for discrete time systems. A novel variational technique, for deriving polynomial equations for LQG controller design.

4 Mixed H_{2}/H_{∞} Stochastic Tracking and Servo Problems
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In this chapter two special problems of mixed H_{2}/H_{∞} control have been presented. The corresponding twodegreesoffreedom controller is made up by a feedforward part solving the underlying H_{∞} mixed sensitivity problem and by a feedforward part that can be carried out independently by solving an H_{2}norm optimization problem.

5 Optimal Filtering Problems
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This chapter discusses the power and utility of the polynomial approach in the area of signal processing and communications. Minimisation of meansquare error criteria by linear filters will be considered. We shall focus on the optimisation of realisable discretetime IIRfilters, to be used for prediction, filtering or smoothing of signals. Stochastic models of possibly complex valued signals are assumed known.

6 H_{∞} Filtering
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The following chapter discusses H_{∞} filtering. The solution of the H_{∞} filtering problem was obtained in polynomial system form. The H_{∞} filter was first proposed by Grimble for use in a range of signal processing problems. The filter enables the power spectrum of the estimation error to be reduced to lower values in chosen frequency ranges than is possible with any other filter.

7 nD Polynomial Equations
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This chapter provides useful tools for control and filter design in 2D and nD systems. Linear equations in scalar nD polynomials has been surveyed from both theoretical and computational point of view.

8 Eigenstructure Assignment in Linear Systems by State Feedback
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This chapter discusses eigenstructure assignment in linear systems by state feedback. Assignment of invariant factors in linear systems has been intensively studied in control theory for more than two decades since it is of great importance in many areas of this theory. For instance, such classical tasks as linear quadratic control and deadbeat control lead to specific requirements for poles placement of closedloop systems.

9 Polynomial Equations, Conjugacy and Symmetry
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This chapter discusses the fundamental notions on polynomial algebra and polynomial equations which are used in control theory. Specially mentioned are operations of conjugacy.

10 JSpectral Factorisation
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This chapter surveys several existing methods for the Jspectral factorisation of a polynomial paraHermitian matrix Z with real coefficients. A polynomial matrix Z is said to be paraHermitian if Z* = Z, where the polynomial matrix Z* is the adjoint of Z, defined by Z(s)Zτ(s).

Back Matter
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