Petko H. Petkov

The sensitivity of computational control problems

The article discussed the sensitivity of a certain problems of linear control theory, including pole assignment, full state feedback linear quadratic control and H/sub /spl infin// control. It was demonstrated that the mathematical formulation and the splitting of the problem into subproblems are essential factors in the conditioning of these problems. It was also shown that standard approaches implemented in numerical toolboxes, which present widely accepted approaches in numerical control, may face problems due to ill conditioning. Some of these problems can be avoided by reformulating the problem, but several open problems remain. To assess the accuracy of calculations and to trust numerical results, such condition and accuracy estimates should accompany computational procedures and must be included in the corresponding computer codes. Users must be aware of possible difficulties accompanying the computational process and know how to avoid them. The issues should also become an essential part of the curriculum for scientist and engineers in learning how to use and develop modern computational software.

Perturbation Analysis of Hamiltonian Schur and Block-Schur Forms

In this paper we present a complete perturbation analysis for the Hamiltonian Schur form of a Hamiltonian matrix under similarity transformations with unitary symplectic matrices. Both linear asymptotic and nonlinear perturbation bounds are presented. The same analysis is also carried out for two less condensed block-Schur forms. It suggests that the block forms are less sensitive to perturbations. The analysis is based on the technique of splitting operators and Lyapunov majorants as well as on a representation of the symplectic unitary group which is convenient for perturbation analysis of condensed forms. As a corollary, a perturbation bound for the stable invariant subspace of Hamiltonian matrices is obtained. Finally, given an

μ-Synthesis and Hardware-in-the-loop Simulation of Miniature Helicopter Control System

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Note on Perturbation Theory for Algebraic Riccati Equations

-perturbation in the initial Hamiltonian matrix, the perturbations in the Hamiltonian Schur form, and the unitary symplectic basis are constructed in the form of a power series expansion in

Robust Real-Time Control of a Two-Rotor Aerodynamic System

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THE METHOD OF SPLITTING OPERATORS AND LYAPUNOV MAJORANTS IN PERTURBATION LINEAR ALGEBRA AND CONTROL

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Modeling of Uncertain Systems

The aim of this paper is to describe in detail the μ-synthesis of a miniature helicopter integral attitude controller of high order and to present results from the hardware-in-the-loop simulation of this controller implementing Digital Signal Processor. The μ-controller designed allows to suppress efficiently wind disturbances in the presence of 25 % input multiplicative uncertainty. A simple position controller is added to ensure tracking of the desired trajectory in 3D space. The results from hardware-in-the-loop simulation are close to the results from double-precision simulation of helicopter control system in Simulink®. The software platform developed allows to implement easily different sensors, servoactuators and control laws and to investigate the closed-loop system behavior in presence of different disturbances and parameter variations.

Perturbation Bounds for the Nonlinear Matrix Equation

The expressions for the induced norms of two complex matrix operators, given in [J.-G. Sun, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 39--65], must be corrected. In this note we give the true values of these induced norms, which are involved in the perturbation analysis of matrix algebraic Riccati equations in the complex domain.

Perturbed spectra of defective matrices

Abstract This paper presents the design and experimental evaluation of a two-degree-of-freedom discrete-time µ-controller for a laboratory two-rotor aerodynamic system with ten uncertain parameters. The controller implemented is of 24th order and ensures robust stability and robust performance of the closed-loop sampled-data system. This controller is realized on a PC by using the Real Time Workshop of MATLAB® with a sampling frequency of 100 Hz. The experimental results are close to the results predicted by using the linearized model of the system and highlight many of the difficulties associated with the practical implementation of robust control laws.

Robust Design Specifications

ABSTRACT In this paper we give a survey of recent results as well as new results in perturbation linear algebra and control, based on the method of splitting operators and Lyapunov majorant functions. Combined with the Schauder or Banach fixed point principles, this method allows to obtain rigorous non-local perturbation bounds for a set of important objects in linear algebra and control theory. Among them are the Schur system of a matrix, the QR decomposition of a matrix, the orthogonal canonical forms of a time-invariant linear system, the state and output feedback gains in pole assignment synthesis, the generalized Schur system of a pair of matrices, the polar decomposition of a matrix, the Hamiltonian Schur and Hamiltonian block-Schur forms of Hamiltonian matrices, and others. We also consider some other issues such as perturbation analysis of problems with non-unique solution and construction of improved asymptotic perturbation bounds. An important technique of the method considered is the constructi...