866 research outputs found
Linear Control Theory with an ââ Optimality Criterion
This expository paper sets out the principal results in ââ control theory in the context of continuous-time linear systems. The focus is on the mathematical theory rather than computational methods
Polynomial solutions to Hâ problems
The paper presents a polynomial solution to the standard Hâ-optimal control problem. Based on two polynomial J-spectral factorization problems, a parameterization of all suboptimal compensators is obtained. A bound on the McMillan degree of suboptimal compensators is derived and an algorithm is formulated that may be used to solve polynomial J-spectral factorization problems
A fractional representation approach to the robust regulation problem for MIMO systems
The aim of this paper is in developing unifying frequency domain theory for
robust regulation of MIMO systems. The main theoretical results achieved are a
new formulation of the internal model principle, solvability conditions for the
robust regulation problem, and a parametrization of all robustly regulating
controllers. The main results are formulated with minimal assumptions and
without using coprime factorizations thus guaranteeing applicability with a
very general class of systems. In addition to theoretical results, the design
of robust controllers is addressed. The results are illustrated by two examples
involving a delay and a heat equation.Comment: 23 pages, 3 figures, submitted to International Journal of Robust and
Nonlinear Contro
Investigation of practical applications of H infinity control theory to the design of control systems for large space structures
The applicability of H infinity control theory to the problems of large space structures (LSS) control was investigated. A complete evaluation to any technique as a candidate for large space structure control involves analytical evaluation, algorithmic evaluation, evaluation via simulation studies, and experimental evaluation. The results of analytical and algorithmic evaluations are documented. The analytical evaluation involves the determination of the appropriateness of the underlying assumptions inherent in the H infinity theory, the determination of the capability of the H infinity theory to achieve the design goals likely to be imposed on an LSS control design, and the identification of any LSS specific simplifications or complications of the theory. The resuls of the analytical evaluation are presented in the form of a tutorial on the subject of H infinity control theory with the LSS control designer in mind. The algorthmic evaluation of H infinity for LSS control pertains to the identification of general, high level algorithms for effecting the application of H infinity to LSS control problems, the identification of specific, numerically reliable algorithms necessary for a computer implementation of the general algorithms, the recommendation of a flexible software system for implementing the H infinity design steps, and ultimately the actual development of the necessary computer codes. Finally, the state of the art in H infinity applications is summarized with a brief outline of the most promising areas of current research
Finite-time behavior of inner systems
In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller
Parameterization of Stabilizing Linear Coherent Quantum Controllers
This paper is concerned with application of the classical Youla-Ku\v{c}era
parameterization to finding a set of linear coherent quantum controllers that
stabilize a linear quantum plant. The plant and controller are assumed to
represent open quantum harmonic oscillators modelled by linear quantum
stochastic differential equations. The interconnections between the plant and
the controller are assumed to be established through quantum bosonic fields. In
this framework, conditions for the stabilization of a given linear quantum
plant via linear coherent quantum feedback are addressed using a stable
factorization approach. The class of stabilizing quantum controllers is
parameterized in the frequency domain. Also, this approach is used in order to
formulate coherent quantum weighted and control problems for
linear quantum systems in the frequency domain. Finally, a projected gradient
descent scheme is proposed to solve the coherent quantum weighted control
problem.Comment: 11 pages, 4 figures, a version of this paper is to appear in the
Proceedings of the 10th Asian Control Conference, Kota Kinabalu, Malaysia, 31
May - 3 June, 201
A construction of multivariable MRACS with fixed compensator using coprime factorization approach
A multivariable model reference adaptive control system (MRACS) with a fixed compensator is proposed. First, a new two-degree-of-freedom (2DOF) compensator with disturbance estimator is derived. Using this structure, a multivariable MRACS with fixed compensator is constructed. Since the proposed method is based on the 2 DOF structure, the fixed compensator is chosen independently of specifications for reference commands. The boundedness of all signals in the closed-loop system and the convergence of the output error are proved. A design method of the fixed compensator for MRACS with low sensitivity is also given. Finally, numerical examples are illustrated in order to show the effectiveness of the proposed method </p
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