State Space Formulas for Coprime Factorization

In this paper we will give a uniform approach to the derivation of state space formulas of coprime factorizations, of different types, for rational matrix functions

A refinement of the generalized chordal distance

For single input single output systems, we give a refinement of the generalized chordal metric. Our metric is given in terms of coprime factorizations, but it coincides with the extension of Vinnicombe's nu-metric given in earlier work by Ball and Sasane if the coprime factorizations happens to be normalized. The advantage of the metric introduced in this article is its easy computability (since it relies only on coprime factorizations, and does not require normalized coprime factorizations). We also give concrete formulations of our abstract metric for standard classes of stable transfer functions.Comment: 13 page

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 $H_2$ and $H_\infty$ control problems for linear quantum systems in the frequency domain. Finally, a projected gradient descent scheme is proposed to solve the coherent quantum weighted $H_2$ 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

Observer theory

AbstractThe paper is devoted to a comprehensive exposition of the theory of partial state observers in the state space context and the elucidation of the connection between this theory and the theory of observers in the behavioral context, as developed in Valcher and Willems [1999]. For this we use several techniques, including geometric control theory, polynomial and rational models, shift realizations, coprime factorizations, partial realizations and the basic results on behaviors and behavior homomorphisms. A connection between observers and the construction of state maps is made

Optimal Control with Information Pattern Constraints

Despite the abundance of available literature that starts with the seminal paper of Wang and Davison almost forty years ago, when dealing with the problem of decentralized control for linear dynamical systems, one faces a surprising lack of general design methods, implementable via computationally tractable algorithms. This is mainly due to the fact that for decentralized control configurations, the classical control theoretical framework falls short in providing a systematic analysis of the stabilization problem, let alone cope with additional optimality criteria. Recently, a significant leap occurred through the theoretical machinery developed in Rotkowitz and Lall, IEEE-TAC, vol. 51, 2006, pp. 274-286 which unifies and consolidates many previous results, pinpoints certain tractable decentralized control structures, and outlines the most general known class of convex problems in decentralized control. The decentralized setting is modeled via the structured sparsity constraints paradigm, which proves to be a simple and effective way to formalize many decentralized configurations where the controller feature a given sparsity pattern. Rotkowitz and Lall propose a computationally tractable algorithm for the design of H2 optimal, decentralized controllers for linear and time invariant systems, provided that the plant is strongly stabilizable. The method is built on the assumption that the sparsity constraints imposed on the controller satisfy a certain condition (named quadratic invariance) with respect to the plant and that some decentralized, strongly stablizable, stabilizing controller is available beforehand. For this class of decentralized feedback configurations modeled via sparsity constraints, so called quadratically invariant, we provided complete solutions to several open problems. Firstly, the strong stabilizability assumption was removed via the so called coordinate free parametrization of all, sparsity constrained controllers. Next we have addressed the unsolved problem of stabilizability/stabilization via sparse controllers, using a particular form of the celebrated Youla parametrization. Finally, a new result related to the optimal disturbance attenuation problem in the presence of stable plant perturbations is presented. This result is also valid for quadratically invariant, decentralized feedback configurations. Each result provides a computational, numerically tractable algorithm which is meaningful in the synthesis of sparsity constrained optimal controllers