Non-minimal Model Research Articles

A Schur method for balanced-truncation model reduction

It is shown that a not-necessarily-balanced state-space realization of the Moore reduced model can be computed directly without balancing via projections defined in terms of arbitrary bases for the left and right eigenspaces associated with the large eigenvalues of the product PQ of the reachability and controllability Grammians. Two specific methods for computing these bases are proposed, one based on the ordered Schur decomposition of PQ and the other based on the Cholesky factors of P and Q. The algorithms perform reliably even for nonminimal models. >

Persistency of excitation results for structured nonminimal models

It is frequently convenient to use specially structured nonminimal models for parameter estimation such as in the case of direct adaptive control where the model is parameterized in terms of the desired control law parameters. This is done, for example, in direct model reference adaptive control and in direct pole assignment adaptive control algorithms. It is shown that the parameters appearing in these nonminimal models can be uniquely estimated if and only if a certain design identity has a unique solution. The result is used to develop persistency of excitation results for these models.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Remarks on persistency of excitation for nonminimal models of systems having purely deterministic disturbances

A persistency of excitation result for nonminimal models of systems having purely deterministic disturbances has been given recently in [1]. In this note we give a direct and simple proof for the case of bounded signals of the result of [1] and show, via a counterexample, that an assumption on system signals boundedness which does not appear in [1] is necessary when arbitrary unbounded signals are allowable. Finally, we give a proper persistency of excitation result which does not require signal boundedness for the case when the system input consists of a bounded external signal and of a constant coefficient feedback component.

Estimation of Models for Systems having Deterministic and Random Disturbances

Abstract The most common model employed in time series analysis and system identification is the well known ARMAX model having relatively prime A, B, C polynomials. However, this model does not account for purely deterministic disturbances such as sinewaves. The model can be generalized to handle this latter case, but in this situation, A, B, C are no longer relatively prime. Instead they have common (uncontrollable) roots on the stability boundary. This paper will present a new algorithm for parameter estimation in these non-minimal ARMAX models. Emphasis will be given to the problem of estimating multiple sinewave frequencies in noise. The effect of low signal to noise ratios and optimal sampling strategies will be considered. Simulation results are included.

Spontaneous CP violation in SU(2) L × SU(2) R × U(1) B−L models

We show that it is impossible even with fine tuning to obtain spontaneous CP violation in the minimal SU(2) L × SU(2) R × U(1) B−L model without getting unacceptable flavor-changing neutral currents. We also present an acceptable nonminimal model.

Formula omitted] mixing in minimal and non-minimal left-right-symmetric theories

Properties of C-invariant left-right symmetric theories are discussed. K− K mixing is computed and is used to derive bounds on the mass of the right-handed gauge boson. The CP violation parameter ϵ is found to be the sum of two distinct terms which arise from two different CP violating phases. All these results are proved to apply also to nonminimal models.

Nonminimal SU(5) model.

The existence of the solution of the symmetry-breaking problem SU(5)\ensuremath{\rightarrow}SU(3) \ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}U(1${)}_{Y}$\ensuremath{\rightarrow}SU(3)\ifmmode\times\else\texttimes\fi{}U(1${)}_{Q}$ is shown in a nonminimal model where the 75-dimensional Higgs field is used instead of the usual 24-dimensional one. The result is given in an explicit and simple form. The relevance of this solution to existing theories and to problems related to proton decay is discussed.

Persistency of excitation for nonminimal models of systems having purely deterministic disturbances

All results to date on the question of persistency of excitation depend on the model being minimal. Thus the results do not apply to systems having purely deterministic disturbances since these automatically give rise to uncontrollable modes on the unil circle. This note presents new results on persistency of excitation applicable to nonminimal models of systems having purely deterministic disturbances.

Renormalization group constraints in supersymmetric grand unification models

The requirement of the absence of the ultraviolet ghost pole up to the Planck scale leads to nontrivial constraints for the supersymmetric models, namely: (1) The unification scale in nonminimal models of grand unification has to be close to the Planck one. (2) The top-quark mass m t ⩽ 120 GeV in the SU(5)-model.

Least order, stable solution of the exact model matching problem

The set of all solutions of the minimal design problem (MDP) is presented in parametric form. This result is obtained by first deriving a parametric representation of all minimal bases of a particular vector space. From this the set of all solutions of the MDP are obtained. Then conditions are placed on the parameters, which conditions define the set of stable solutions of the MDP. Solutions to the nonminimal model matching problem are also presented in parametric form, and it is shown how in principle solutions of successively higher degree can be searched for a stable solution, should the MDP have no stable solution, so that a solution to the model matching problem can be found which has the lowest order consistent with a stability constraint.

Least Order, Stable Solution of the Exact Model Matching Problem

The set of all solutions of the minimal design problem is presented in parametric form. Then conditions are placed on the parameters, which conditions define the set of stable solutions of the minimal design problem. Solutions to the nonminimal model matching problem are also presented in parametric form, and it is shown how solutions of successively higher order can be searched for a stable solution. In this way a solution to the model matching problem can be found which has the lowest order consistent with a stability constraint.