Solving systems of matrix equations of the second degree

Matrix equations and systems of matrix equations are widely used in control system optimization problems. However, the methods for their solving are developed only for the most popular matrix equations – Riccati and Lyapunov equations, and there is no universal approach for solving problems of this class. This paper summarizes the previously considered method of solving systems of algebraic equations over a field of real numbers [1] and proposes a scheme for systems of polynomial matrix equations of the second degree with many unknowns. A recurrent formula for fractionalization a solution into a continued matrix fraction is also given. The convergence of the proposed method is investigated. The results of numerical experiments that confirm the validity of theoretical calculations and the effectiveness of the proposed scheme are presented.

Human Papillomavirus 31 Tyrosine 102 Regulates Interaction with E2 Binding Partners and Episomal Maintenance

ABSTRACT Several serine and threonine residues of the papillomavirus early E2 protein have been found to be phosphorylated. In contrast, only one E2 tyrosine phosphorylation site in BPV-1 (tyrosine 102) and one in HPV-16/31 (tyrosine 138) site have been characterized. Between BPV-1 and HPV-31 E2, 8 of the 11 tyrosines are conserved in the N-terminal domain, suggesting that phosphorylation of tyrosines has an essential role in E2 biology. In this study, we examine the effect of Y102 phosphorylation on HPV-31 E2 biology. Y102 proteins mutated either to the potential phospho-mimetic glutamic acid (Y102E) or to the nonphosphorylated homologue phenylalanine (Y102F) remain nuclear; however, Y102E is more associated with the nuclear matrix fraction. This is consistent with the inability of Y102E to bind TopBP1. Both BPV-1 and HPV-31 Y102E are similar in that neither binds the C terminus of Brd4, but in all other aspects the mutant behaves differently between the two families of papillomaviruses. BPV-1 Y102E was unable to bind E1 and did not replicate in a transient in vitro assay, while HPV-31 Y102E binds E1 and was able to replicate, albeit at lower levels than wild type. To examine the effect of E2 mutations under more native-like infection conditions, a neomycin-selectable marker was inserted into L1/L2 of the HPV-31 genome, creating HPV-31neo. This genome was maintained in every cell line tested for at least 50 days posttransfection/infection. Y102E in both transfection and infection conditions was unable to maintain high episome copy numbers in epithelial cell lines. IMPORTANCE Posttranslational modifications by phosphorylation can change protein activities, binding partners, or localization. Tyrosine 102 is conserved between delta papillomavirus BPV-1 and alpha papillomavirus HPV-31 E2. We characterized mutations of HPV-31 E2 for interactions with relevant cellular binding partners and replication in the context of the viral genome.

Robust block roots assignment in linear discrete-time sliding mode control for a class of multivariable system: gas turbine power plant application

This paper deals with the development of a new extended robust control algorithm based on the assignment of robust block roots to extended linear discrete-time sliding mode control; matrix fraction description (MFD) theory is used to improve the performance of the proposed control algorithm and make it more robust. To validate the proposed control algorithm, an application on a gas turbine system (GE MS5001P), which is used in electrical power generation plants, is presented in this paper. An autoregressive model with exogenous excitation is obtained for the studied system, based on the left MFD multivariable least-squares estimator, using real data obtained on-site in order to obtain a minimum-order model with optimum validation criteria. The main objective of the implementation of the proposed control algorithm within the presented application is to ensure stability in the dynamic behaviour of the gas turbine system. Furthermore, a comparison with some classical and modern controllers has been made to prove the effectiveness and robustness of the proposed control algorithm.

Proxy-Based Optimal Dynamic Control Allocation for Multi-Input, Multi-Output Over-Actuated Systems

In over-actuated systems, an output can be realized through various control effort combinations. It is desirable to allocate the control efforts dynamically (as opposed to statically) in an optimal manner. In this paper, a proxy-based control allocation approach is proposed for multi-input, multi-output over-actuated systems. Instead of using real-time optimization for control allocation, the proposed method establishes an energy optimal subspace; it then defines a causally implementable proxy to accurately measure the deviation of the controlled system from the energy optimal subspace using matrix fraction description and spectral factorization. The control allocation problem is thus converted to a regulation problem, and is solved using a standard H∞ approach. The proposed method is validated through simulation examples, in comparison with an existing dynamic control allocation method. Significant improvements in energy efficiency without affecting the controlled output are demonstrated.