A quasi-Newton optimal method for the global linearisation of the output feedback pole assignment

The paper deals with the problem of output feedback pole assignment by static and dynamic compensators using a powerful method referred to as global linearisation which has addressed both solvability conditions and computation of solutions. The method is based on the asymptotic linearisation of the pole assignment map around a degenerate point and is aiming to reduce the multilinear nature of the problem to the solution of a linear set of equations by using algebro-geometric notions and tools. This novel framework is used as the basis to develop numerical techniques which make the method less sensitive to the use of degenerate solutions. The proposed new computational scheme utilizes a quasi-Newton method modified accordingly so it can be used for optimization goals while achieving (exact or approximate) pole placement. In the present paper the optimisation goal is to maximise the angle between a solution and the degenerate compensator so that less sensitive solutions are achieved

A Grassmann Matrix Approach for the Computation of Degenerate Solutions for Output Feedback Laws

The paper is concerned with the improvement of the overall sensitivity properties of a method to design feedback laws for multivariable linear systems which can be applied to the whole family of determinantal type frequency assignment problems, expressed by a unified description, the so-called Determinantal Assignment Problem (DAP). By using the exterior algebra/algebraic geometry framework, DAP is reduced to a linear problem (zero assignment of polynomial combinants) and a standard problem of multilinear algebra (decomposability of multivectors) which is characterized by the set of Quadratic Plücker Relations (QPR) that define the Grassmann variety of P. This design method is based on the notion of degenerate compensator, which are the solutions that indicate the boundaries of the control design and they provide the means for linearising asymptotically the nonlinear nature of the problems and hence are used as the starting points to generate linearized feedback laws. A new algorithmic approach is introduced for the computation and the selection of degenerate solutions (decomposable vectors) which allows the computation of static and dynamic feedback laws with reduced sensitivity (and hence more robust solutions). This approach is based on alternative, linear algebra type criterion for decomposability of multivectors to that defined by the QPRs, in terms of the properties of structured matrices, referred to as Grassmann Matrices. The overall problem is transformed to a nonlinear maximization problem where the objective function is expressed via the Grassmann Matrices and the first order conditions for optimality are reduced to a nonlinear eigenvalue-eigenvector problem. Hence, an iterative method similar to the power method for finding the largest modulus eigenvalue and the corresponding eigenvector is proposed as a solution for the above problem

Robust estimators of ar-models : a comparison

Many regression-estimation techniques have been extended to cover the case of dependent observations. The majority of such techniques are developed from the classical least squares, M and GM approaches and their properties have been investigated both on theoretical and empirical grounds. However, the behavior of some alternative methods- with satisfactory performance in the regression case- has not received equal attention in the context of time series. A simulation study of four robust estimators for autoregressive models containing innovation or additive outliers is presented. The robustness and efficiency properties of the methods are exhibited, some finite-sample results are discussed in combination with theoretical properties and the relative merits of the estimators are viewed in connection with the outlier-generating scheme.peer-reviewe

Structure assignment problems in linear systems: Algebraic and geometric methods

The Determinantal Assignment Problem (DAP) is a family of synthesis methods that has emerged as the abstract formulation of pole, zero assignment of linear systems. This unifies the study of frequency assignment problems of multivariable systems under constant, dynamic centralized, or decentralized control structure. The DAP approach is relying on exterior algebra and introduces new system invariants of rational vector spaces, the Grassmann vectors and Plücker matrices. The approach can handle both generic and non-generic cases, provides solvability conditions, enables the structuring of decentralisation schemes using structural indicators and leads to a novel computational framework based on the technique of Global Linearisation. DAP introduces a new approach for the computation of exact solutions, as well as approximate solutions, when exact solutions do not exist using new results for the solution of exterior equations. The paper provides a review of the tools, concepts and results of the DAP framework and a research agenda based on open problems

An Innovative Control Framework for District Heating Systems: Conceptualisation and Preliminary Results

This paper presents a holistic innovative solution for the transformation of the current district heating and cooling systems to automated more efficient systems. A variety of technological advancements have been developed and integrated to support the effective energy management of future district heating and cooling sector. First, we identify and discuss the main challenges and needs that are in line with the EU objectives and policy expectations. We give an overview of the main parts that our solution consists of, with emphasis on the forecasting tools and an advanced control system that addresses unit commitment and economic load dispatch problems. The proposed control approach employs distributed and scalable optimisation algorithms for optimising the short-term operations of a district heating and cooling plant subject to technical constraints and uncertainties in the energy demand. To test the performance and validate the proposed control system, a district heating plant with multiple energy generation units and real-life heat load data were used. Simulation experiments were also used to evaluate the benefits of using thermal storage units in district heating systems. The results show that the proposed method could achieve significant cost savings when energy storage is employed. The proposed control strategy can be applied for both operating optimally district heating plants with storage and supporting investment planning for new storage units

Fourier methods for analysing piecewise constant volatilities

We develop procedures for testing the hypothesis that a parameter of a distribution is constant throughout a sequence of independent random variables. Our proposals are illustrated considering the variance and the kurtosis. Under the null hypothesis of constant variance, the modulus of a Fourier type transformation of the volatility process is identically equal to one. The approach proposed utilizes this property considering a canonical estimator for this modulus under the assumption of indepen- dent and piecewise identically distributed observations with zero mean. Using blockwise estimators we introduce several test statistics resulting from different weight functions which are all given by simple explicit for- mulae. The methods are compared to other tests for constant volatility in extensive Monte Carlo experiments. Our proposals offer comparatively good power particularly in the case of multiple structural breaks and allow adequate estimation of the positions of the structural breaks. An appli- cation to process control data is given, and it is shown how the methods can be adapted to test for constancy of other quantities like the kurtosis

Development of Future EU District Heating and Cooling Network Solutions, Sharing Experiences and Fostering Collaborations

Heating and cooling consume half of the EU’s energy and much of it is wasted. The lion’s share of heating and cooling is still generated from fossil fuels, mainly natural gas, while only 18% is generated from renewable energy. In order to fulfil the EU’s climate and energy goals, the heating and cooling sector must therefore sharply reduce its energy consumption and cut its use of fossil fuels. To this end the European Commission adopted a heating and cooling strategy in February 2016 as part of the wider Energy Union Package. A number of activities and projects funded by the programmes of European Union are supporting this new EU heating and cooling strategy

Test for exponentiality against Weibull and gamma decreasing hazard rate alternatives

summary:A sub-exponential Weibull random variable may be expressed as a quotient of a unit exponential to an independent strictly positive stable random variable. Based on this property, we propose a test for exponentiality which is consistent against Weibull and Gamma distributions with shape parameter less than unity. A comparison with other procedures is also included

Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach

We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard symmetric stable distribution with the characteristic exponent $\alpha$ estimated from the data. We treat $\alpha$ as an unknown parameter, but for theoretical simplicity we also consider the case that $\alpha$ is fixed. For estimation of parameters and the standardization of data we use maximum likelihood estimator (MLE) and an equivariant integrated squared error estimator (EISE) which minimizes the weighted integral. We derive the asymptotic covariance function of the characteristic function process with parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of the covariance function are numerically evaluated and asymptotic distribution of the test statistic is obtained using complex integration. Simulation studies show that the asymptotic distribution of the test statistics is very accurate. We also present a formula of the asymptotic covariance function of the characteristic function process with parameters estimated by an efficient estimator for general distributions