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1

Nonlinear state observers and extended Kalman filters for battery systems

Rauh A., Butt S. S., Aschemann H.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 3

539--556

EN

The focus of this paper is to develop reliable observer and filtering techniques for finite-dimensional battery models that adequately describe the charging and discharging behaviors. For this purpose, an experimentally validated battery model taken from the literature is extended by a mathematical description that represents parameter variations caused by aging. The corresponding disturbance models account for the fact that neither the state of charge, nor the above-mentioned parameter variations are directly accessible by measurements. Moreover, this work provides a comparison of the performance of different observer and filtering techniques as well as a development of estimation procedures that guarantee a reliable detection of large parameter variations. For that reason, different charging and discharging current profiles of batteries are investigated by numerical simulations. The estimation procedures considered in this paper are, firstly, a nonlinear Luenberger-type state observer with an offline calculated gain scheduling approach, secondly, a continuous-time extended Kalman filter and, thirdly, a hybrid extended Kalman filter, where the corresponding filter gains are computed online.

2

Conditioning and error estimates in LQG design

Petkov P. Hr., Konstantinov M. M., Christov N. D.

Control and Cybernetics

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2008

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Vol. 37, no 1

85-87

EN

Efficient conditioning and error estimates are presented for the numerical solution of matrix Riccati equations in the continuous-time and discrete-time LQG design. The estimates implemented involve the solution of triangular Lyapunov equations along with usage of the LAPACK norm estimator.

3

A reliable synthesis of discrete-time Η∞ control. Part I: basic theorems and J-lossless conjugators

Suchomski P. J.

Control and Cybernetics

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2007

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Vol. 36, no 1

97-141

EN

The paper gives a basis for solving many problems of numerically reliable synthesis of sub-optimal discrete-time control in Η∞. The approach is based on J-lossless factorisations of the delta-domain chain-scattering descriptions of continuous-time plants being controlled. Relevant properties of poles and zeros of chain-scattering models are given. Necessary and sufficient conditions for the existence of stabilising J-lossless conjugators are presented and discussed. Some aspects of numerical conditioning of synthesis of such conjugators are considered. A numerical example illustrating synthesis of stabilising right J-lossless conjugators is also included.

4

Second order conditions for periodic optimal control problems

Allwright J., Vinter R.

Control and Cybernetics

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2005

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Vol. 34, no 3

617-643

EN

This paper concerns second order sufficient conditions of optimality, involving the Riccati equation, for optimal control problems with periodic boundary conditions. The problems considered involve no pathwise constraints and are 'regular', in the sense that the strengthened Legendre-Clebsch condition is assumed to be satisfied. A well-known sufficient, condition, which we refer to as the Riccati sufficient condition, requires the existence of a global solution to the Riccati equation whose endpoint values satisfy a certain inequality. A sharper condition, named the extended sufficient, condition, takes the form of an inequality involving the solutions of a Riccati equation and two additional linear matrix equations. We highlight the superiority of the extended Riccati sufficient condition and develop a number of equivalent formulations of this condition. Not only does the extended Riccati sufficient, condition supply more information about, minimizers, but it is the basis of simpler numerical tests for assessing whether an extremal is a minimizer, at least in a local sense. The Riccati and also the extended Riccati sufficient conditions are applied to a variant of Speyer's 'sailboat' problem, involving parameters. It is found that the extended Riccati sufficient condition identifies a much larger set of points on parameter space for which a nominal control is optimal, in comparison to the Riccati sufficient condition.

5

Reproducing Kernels and Riccati Equations

Dym H.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 1

35-53

EN

The purpose of this paper is to exhibit a connection between the Hermitian solutions of matrix Riccati equations and a class of finite dimensional reproducing kernel Krein spaces. This connection is then exploited to obtain minimal factorizations of rational matrix valued functions that are J-unitary on the imaginary axis in a natural way.

6

Second order sufficient conditions and sensitivity analysis for optimal multiprocess control problems

Augustin D., Maurer H.

Control and Cybernetics

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2000

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Vol. 29, no 1

11-31

EN

Second order sufficient optimality conditions (SSC) are derived for optimal multiprocess control problems. For that purpose the multiprocess control problem is transformed into a single stage control problem with augmented state variables which comprise the state variables of all individual stages as well as the switching times as choice variables. This toansformation allows to apply the known SSC for single stage control problems. A numerical test of SSC involves the solution of an associated Riccati equation together with boundary conditions adapted to the multiprocess. Sensitivity analysis of parametric multiprocess problems can be based on SSC. A numerical example of the optimal two-stage control of a robot illustrates both SSC and sensitivity analysis.

7

On the bounds on the solutions of the algebraic Lyapunov and Riccati equations

Czornik A., Nawrat A.

Archives of Control Sciences

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2000

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Vol. 10, no. 3/4

197-244

EN

Different types of bounds for solutions of continuous and discrete Lyapunov and Riccati equations obtained up to now are summarized in this paper. Some new bounds are also presented. The efficiency of each bound is illustrated with three numerical examples. A discussion and comparison are given as well. The results may be particularly convenient to get the ready estimate of the solution while solving the equations numerically or to develop theoretical results that rely on these bounds.