Wyniki wyszukiwania - BazTech

1

On-line parameter and delay estimation of continuous-time dynamic systems

Kozłowski J., Kowalczuk Z.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 2

223--232

EN

The problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous identification of input delay and spectral parameters of the system models. The performance of the proposed estimation algorithms is verified in an illustrative numerical simulation study.

2

A Dynamic Piezoelectric Contact Problem

Barboteu M., Sofonea M.

Machine Dynamics Problems

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2008

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Vol. 32, No. 1

23-32

EN

We consider a mathematical model, which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. The material's behavior is modeled with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition and a regularized electrical conductivity condition. We state the variational formulation for the problem, and then we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We implement this scheme in a numerical code and, in order to verify its accuracy, we present numerical simulations in the study of a two-dimensional test problem.

3

Adaptacyjna identyfikacja ciągłoczasowych modeli procesów niestacjonarnych z uwzględnieniem przekłamań pomiarowych

Kozłowski J., Kowalczuk Z.

Pomiary Automatyka Kontrola

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2005

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R. 51, nr 9 bis

68--70

PL

W pracy wykorzystuje się metody identyfikacji parametrycznej do pozyskiwania użytecznej dla diagnostyki informacji o zmianach dynamiki nadzorowanych procesów. Analizie poddaje się procesy przemysłowe modelowane za pomocą liniowych i nieliniowych równań różniczkowych zwyczajnych, zaś zadanie śledzenia zmiennych w czasie parametrów procesowych rozwiązuje się stosując metodę najmniejszej ważonej sumy kwadratów błędów. Ponieważ klasyczny algorytm najmniejszych kwadratów nie jest odporny na błędy grube w danych, proponuje się zastosowanie odpornego na przekłamania estymatora w sensie najmniejszej sumy modułów błędów. Skuteczność omawianych metod ilustrują testy symulacyjne.

EN

In this paper specific parameter estimation methods are used to obtain relevant diagnostic information on the evolution of dynamics of supervised industrial processes. The analyzed processes are modeled with the aid of linear and nonlinear ordinary differential equations, and the weighted least-squares estimator is employed to track time-variant model parameters. As the classical least-squares procedure is not robust to possible outliers in measurement data, an estimation algorithm in the sense of the least sum of absolute errors is put into practice. The efficiency of the discussed routines is illustrated by means of simulation tests.

4

Optimal control of semilinear evolution inclusions via discrete approximations

Mordukhovich B. S., Wang D.

Control and Cybernetics

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2005

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Vol. 34, no 3

849-870

EN

This paper studies a Mayer type optimal control problem with general endpoint constraints for semilinear unbounded evolution inclusions in reflexive and separable Banach spaces. First, we construct a sequence of discrete approximations to the original optimal control problem for evolution inclusions and prove that optimal solutions to discrete approximation problems uniformly converge to a given optimal solution for the original continuous-time problem. Then, based on advanced tools of generalized differentiation, we derive necessary optimality conditions for discrete-time problems under fairly general assumptions. Combining these results with recent achievements of variational analysis in infinite-dimensional spaces, we establish new necessary optimality conditions for constrained continuous-time evolution inclusions by passing to the limit from discrete approximations.

5

Error analysis of discrete approximations to bang-bang optimal control problems: the linear case

Veliov V. M.

Control and Cybernetics

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2005

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Vol. 34, no 3

967-982

EN

The paper presents an error estimate for Runge-Kutta direct discretizations of terminal optimal control problems for linear systems. The optimal control for such problems is typically discontinuous, and Lipschitz stability of the solution with respect to perturbations does not necessarily hold. The estimate (in terms of the optimal controls) is of first order if certain recently obtained sufficient conditions for structural stability hold, and of fractional order, otherwise. The main tool in the proof is the established relation between the local convexity index of the reachable set and the multiplicity of zeros of appropriate switching functions associated with the problem.

6

Optimal control of constrained delay-differential inclusions with multivalued initial conditions

Mordukhovich B. S., Wang L.

Control and Cybernetics

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2003

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Vol. 32, no 3

585-609

EN

This paper studies a general optimal control problem for nonconvex delay-differential inclusions with endpoint constraints. In contrast to previous publications on this topic, we incorporate time-dependent set constraints on the initial interval, which are specific for systems with delays and provide an additional source for optimization. Our variational analysis is based on well-posed discrete approximations of constrained delay-differential inclusions by a family of time-delayed systems with discrete dynamics and perturbed constraints. Using convergence results for discrete approximations and advanced tools of nonsmooth variational analysis, we derive necessary optimality conditions for constrained delay-differential inclusions in both Euler-Lagrange and Hamiltonian forms involving nonconvex generalized differential constructions for nonsmooth functions, sets, and set-valued mappings.