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517.93

THE CONSTRUCTION OF CONTROL FOR THE DYNAMICAL SYSTEM, UNDER THE CONDITIONS INTO THE SUBSPACES

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, ., e-mail -. , Java-Script ,

. , e-mail -. , Java-Script . .. , . ,

e-mail -. , Java-Script DOI: 102737/16195

Summary: The completely observed descriptor system is considered. The control components of the spaces initially satisfy the specified conditions. The control that provides at the output of originally desired result is built. The formula for building a state function is obtained.

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Keywords: dynamical system, the complete observability, state function, the control.

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The dynamic system is considered

Here x{t) G Rn- is the state function, u(t) G Rn - the control, f (t) G Rn- the input function, (t) G Rm - the output function; , - are matrix coefficients, tG[0,T],T is finite or infinite.

For each of known u(t), with the realizing input and output functions, the state of the system at any given time defined by uniquely, i.e. the system (1), (2) is assumed completely observed.

The aim is of constructing such control that provides at the output of originally desired result, while the control components of the spaces initially satisfy the specified conditions. Here is considered the general case of the irreversible rectangular matrix , which are corresponds the decomposition space into a direct sum

here: Iwi - the set of values in Rm,

Ker - the set of solutions BxO in Rnhere dim KerB = n^ >0);

Coim - the direct complement to the subspace Ker in R ,

Co ker B- the direct complement to the subspace IttlB in Rm .

The research is being by the method of cascade splitting the original space and the transition to the system in the subspaces.

This method is economical in solving practical problems, it was used in the study of complete observability of different systems, in the study of dynamical systems invariance with respect to various perturbations, in solving problems of controls with control points [1].

The solution of the problem is realized a few steps (the maximum number does not exceed the dimension of the original space).

The algorithm and a block diagram of a phased construction of the control is given. The flow diagram splitting spaces are built. The formula for building a state function is obtained.

The list of the literature

1. Zubova, S.P. On polinomial solutions of the linear stationary control system / S.P. Zubova, E.V. Raetskaya, L.H. Thung // "Automation and Remote Control". 2008. T. 69, 11. P. 1852-1858.

517.9

 
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