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1
Content available remote Stochastic controllability of systems with multiple delays in control
Klamka J.
International Journal of Applied Mathematics and Computer Science
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2009
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Vol. 19, no 1
39-47
EN
Finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that, under suitable assumptions, relative controllability of an associated deterministic linear dynamic system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamic system. As a special case, relative stochastic controllability of dynamic systems with a single point delay is also considered. Some remarks and comments on the existing results for stochastic controllability of linear dynamic systems are also presented.
2
Content available remote Stochastic controllability of systems with variable delay in control
Klamka J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2008
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Vol. 56, nr 3
279-284
EN
In the paper finite-dimensional time-variable dynamical control systems described by linear stochastic ordinary differential state equations with single time-variable point delay in the control are considered. Using notations, theorems and methods taken directly from deterministic controllability problems necessary and sufficient conditions for different kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that under suitable assumptions relative controllability of a deterministic linear associated dynamical system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamical system. Some remarks and comments on the existing results for stochastic controllability of linear dynamical systems are also presented.
3
Content available remote Stochastic controllability of linear systems with state delays
Klamka J.
International Journal of Applied Mathematics and Computer Science
|
2007
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Vol. 17, no 1
5-13
EN
A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated deterministic linear dynamic system is equivalent to the stochastic relative exact controllability and the stochastic relative approximate controllability of the original linear stochastic dynamic system. Some remarks and comments on the existing results for the controllability of linear dynamic systems with delays are also presented. Finally, a minimum energy control problem for a stochastic dynamic system is formulated and solved.
4
Content available remote Laplace transforms for MIMO SD systems with delay
Lampe B. P., Rosenwasser E. N.
Archives of Control Sciences
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2006
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Vol. 16, no. 4
363-381
EN
The paper constructs the Laplace transform of the solution with zero initial energy for a MIMO sampled-data system containing pure time-delays in its stationary elements. The properties of the Laplace transform as a function of the complex variable are studied.
5
Content available remote 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
Invariant zeros in singular systems - Algebraic criterions of nondegeneracy
Tokarzewski J.
Systems Science
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2003
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Vol. 29, nr 1
61-78
EN
The question of how the classical concept of the Smith zeros of a LTI continuous-time singular control system S(E,A,B,C,D) can be generalized and related to state-space methods is discussed. The zeros are defined as those complex numbers for which there exists a zero direction with nonzero state-zero direction. Such a definition admits an infinite number of zeros (then the system is called degenerate). Algebraic criterions of degeneracy/nondegeneracy based on Weierstrass-Kronecker canonical form of the system and on the first nonzero Markov parameter are analyzed.
7
Controlled balanced growth of positive linear discrete-time systems
Rumchev V.G., James D.J.G.
Systems Science
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2003
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Vol. 29, nr 1
5-14
EN
In this paper properties of M-matrices are used to develop procedures to ensure that a positive discrete-time linear system achieves a specified desired balanced growth rate. Both closed-loop and open-loop control procedures are considered, with state feedback being adopted for implementing the closed-loop control. Procedures developed are illustrated by simple examples.
8
Computation of minimal realizations for compartmental linear systems
Kaczorek T.
Systems Science
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2003
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Vol. 29, nr 1
15-29
EN
A new method for computation of minimal compartmental realizations of a proper transfer function is proposed. The method is based on a suitable transformation of an asymptotically stable positive realization to the desired compartmental realization. The transformation is characterized by a generalized permutation matrix. Sufficient conditions for the existence of minimal compartmental realizations are established. Two-step procedures for computation of minimal compartmental realizations for both continuous-time and discrete-time linear systems are derived and illustrated by a numerical example.
9
Synthesis of the control systems via reflection onto auxiliary surfaces
Pilishkin V.N.
Systems Science
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2001
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Vol. 27, nr 2
15-25
EN
A new approach to robust control systems synthesis, both linear and nonlinear, and non-stationary is offered. The control is carried out, providing the given phase constrains varied in acceptable limits, in view of constraints on its value and incompleteness of the information about functioning disturbances. The approach is based on introduction of auxiliary integral surfaces, on which the initial moving is projected. As a result the reduced equivalent moving is formed, being described by the scalar equation which in many important cases can be integrated directly. On the basis of the equation obtained solving a synthesis task is carried out and can be reduced to algebraic or integral inequalities. The final relations defined for linear equivalent moving are presented.
10
A fractional-flow model of serial manufacturing systems with rework and its reachability and controllability properties
James G., Rumchev V.
Systems Science
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2001
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Vol. 27, nr 2
49-59
EN
A dynamic fractional-flow model of a serial manufacturing system incorporating rework is considered. Using some recent results on reachability and controllability of positive linear systems the ability of serial manufacturing systems with rework to "move in space", that is their reachability and controllability properties, are studied. These properties are important not only for optimising the performance of the manufacturing system, possibly off-line, but also to improve its functioning by using feedback control on-line.
11
Generic two-degree of freedom control systems for linear and nonlinear processes
Keviczky L., Banyasz C.
Systems Science
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2000
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Vol. 26, nr 4
5-24
EN
The paper discusses a generic two-degree of freedom controller scheme for linear plants and then extends the results to block-oriented factorable nonlinear processes. This generalization is quite straightforward for both IS and IU Hammerstein models, however, it can be performed only for IS Wiener models. An iterative controller refinement scheme is also presented.
12
Feedback holdability of singular discrete-time linear systems
Kaczorek T.
Systems Science
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2000
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Vol. 26, nr 4
25-37
EN
The feedback holdability problem for singular discrete-time linear systems is considered. Conditions are established for the existence of solutions to the following three problems for singular system (1) with regular pencil (E, A). Problem 1: find a gain matrix K such that the closed-loop trajectory is inside the nonnegative orthant R+n. Problem 2: find a gain matrix K such that the state vector xi of the closed-loop system xi = 0 for i greater than or equal k - 1, k = 1,...,n. Problem 3: find a gain matrix K such that ui = Kxi ∈ R+m and the trajectory of closed-loop system is inside R+n
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