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1

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

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

Stochastic controllability of linear systems with state delays

Klamka J.

International Journal of Applied Mathematics and Computer Science

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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

Stochastic controllability of linear systems with delay in control

Klamka J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2007

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Vol. 55, nr 1

23-29

EN

In the paper finite--dimensional stationary dynamical control systems described by linear stochastic ordinary differential state equations with single point delay in the control are considered. Using notations, theorems and methods taken directly from deterministic controlla-bility problems, necessary and sufficient conditions for different kinds of stochastic relative controllability 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. Same remarks and comments on the existing results for stochastic controllability of linear dynamical systems with delays are also presented. Finally, minimum energy control problem for stochastic dynamical system is formulated and solved.

5

Self-tuning control under input variance constraint

Królikowski A., Kubiak T., Lemos J.M.

Systems Science

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2003

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Vol. 29, nr 1

135-149

EN

In this paper, a variance-constrained self-tuning control is considered for a plant given by discrete-time ARMAX model. A minimization of a quadratic cost function under constraint is approached by LQG and stochastic approximation (SA) methods, as well as by MUSMAR, a predictive adaptive controller based on multiple identifiers. The optimization algorithms obtained are simulated for unstable plant model and different structures of the controller.