Jerzy Klamka

Controllability of dynamical systems

The paper contains systems descriptions and fundamental results concerning the solution of the most popular linear continuous-time control models with constant coefficients. First, different kinds of stability are discussed. Next fundamental definitions of controllability both for finite-dimensional and infinite-dimensional systems are recalled and necessary and sufficient conditions for different kinds of controllability are formulated. Moreover, fundamental definitions of controllability both for finite-dimensional and infinite-dimensional control systems are presented and necessary and sufficient conditions for different kinds of controllability are given. Finally, concluding remarks and comments concerning possible extensions are presented.

Minimum energy control of 2-D linear systems with variable coefficients

The definition of the state-transition matrix for Roessers model of 2-D systems with variable coefficients is introduced and the general response formula is derived. Necessary and sufficient conditions for local controllability are formulated. The minimum energy control problem for Roessers model of 2-D systems with variable coefficients is formulated and solved.

Some remarks about stochastic controllability

The stochastic e-controllability of continuous nonlinear stochastic dynamical systems is considered. Using a stochastic Lyapunov-like approach, the sufficient conditions for the stochastic e-controllability are formulated. Finally, a simple example of a stochastic e-controllable system is given.

Stochastic controllability and minimum energy control of systems with multiple delays in control

In the paper finite-dimensional stationary dynamical control systems described by linear stochastic ordinary differential state equations with multiple point delays in the control are considered. Using notations, theorems and methods taken directly from deterministic controllability problems for linear dynamical systems with delays in control, 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. As a special case relative stochastic controllability of dynamical systems with single point delay is also considered. Some remarks and comments on the existing results for stochastic controllability of linear dynamical systems are also presented. In the second part of the paper minimum energy control problem is considered. Under the assumption that system is stochastically relatively exactly controllable analytical formula for minimum energy control is given.

Observer for linear feedback control of systems with distributed delays in controls and outputs

This paper presents a design method for a linear observer for a multivariable dynamical system with distributed delays in controls and outputs The results of this paper extend the results recently obtained for a special case in the paper [6]to the most general dvnamical systems Other special cases arc also discussed

Stochastic Controllability of Linear Systems With State Delays

Stochastic Controllability of Linear Systems With State Delays 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.

Relative controllability and minimum energy control of linear systems with distributed delays in control

The first part of this correspondence is devoted to a study of controllability of linear time-varying systems with distributed delays in the control. The controllability matrix for these systems is defined, and the necessary and sufficient condition for relative controllability of the considered systems are derived. In the second part the problem of minimum energy control is studied, and the explicit formula for control law is also given.

Controllability and minimum energy control of linear fractional discrete-time infinite-dimensional systems

The main purpose of the paper is to discuss controllability problem for infinite-dimensional fractional linear discrete-time control systems. Moreover, the minimum energy control problem of infinite-dimensional fractional-discrete time linear systems is also addressed. Using theory of linear operators necessary and sufficient conditions for the exact controllability of the system are established. Sufficient conditions for the solvability of the minimum energy control of the infinite-dimensional fractional discrete-time systems are given. A procedure for computation of the optimal sequence of inputs minimizing the quadratic performance index is proposed.

Constrained exact controllability of semilinear systems

In the paper infinite-dimensional dynamical control systems described by semilinear abstract differential equations are considered. Using a generalized open-mapping theorem, sufficient conditions for constrained exact local controllability are formulated and proved. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Constrained exact local controllability of semilinear abstract second-order dynamical systems are also formulated and proved. As an illustrative example, constrained exact local controllability problem for semilinear hyperbolic type distributed parameters dynamical system is solved in details. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.

Stochastic Controllability of Systems with Multiple Delays in Control

Stochastic Controllability of Systems with Multiple Delays in Control 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.