Leslaw Socha - Academia.edu (original) (raw)

Papers by Leslaw Socha

Research paper thumbnail of Large-Scale Stochastic Control Systems: Stability and Stabilization

Research paper thumbnail of Analysis fo the suboptimally of large-scale systems with stochastic perturbations

International Journal of Systems Science, 1987

Research paper thumbnail of Stability and open loop control for stochastic quasilinear systems

Research paper thumbnail of Statistical and Equivalent Linearization Techniques with Probability Density Criteria

Journal of Theoretical and Applied Mechanics

Research paper thumbnail of Application of Probability Metrics to the Nonlinearization Analysis of Stochastic Dynamical Systems

Research paper thumbnail of String stability of stochastic composite systems

Proceedings of the IEEE Conference on Decision and Control

The sufficient conditions of exponential string stability for a few class of nonlinear composite ... more The sufficient conditions of exponential string stability for a few class of nonlinear composite stochastic systems are established. The excitations are assumed to be parametric white noises. In this case the objective is to analyze composite systems in their lower order subsystems and in terms of their interconnecting structure. The cases of exponential string stability for weak coupling systems, vehicle-following systems and l2 string stability for weak coupling systems are considered

Research paper thumbnail of Steinhaus chessboard theorem

The following statement is due to H. Steinhaus [Kalejdoskop matematyczny, PWN Warszawa 1954]. Con... more The following statement is due to H. Steinhaus [Kalejdoskop matematyczny, PWN Warszawa 1954]. Consider a chessboard with some “mined” squares on. Assume that the king cannot go across the chessboard from the left edge to the right one without meeting a mined square. Then the rook can go across the chessboard from upper edge to the lower one moving exclusively on mined squares. According to W. Surówka several proofs of the Steinhaus Theorem seem to be incomplete or use induction on the size of the chessboard [W. Surówka, Pr. Nauk. Uniw. Slask. Katowicach Ann. Math. Silesianae 1399(7), 57-61 (1993; Zbl 0807.52018)]. In this note we generalize the Steinhaus Theorem assuming that the chessboard (= square) is divided into arbitrary polygons (not necessarily squares) and we show an algorithm allowing to find rook’s or king’s route between chosen opposite edges of the chessboard.

Research paper thumbnail of Iterative Procedures for the Determination of Quasi- Optimal Control for Stochastic Polynomial Hybrid Systems

Research paper thumbnail of Quasi Optimal Control in Polynomial Tracking Problem

Research paper thumbnail of Application of true linearization in stochastic quasi-optimal control problems

Journal of Structural Control, 2000

The problem of quasi-optimal linear feedback control laws for nonlinear systems with quadratic pe... more The problem of quasi-optimal linear feedback control laws for nonlinear systems with quadratic performance criteria under Gaussian white noise excitations is considered. To determine the quasi-optimal control a modified version of standard iterative procedure is used, where three versions of statistical linearization methods and true linearization method were combined with the optimal control method for linear systems with the mean-square criterion. The validity of this method is shown by analytical and numerical calculations for examples.

Research paper thumbnail of Stability of two-time scale linear stochastic hybrid systems

Probabilistic Engineering Mechanics, 2014

Research paper thumbnail of Some remarks about open‐loop control in stochastic quasilinear systems

Optimal Control Applications and Methods, 1986

A method of obtaining the optimal control in quasilinear systems which are influenced by disturba... more A method of obtaining the optimal control in quasilinear systems which are influenced by disturbances is presented. The analysis is carried out for second‐order stationary and non‐stationary Gaussian processes. First, the stochastic problem is changed into an equivalent deterministic problem, and next the optimal control is constructed from the maximum principle. This method is applied to the optimal temperature profile in a chemical reactor. The results are illustrated by a numerical example.

Research paper thumbnail of The sensitivity analysis of stochastic non-linear dynamical systems

Journal of Sound and Vibration, 1986

The concept of stochastic sensitivity in linear and a class of non-linear continuous stochastic d... more The concept of stochastic sensitivity in linear and a class of non-linear continuous stochastic dynamical systems is considered in this paper. New definitions of output sensitivity measures are introduced. Detailed applications for linear systems with stochastic coefficients under noise excitation and for a non-linear oscillator are analysed. The cases of white and coloured noise are considered. An example is given to illustrate the results obtained.

Research paper thumbnail of Application of Yakubovich criterion for stability of nonlinear stochastic systems

IEEE Transactions on Automatic Control, 1980

Frequency domain criteria for stability of a class of multiloop nonlinear stochastic systems are ... more Frequency domain criteria for stability of a class of multiloop nonlinear stochastic systems are presented in this paper. The Yakubovich criterion is used in the investigation of asymptotic stability with probability one. The obtained results are illustrated by the example.

Research paper thumbnail of Frequency-domain criteria for stability of a class of nonlinear systems with random parameters

IEEE Transactions on Automatic Control, 1975

The frequency criterion of stochastic stability of nonlinear systems is presented in this corresp... more The frequency criterion of stochastic stability of nonlinear systems is presented in this correspondence. The Popov condition is used in the investigation of stability in large, stability with probability one, and exponential p -stability.

Research paper thumbnail of Some remarks about moment controllability for linear stochastic systems

IEEE Transactions on Automatic Control, 1984

The moment controllability of linear systems containing white multiplicative noise processes is c... more The moment controllability of linear systems containing white multiplicative noise processes is considered. We introduce the definition of p th moment controllability and we present a technique for obtaining sufficient conditions for this controllability. An example is given to illustrate the technique.

Research paper thumbnail of Control of the Duffing oscillator under non-Gaussian external excitation

European Journal of Mechanics - A/Solids, 2002

ABSTRACT The problem of suboptimal linear feedback control laws with mean-square criteria for the... more ABSTRACT The problem of suboptimal linear feedback control laws with mean-square criteria for the linear oscillator and the Duffing oscillator under external non-Gaussian excitations is considered. The input process is modeled as a polynomial of a Gaussian process or as a renewal driven impulse process. To determine the suboptimal control, a modified iterative procedure is proposed, where four criteria of statistical linearization are combined with an optimal control strategy. The results indicate that the obtained minima do not depend on the linearization criterion. The nonlinearity tends to reduce this minimum.

Research paper thumbnail of The asymptotic stochastic stability in large of the composite stochastic systems

Automatica, 1986

The sufficient conditions of asymptotic stochastic stability in large of non-linear composite sto... more The sufficient conditions of asymptotic stochastic stability in large of non-linear composite stochastic systems are established. In this case the objective is to analyze composite systems in their lower order subsystems and in terms of their interconnecting structure. Non-linear systems are considered, with random noise which obeys the law of large numbers. An example is given to illustrate the criteria.

Research paper thumbnail of Some remarks on exact linearization of a class of stochastic dynamical systems

IEEE Transactions on Automatic Control, 1994

Research paper thumbnail of Application of Continuous Non-Gaussian Mortality Models with Markov Switchings to Forecast Mortality Rates

Applied Sciences

The ongoing pandemic has resulted in the development of models dealing with the rate of virus spr... more The ongoing pandemic has resulted in the development of models dealing with the rate of virus spread and the modelling of mortality rates μx,t. A new method of modelling the mortality rates μx,t with different time intervals of higher and lower dispersion has been proposed. The modelling was based on the Milevski–Promislov class of stochastic mortality models with Markov switches, in which excitations are modelled by second-order polynomials of results from a linear non-Gaussian filter. In contrast to literature models where switches are deterministic, the Markov switches are proposed in this approach, which seems to be a new idea. The obtained results confirm that in the time intervals with a higher dispersion of μx,t, the proposed method approximates the empirical data more accurately than the commonly used the Lee–Carter model.

Research paper thumbnail of Large-Scale Stochastic Control Systems: Stability and Stabilization

Research paper thumbnail of Analysis fo the suboptimally of large-scale systems with stochastic perturbations

International Journal of Systems Science, 1987

Research paper thumbnail of Stability and open loop control for stochastic quasilinear systems

Research paper thumbnail of Statistical and Equivalent Linearization Techniques with Probability Density Criteria

Journal of Theoretical and Applied Mechanics

Research paper thumbnail of Application of Probability Metrics to the Nonlinearization Analysis of Stochastic Dynamical Systems

Research paper thumbnail of String stability of stochastic composite systems

Proceedings of the IEEE Conference on Decision and Control

The sufficient conditions of exponential string stability for a few class of nonlinear composite ... more The sufficient conditions of exponential string stability for a few class of nonlinear composite stochastic systems are established. The excitations are assumed to be parametric white noises. In this case the objective is to analyze composite systems in their lower order subsystems and in terms of their interconnecting structure. The cases of exponential string stability for weak coupling systems, vehicle-following systems and l2 string stability for weak coupling systems are considered

Research paper thumbnail of Steinhaus chessboard theorem

The following statement is due to H. Steinhaus [Kalejdoskop matematyczny, PWN Warszawa 1954]. Con... more The following statement is due to H. Steinhaus [Kalejdoskop matematyczny, PWN Warszawa 1954]. Consider a chessboard with some “mined” squares on. Assume that the king cannot go across the chessboard from the left edge to the right one without meeting a mined square. Then the rook can go across the chessboard from upper edge to the lower one moving exclusively on mined squares. According to W. Surówka several proofs of the Steinhaus Theorem seem to be incomplete or use induction on the size of the chessboard [W. Surówka, Pr. Nauk. Uniw. Slask. Katowicach Ann. Math. Silesianae 1399(7), 57-61 (1993; Zbl 0807.52018)]. In this note we generalize the Steinhaus Theorem assuming that the chessboard (= square) is divided into arbitrary polygons (not necessarily squares) and we show an algorithm allowing to find rook’s or king’s route between chosen opposite edges of the chessboard.

Research paper thumbnail of Iterative Procedures for the Determination of Quasi- Optimal Control for Stochastic Polynomial Hybrid Systems

Research paper thumbnail of Quasi Optimal Control in Polynomial Tracking Problem

Research paper thumbnail of Application of true linearization in stochastic quasi-optimal control problems

Journal of Structural Control, 2000

The problem of quasi-optimal linear feedback control laws for nonlinear systems with quadratic pe... more The problem of quasi-optimal linear feedback control laws for nonlinear systems with quadratic performance criteria under Gaussian white noise excitations is considered. To determine the quasi-optimal control a modified version of standard iterative procedure is used, where three versions of statistical linearization methods and true linearization method were combined with the optimal control method for linear systems with the mean-square criterion. The validity of this method is shown by analytical and numerical calculations for examples.

Research paper thumbnail of Stability of two-time scale linear stochastic hybrid systems

Probabilistic Engineering Mechanics, 2014

Research paper thumbnail of Some remarks about open‐loop control in stochastic quasilinear systems

Optimal Control Applications and Methods, 1986

A method of obtaining the optimal control in quasilinear systems which are influenced by disturba... more A method of obtaining the optimal control in quasilinear systems which are influenced by disturbances is presented. The analysis is carried out for second‐order stationary and non‐stationary Gaussian processes. First, the stochastic problem is changed into an equivalent deterministic problem, and next the optimal control is constructed from the maximum principle. This method is applied to the optimal temperature profile in a chemical reactor. The results are illustrated by a numerical example.

Research paper thumbnail of The sensitivity analysis of stochastic non-linear dynamical systems

Journal of Sound and Vibration, 1986

The concept of stochastic sensitivity in linear and a class of non-linear continuous stochastic d... more The concept of stochastic sensitivity in linear and a class of non-linear continuous stochastic dynamical systems is considered in this paper. New definitions of output sensitivity measures are introduced. Detailed applications for linear systems with stochastic coefficients under noise excitation and for a non-linear oscillator are analysed. The cases of white and coloured noise are considered. An example is given to illustrate the results obtained.

Research paper thumbnail of Application of Yakubovich criterion for stability of nonlinear stochastic systems

IEEE Transactions on Automatic Control, 1980

Frequency domain criteria for stability of a class of multiloop nonlinear stochastic systems are ... more Frequency domain criteria for stability of a class of multiloop nonlinear stochastic systems are presented in this paper. The Yakubovich criterion is used in the investigation of asymptotic stability with probability one. The obtained results are illustrated by the example.

Research paper thumbnail of Frequency-domain criteria for stability of a class of nonlinear systems with random parameters

IEEE Transactions on Automatic Control, 1975

The frequency criterion of stochastic stability of nonlinear systems is presented in this corresp... more The frequency criterion of stochastic stability of nonlinear systems is presented in this correspondence. The Popov condition is used in the investigation of stability in large, stability with probability one, and exponential p -stability.

Research paper thumbnail of Some remarks about moment controllability for linear stochastic systems

IEEE Transactions on Automatic Control, 1984

The moment controllability of linear systems containing white multiplicative noise processes is c... more The moment controllability of linear systems containing white multiplicative noise processes is considered. We introduce the definition of p th moment controllability and we present a technique for obtaining sufficient conditions for this controllability. An example is given to illustrate the technique.

Research paper thumbnail of Control of the Duffing oscillator under non-Gaussian external excitation

European Journal of Mechanics - A/Solids, 2002

ABSTRACT The problem of suboptimal linear feedback control laws with mean-square criteria for the... more ABSTRACT The problem of suboptimal linear feedback control laws with mean-square criteria for the linear oscillator and the Duffing oscillator under external non-Gaussian excitations is considered. The input process is modeled as a polynomial of a Gaussian process or as a renewal driven impulse process. To determine the suboptimal control, a modified iterative procedure is proposed, where four criteria of statistical linearization are combined with an optimal control strategy. The results indicate that the obtained minima do not depend on the linearization criterion. The nonlinearity tends to reduce this minimum.

Research paper thumbnail of The asymptotic stochastic stability in large of the composite stochastic systems

Automatica, 1986

The sufficient conditions of asymptotic stochastic stability in large of non-linear composite sto... more The sufficient conditions of asymptotic stochastic stability in large of non-linear composite stochastic systems are established. In this case the objective is to analyze composite systems in their lower order subsystems and in terms of their interconnecting structure. Non-linear systems are considered, with random noise which obeys the law of large numbers. An example is given to illustrate the criteria.

Research paper thumbnail of Some remarks on exact linearization of a class of stochastic dynamical systems

IEEE Transactions on Automatic Control, 1994

Research paper thumbnail of Application of Continuous Non-Gaussian Mortality Models with Markov Switchings to Forecast Mortality Rates

Applied Sciences

The ongoing pandemic has resulted in the development of models dealing with the rate of virus spr... more The ongoing pandemic has resulted in the development of models dealing with the rate of virus spread and the modelling of mortality rates μx,t. A new method of modelling the mortality rates μx,t with different time intervals of higher and lower dispersion has been proposed. The modelling was based on the Milevski–Promislov class of stochastic mortality models with Markov switches, in which excitations are modelled by second-order polynomials of results from a linear non-Gaussian filter. In contrast to literature models where switches are deterministic, the Markov switches are proposed in this approach, which seems to be a new idea. The obtained results confirm that in the time intervals with a higher dispersion of μx,t, the proposed method approximates the empirical data more accurately than the commonly used the Lee–Carter model.