Słowa kluczowe:
hyperchaos
hyperchaotic systems
bifurcation analysis
multi-stability analysis
synchronization
Multisim
circuit simulation

In this work, we present new results for a two-scroll 4-D hyperchaotic system with a unique saddle point equilibrium at the origin. The bifurcation and multi-stability analysis for the new hyperchaotic system are discussed in detail. As a control application, we develop a feedback control based on integral sliding mode control (ISMC) for the complete synchronization of a pair of two-scroll hyperchaotic systems developed in this work. Numerical simulations using Matlab are provided to illustrate the hyperchaotic phase portraits, bifurcation diagrams and synchronization results. Finally, as an electronic application, we simulate the new hyperchaotic system using Multisim for real-world implementations.

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Słowa kluczowe:
multi-agent systems
deployment problem
robust invariant sets
set-theoretic analysis
disturbance

The paper is dedicated to the robustness analysis of scalar multi-agent dynamical systems. The open problem we aim to address is the one related to the impact of additive disturbances. Set-theoretic methods are used to achieve the main results in terms of positive invariance and admissible bounds on the disturbances.

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Słowa kluczowe:
observer design
unmeasurable decision variable
SVD approach
Lyapunov function
LMIs

The studied problem in this paper, treat the issue of state and fault estimation using a fuzzy observer in the case of unmeasurable decision variable for Discrete-Time Takagi-Sugeno Singular Sytems (DTSSS). First, an augmented system is introduced to gather state and fault into a single vector, then on the basis of Singular Value Decomposition (SVD) approach, this observer is designed in explicit form to estimate both of state and fault of a nonlinear singular system. The exponential stability of this observer is studied using Lyapunov theory and the convergence conditions are solved with Linear Matrix Inequalities (LMIs). Finally a numerical example is simulated, and results are given to validate the offered approach.

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Słowa kluczowe:
backstepping integrator algorithm
holonomic manipulator
non-orthogonal projection
path following
Serret–Frenet parametrization

In this paper an application of the Serret–Frenet parametrization of a curve to the path following task is presented. This curvilinear parametrization method is used to obtain a control object description relative to the desired curve defined in the three-dimensional space. In order to derive proper equations, the innovative approach of the non-orthogonal projection of a control object on the given path is investigated. The non-orthogonal projection allows to design a global control algorithm. The proposed solution results in a cascade structure of the control system. Thus, the backstepping integrator algorithm was applied to create a control law. Due to the partial knowledge of control object dynamic parameters, an adaptive algorithm is taken into account. Theoretical considerations are confirmed with simulation study. Conducted simulations illustrated following paths at different levels of complexity by a holonomic non-redundant manipulator with a fixed base.

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Słowa kluczowe:
crow search algorithm
dish-stirling solar system
AGC
RT Lab
FOPDN-FOPIDN controller

This article validates the application of RT-Lab for the AGC studies of three-area systems. All the areas are employed with thermal-DSTS systems. A new controller named cascade FOPDN-FOPPIDN is employed. Its parameters are optimized using a CSA, subjecting to a new PI named HPA-ISE. The responses of the FOPDN-FOPIDN controller are related and are superior over PIDN and TIDN controllers. Moreover, the dominance of HPA-ISE is verified with ISE, and it performs better in terms of system dynamics. Further, the system performance reliability is analyzed with the AC-HVDC and is better than the AC system. Besides, sensitivity analysis recommends that the proposed FOPDN-FOPIDN at diverse conditions is robust and more reliability.

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Słowa kluczowe:
instrumental variable
non-linear continuous-time models
optimization
supervisory or security systems
system identification

The paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned ‘integrating filters’ of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization and can be identified, for example, by the classical least squares procedure. Since in the presence of correlated noise, the estimated parameter values are burdened with an unavoidable systematic error (manifested by asymptotic bias of the estimates), in order to significantly improve the identification consistency, the method of instrumental variables is used here. In our research we use an estimation algorithm based on the least absolute values (LA) criterion of the least sum of absolute values, which is optimal in identifying linear and non-linear systems in the case of sporadic measurement errors. In the paper, we propose a procedure for determining the instrumental variable for a continuous model with non-linearity (related to the Wienerian system) in order to remove the evaluation bias, and a recursive sub-optimal version of the LA estmator. This algorithm is given in a simple (LA) version and in an instrumental variable version (IV-LA), which is robust to outliers, removes evaluation bias, and is suited to the task of identifying processes with non-linear dynamics (semi-Wienerian/NLID). In conclusion, the effectiveness of the proposed algorithmic solutions has been demonstrated by numerical simulations of the mechanical system, which is an essential part of the suspension system of a wheeled vehicle.

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Słowa kluczowe:
time-varying systems
asymptotic stability
Bohl exponent

In this note, a formula for the lower Bohl exponent of a discrete system with variable coefficients and weak variation was proved. This formula expresses the Bohl exponent through the eigenvalues of the coefficient matrix. Based on these formulas a necessary and sufficient condition for an uniform exponential instability of such systems is also presented.

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Słowa kluczowe:
Bode’s ideal transfer function
fractional order control
classical PIDA controller
fractional order PI λD µA controller
robustness

The fractional order proportional, integral, derivative and acceleration (PI ^{λ}D ^{µ}A) controller is an extension of the classical PIDA controller with real rather than integer integration action order λ and differentiation action order µ. Because the orders λ and µ are real numbers, they will provide more flexibility in the feedback control design for a large range of control systems. The Bode’s ideal transfer function is largely adopted function in fractional control systems because of its iso-damping property which is an essential robustness factor. In this paper an analytical design technique of a fractional order PI ^{λ}D ^{µ}A controller is presented to achieve a desired closed loop system whose transfer function is the Bode’s ideal function. In this design method, the values of the six parameters of the fractional order PI ^{λ}D ^{µ}A controllers are calculated using only the measured step response of the process to be controlled. Some simulation examples for different third order motor models are presented to illustrate the benefits, the effectiveness and the usefulness of the proposed fractional order PI ^{λ}D ^{µ}A controller tuning technique. The simulation results of the closed loop system obtained by the fractional order PI ^{λ}D ^{µ}A controller are compared to those obtained by the classical PIDA controller with different design methods found in the literature. The simulation results also show a significant improvement in the closed loop system performances and robustness using the proposed fractional order PI ^{λ}D ^{µ}A controller design.

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