Archives of Control Sciences

Many nonlinear dynamical systems can present a challenge for the stability analysis in particular the estimation of the region of attraction of an equilibrium point. The usual method is based on Lyapunov techniques. For the validity of the analysis it should be supposed that the initial conditions lie in the domain of attraction. In this paper, we investigate such problem for a class of dynamical systems where the origin is not necessarily an equilibrium point. In this case, a small compact neighborhood of the origin can be estimated as an attractor for the system. We give a method to estimate the basin of attraction based on the construction of a suitable Lyapunov function. Furthermore, an application to Lorenz system is given to verify the effectiveness of the proposed method.

In this paper, a parallel multi-path variant of the well-known TSAB algorithm for the job shop scheduling problem is proposed. Coarse-grained parallelization method is employed, which allows for great scalability of the algorithm with accordance to Gustafon’s law. The resulting P-TSAB algorithm is tested using 162 well-known literature benchmarks. Results indicate that P-TSAB algorithm with a running time of one minute on a modern PC provides solutions comparable to the ones provided by the newest literature approaches to the job shop scheduling problem. Moreover, on average P-TSAB achieves two times smaller percentage relative deviation from the best known solutions than the standard variant of TSAB. The use of parallelization also relieves the user from having to fine-tune the algorithm. The P-TSAB algorithm can thus be used as module in real-life production planning systems or as a local search procedure in other algorithms. It can also provide the upper bound of minimal cycle time for certain problems of cyclic scheduling.

In this paper, a new set of intuitionistic fuzzy aggregation operators have been introduced under the environment of intuitionistic fuzzy sets (IFSs). For this, firstly focused on some existing aggregation operators and then new operational rules known as Dombi operation have been pro- posed which make the advancement of flexibility behavior with the parameter. Based on Dombi operation laws, some new averaging and geometric aggregation operators namely, intuitionistic fuzzy Dombi weighted averaging, ordered weighted averaging and hybrid weighted averaging operator, classified as IFDWA, IFDOWA and IFDHWA operators respectively and intuitionistic fuzzy Dombi geometric, ordered weighted geometric and hybrid weighted geometric operators, labeled as IFDWG, IFDOWG and IFDHWG operators respectively have been proposed. Further, some properties such as idempotency, boundedness, monotonicity and commutative are investigated. Finally, a multi-attribute decision-making model has been developed for the proposed operators to select the best mutual fund for investment. The execution of the comparative study has been examined with the existing operators in this environment.

Electromagnetic mill installation for dry grinding represents a complex dynamical system that requires specially designed control system. The paper presents model-based predictive control which locates closed loop poles in arbitrary places. The controller performs as gain scheduling prototype where nonlinear model – artificial recurrent neural network, is parameterized with additional measurements and serves as a basis for local linear approximation. Application of such a concept to control electromagnetic mill load allows for stable performance of the installation and assures fulfilment of the product quality as well as the optimization of the energy consumption.

This paper proposes a design procedure for observer-based controllers of discrete-time switched systems, in the presence of state’s time-delay, nonlinear terms, arbitrary switching signals, and affine parametric uncertainties. The proposed switched observer and the state- feedback controller are designed simultaneously using a set of linear matrix inequalities (LMIs). The stability analysis is performed based on an appropriate Lyapunov–Krasovskii functional with one switched expression, and in the meantime, the sufficient conditions for observer-based stabilization are developed. These conditions are formulated in the form of a feasibility test of a proposed bilinear matrix inequality (BMI) which is a non-convex problem. To make the problem easy to solve, the BMI is transformed into a set of LMIs using the singular value decomposition of output matrices. An important advantage of the proposed method is that the established sufficient conditions depend only on the upper bound of uncertain parameters. Furthermore, in the proposed method, an admissible upper bound for unknown nonlinear terms of the switched system may be calculated using a simple search algorithm. Finally, the efficiency of the proposed controller and the validity of the theoretical results are illustrated through a simulation example.

Consider the semilinear system defined by

x(i+1) = Ax(i) + f(x(i)), i≥ 0

x(0) = x0 ϵ ℜn

and the corresponding output signal y(i)=Cx(i), i ≥ 0, where A is a n x n matrix, C is a p x n matrix and f is a nonlinear function. An initial state x(0) is output admissible with respect to A, f, C and a constraint set Ω in ℜp if the output signal (y(i))i associated to our system satisfies the condition y(i) in Ω, for every integer i ≥ 0. The set of all possible such initial conditions is the maximal output admissible set Γ(Ω). In this paper we will define a new set that characterizes the maximal output set in various systems (controlled and uncontrolled systems). Therefore, we propose an algorithmic approach that permits to verify if such set is finitely determined or not. The case of discrete delayed systems is taken into consideration as well. To illustrate our work, we give various numerical simulations.

In this paper we have studied the driftless control system on a Lie group which arises due to the invariance of Black-Scholes equation by conformal transformations. These type of studies are possible as Black-Scholes equation can be mapped to one dimensional free Schrödinger equation. In particular we have studied the controllability, optimal control of the resulting dynamics as well as stability aspects of this system.We have also found out the trajectories of the states of the system through two unconventional integrators along with conventional Runge-Kutta integrator.

A new 4-D dynamical system with hyperchaos is reported in this work. It is shown that the proposed nonlinear dynamical system with hyperchaos has no equilibrium point. Hence, the new dynamical system exhibits hidden hyperchaotic attractor. An in-depth dynamic analysis of the new hyperchaotic system is carried out with bifurcation transition diagrams, multistability analysis, period-doubling bubbles and offset boosting analysis. Using Integral Sliding Mode Control (ISMC), global hyperchaos synchronization results of the new hyperchaotic system are described in detail. Furthermore, an electronic circuit realization of the new hyperchaotic system has been simulated in MultiSim software version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB.

Many real-time systems can be described as cascade space-state models of different orders. In this paper, a new predefined controller is designed using a Strongly Predefined Time Sliding Mode Control (SPSMC) scheme for a cascade high-order nonlinear system. The proposed control scheme based-on SMC methodology is designed such that the system states reach zero within a determined time prior to performing numerical simulation. Moreover, Fixed Time Sliding Mode Control (FSMC) and Terminal Sliding Mode Control (TSMC) schemes are presented and simulated to provide a comparison with the proposed predefined time scheme. The numerical simulation is performed in Simulink/MATLAB for the proposed SPSMC and the other two existing methods on two examples: second and of third order to demonstrate the effectiveness of the proposed SPSMC method. The trajectory tracking of the ship course system is addressed as an example of a second-order system. Synchronization of two chaotic systems, Genesio Tesi and Coullet, is considered as an example of a third-order system. Also, by using two performance criteria, a thorough comparison is made between the proposed predefined time scheme, SPSMC, and the two no predefined time schemes, FSMC and TSMC.