Abstract In the paper we consider the problems of equitable and semi-equitable coloring of vertices of cubic graphs. We show that in contrast to the equitable coloring, which is easy, the problem of semi-equitable coloring is NP-complete within a broad spectrum of graph parameters. This affects the complexity of batch scheduling of unit-length jobs with cubic incompatibility graph on three uniform processors to minimize the makespan.

Abstract In the paper a description of a manipulator relative to a desired three-dimensional path was presented. The path is parameterized orthogonally to the Serret-Frenet frame which is moving along the curve. For the path two different time parameterizations were chosen. The control law for the RTR manipulator which ensures realization of the task was specified. Theoretical considerations were illustrated by simulation results.

Abstract A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n ⩾ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n ⩾ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel hyperjerk system are obtained as L1 = 0.1448, L2 = 0.0328, L3 = 0 and L4 = −1.1294. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as DKY= 3.1573. Next, an adaptive backstepping controller is designed to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global hyperchaos synchronization of the identical novel hyperjerk systems with three unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using SPICE is presented in detail to confirm the feasibility of the theoretical hyperjerk model.

Abstract We propose a generalization of the Butkovskiy's method of control with compact support [1] allowing to derive exact controllability conditions and construct explicit solutions in control problems for systems with distributed parameters. The idea is the introduction of a new state function which is supported in considered bounded time interval and coincides with the original one therein. By means of techniques of the distributions theory the problem is reduced to an interpolation problem for Fourier image of unknown function or to corresponding system of integral equalities. Treating it as infinite dimensional problem of moments, its L1, L2 and L∞-optimal solutions are constructed explicitly. The technique is explained for semilinear wave equation with distributed and boundary controls. Particular cases are discussed.

Abstract An autonomous mobile robot is a robot which can move and act autonomously without the help of human assistance. Navigation problem of mobile robot in unknown environment is an interesting research area. This is a problem of deducing a path for the robot from its initial position to a given goal position without collision with the obstacles. Different methods such as fuzzy logic, neural networks etc. are used to find collision free path for mobile robot. This paper examines behavior of path planning of mobile robot using three activation functions of wavelet neural network i.e. Mexican Hat, Gaussian and Morlet wavelet functions by MATLAB. The simulation result shows that WNN has faster learning speed with respect to traditional artificial neural network.

Abstract The paper presents the approximation problem of the inverse kinematics algorithms for the redundant manipulators. We introduce the approximation of the dynamically consistent Jacobian by the extended Jacobian. In order to do that, we formulate the approximation problem and suitably defined approximation error. By the minimization of this error over a certain region we can design an extended Jacobian inverse which will be close to the dynamically consistent Jacobian inverse. To solve the approximation problem we use the Cholesky decomposition and the Ritz method. The computational example illustrates the theory.

Abstract Stability analysis and design for continuous-time proportional plus derivative state observers is presented in the paper with the goal to establish the system state and actuator fault estimation. Design problem accounts a descriptor principle formulation for non-descriptor systems, guaranteing asymptotic convergence both the state observer error as fault estimate error. Presented in the sense of the second Lyapunov method, an associated structure of linear matrix inequalities is outlined to possess parameter existence of the proposed estimator structure. The obtained design conditions are verified by simulation using a numerical illustrative example.

Abstract The paper presents the dynamic multivariable model of Nuclear Power Plant steam turbine. Nature of the processes occurring in a steam turbine causes a task of modeling it very difficult, especially when this model is intended to be used for on-line optimal process control (model based) over wide range of operating conditions caused by changing power demand. Particular property of developed model is that it enables calculations evaluated directly from the input to the output, including pressure drop at the stages. As the input, model takes opening degree of valve and steam properties: mass flow and pressure. Moreover, it allows access to many internal variables (besides input and output) describing processes within the turbine. The model is compared with the static steam turbine model and then verified by using archive data gained from researches within previous Polish Nuclear Power Programme. Presented case study concerns the WWER-440 steam turbine that was supposed to be used in Żarnowiec. Simulation carried out shows compliance of the static and dynamic models with the benchmark data, in a steady state conditions. Dynamic model also shows good behavior over the transient conditions.

Abstract This paper presents techniques which base on the concept of flows thinning together with the identification techniques. These methods are proposed to determine the expected number of failures to assess the efficiency of technical diagnostics of instruments. Additionally, this research focuses on the improvement of multi-machine troubleshooting systems, based on the ‘AND-OR’ graphs. Respective algorithms are presented. The majority principle uses the input information to check the correctness of the decision regarding identification of faulty machines. In this paper we base on the complete testing algorithm for elements of multi-computer complexes searching by criteria of failed element.