This paper introduces a solution to the reference trajectory tracking problem done by a differential wheeled mobile robot Khepera II. The paper includes a kinematic part and a dynamic part of the mathematical model of mobile robot. In this paper two approaches of the artificial intelligence are used i.e. genetic algorithm approach from evolutionary computing techniques and theory of neural networks. Genetic algorithm is used for parameters optimizing PID controller and K parameter so-called parameter speed of rotation at the tracking reference trajectory into defined control structure. For the creation forward and inverse neural model by the approach of neural networks are used forward neural networks of MLP type. The neural models are verified using Neural Network Toolbox. The forward neural model of the mobile robot is implemented into the IMC control structure together with the inverse neural model, which is used as a nonparametric neural controller. The purpose of the designed control structure is tracking the defined trajectory of the mobile robot using approaches of the artificial intelligence, which are verified by the simulations in the language Matlab/Simulink.
The chapter deals with the issues of an approximation of the solution to the problem of optimal control of a distributed parameter process. A mathematical model of the problem is expressed by a two-dimensional partial differential equation of heat transfer with boundary and initial conditions and an optimality selected criterion. In order to obtain an approximated solution to the defined problem, the least squares method has been applied, thereby it has been proved that the obtained solution is the approximation of the Green's function, eventually that of an impulse transition function. The possibility of the application of the least squares method algorithm to the solution of the mathematical model of a distributed parameter process control has also been indicated.
Purpose -The aim of the paper is to present the theory and algorithms based on the methods of systems optimal control for a numerical solution of a defined mathematical model of a system as well as that of a mathematical model of game theory. Design/methodology/approach -The paper brings a formulation of the mathematical model of a problem of systems optimal control with distributed parameters in Hilbert space. The mathematical model of the optimal control problem includes equations that also occur in the defined mathematical model of the theory of a two player zero-sum game. Optimization problems of game theory have been defined for the purpose of finding a saddle point of a functional satisfying task constraints 1 . 0. Findings -In order to find a saddle point of a functional and that one of a functional with a limitation, a designed algorithm of an iterative gradient method is presented. Furthermore, the paper contains a concept of algorithms designing that can be applied to a numerical solution of the defined problem of game theory. These algorithms can be realized on the basis of the methods of systems optimal control. After an adjoint state of the system is defined, a saddle point of a functional will be characterized by equations and inequalities. Originality/value -The contribution of the paper lies in the formulation of the theorems which express the necessary and sufficient conditions of optimality for saddle points of a functional. Furthermore, it has been proved that algorithms of methods of systems optimal control with distributed parameters can be used for the solution of a mathematical model of game theory. The paper contains original results achieved by the authors within scientific projects.
This paper introduces a methodology for one of the challenges regarding cyber-physical systems, ie modelling and control design them as hybrid systems. The proposed methodology comprises modules with specific steps to accomplish the tasks. Specifically, the paper aims to utilize hybrid systems framework onto the chosen hydraulic hybrid system with complex dynamics to showcase different aspects of hybrid systems. The mathematical model was derived using hybrid automata framework and then transformed into the linear form either using Jacobi matrices or using linear approximations without Jacobi matrices. After that the system was validated and analysed and the control design utilizing piecewise linear-quadratic regulator optimal control was proposed. Furthermore, parameters of control algorithm were tuned using particle swarm optimization algorithm. The whole logic, system dynamics and constrains are implemented within MATLAB/Simulink simulation environment using s -functions. The proposed methodology can be implemented on the various types of cyber-physical systems as far as they can be described as hybrid systems.
This paper deals with one of the challenges of cyber-physical systems, namely modelling them as hybrid systems. Specifically the paper aims to utilize hybrid systems framework onto the lift system which comes from the real laboratory lift. The mathematical model was derived using hybrid automata framework in synergy with linear temporal logic. Hybrid automata framework was used to describe continuous dynamics as well as discrete dynamics of the lift system mathematical model. Linear temporal logic was used to formally define rules according to which the lift system is constrained. The whole logic, system dynamics and constrains are then implemented within MATLAB/Simulink environment using Stateflow toolbox. Finally, the verification of the lift mathematical model is performed within chosen scenarios.
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