Modelling, analysis and control design of hybrid dynamical systems

Dominik Vošček – Anna Jadlovská – Dominik Grigľák

   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.

Keywords: cyber-physical system, hydraulic hybrid system, methodology, particle swarm optimization, piecewise affine system, piecewise LQR optimal control

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