Modeling and stability analysis of autonomously controlled production networks

We present methods and tools for modeling autonomously controlled production networks and investigation of their stability properties. Production networks are described as an interconnected dynamical systems of two types: systems of ordinary differential equations and time-delay systems. In particular with the help of time-delays we incorporate transportation times and implement an autonomous control method, namely the queue length estimator (QLE). By stability we mean, roughly speaking, boundedness of the state of a system (e.g., the inventory level or the work in progress) over the time under bounded external inputs. In our stability analysis we consider the case, when all the subsystems describing logistics locations are stable. We derive sufficient conditions that guarantee stability of the network. To this end we utilize Lyapunov functions and a small gain condition.