Modeling and stability analysis of autonomously controlled production networks

Abstract

We present methods and tools for modeling autonomously controlled production networks and investigation of their stability properties. Production networks are described as interconnected dynamical systems of two types: systems of ordinary differential equations and timedelay systems. In particular with the help of time-delays, we incorporate transportation times and implement an autonomous control method, namely the queue length estimator. 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.

Game Analysis of Determinants of Stability of Semiconductor Modular Production Networks

“…[11]. Therefore, the stability of modular production network refers to the normal fluctuation state of a harmonious networking relationships maintained by member enterprises in a modular production network for given production goals [12].…”

“…Therefore, the stability of modular production network refers to the normal fluctuation state of a harmonious networking relationships maintained by member enterprises in a modular production network for given production goals [12]. The stability usually has two meanings: one indicates relatively dynamic stability [11]. As an open and dynamic system, modular production networks will change with the market.…”

Autonomous and Central Control of Production Networks

“…The proof can be found in [6]. For certain scenarios of production networks it may happen that the conditions to guarantee stability in Proposition 1 are conservative, which means that one can find parameters which do not satisfy the conditions, but the trajectory of the state of the network is bounded (stable).…”

“…f : C [−θ , 0] ; R N × R M → R N is a locally Lipschitz continuous functional on any bounded set. Using interconnections of time-delay systems one can model general production networks with transportation times, where (1) or (2) must be adapted accordingly (see [6]). Also the ISS property has to be defined for systems of the form (14) and interconnected systems of such type.…”

“…It was shown in [11] that if each subsystem of an interconnected system with timedelays admits a LR or a LK function(al) and if the small-gain condition (12) is satisfied, then the whole network possesses the ISS property. A certain scenario of an autonomously controlled production network was investigated using the mentioned tools in [6,7].…”