A state space model for modeling and control of manufacturing processes

In this paper, a constrained discrete-time nonlinear state space model is proposed for modeling the dynamics of general manufacturing system. The model is an extension/modification of the one proposed by Rovithakis and Christodoulou. The proposed system possesses certain advantages over the existing ones, such as generality and ability to solve optimal policy tasks using optimal control methods as well as ability to model both deterministic and stochastic processing times; moreover its stability and robustness properties can be easily identified. The optimal control of such a system is shown to be equivalent to the solution of a system of static nonlinear equations. Despite the fact that no close form solution is obtained, it is believed that the resulted control policy obtained from the solution of the aforementioned system of equations is locally optimal. Simulations performed on a very simple manufacturing process are also presented.