The convergence of assembly discrete event systems using Markov chains

A new approach to the planning and analysis of the successful convergence of assembly is presented. The convergence is referred to as p-convergence, since it is derived within a probability framework. The assembly is modeled as a hybrid dynamic system (HDS) accounting for the presence of the discrete change of contact and the continuous movement during the process. The continuous property is then employed to represent an assembly DES as a Markov chain such that p-convergence can be proposed. To derive conditions for p-convergence of the full assembly, methods for estimating the transition probability matrix are derived for the perfect case, the tracking error case, and the case of parameter uncertainty. It is shown that p-convergence for an assembly DES requires a control effort which is significantly more realistic for practical implementation than current methods presented in the literature