Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices.

In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition is 'exact' in the sense that it preserves all the information about the original system and the objective function. Previous work in this area has focused on strategies that exploit symmetries of the underlying system and of the objective function. Here, instead, we implement the algebraic method of simultaneous block diagonalization of matrices (SBD), which we show provides advantages both in terms of the dimension of the subproblems that are obtained and of the computation time. We provide practical examples with networked systems that demonstrate the benefits of applying the SBD decomposition over the decomposition method based on group symmetries.

Production Loss Analysis in Mobile Multi-skilled Robot Operated Flexible Serial Production Systems.

In a world where demand and supply can change instantaneously as demonstrated by the recent coronavirus pandemic, it is very important for our production lines to be able to handle abrupt changes very effectively. Flexible manufacturing systems (FMS) are designed to be able to ramp production up and down quickly to make this possible. In this paper, we propose a novel data-enabled method of modelling an FMS using mobile multi-skilled robots and evaluate its dynamic performance. We use permanent production loss as the performance metric and derive expressions for its evaluation and attribution and validate them using two case studies.

Supermodal Decomposition of the Linear Swing Equation for Multilayer Networks.

We study the swing equation in the case of a multilayer network in which generators and motors are modeled differently; namely, the model for each generator is given by second order dynamics and the model for each motor is given by first order dynamics. We also remove the commonly used assumption of equal damping coefficients in the second order dynamics. Under these general conditions, we are able to obtain a decomposition of the linear swing equation into independent modes describing the propagation of small perturbations. In the process, we identify symmetries affecting the structure and dynamics of the multilayer network and derive an essential model based on a 'quotient network.' We then compare the dynamics of the full network and that of the quotient network and obtain a modal decomposition of the error dynamics. We also provide a method to quantify the steady-state error and the maximum overshoot error. Two case studies are presented to illustrate application of our method.