Minimally Constrained Stable Switched Systems and Application to Co-simulation

We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is motivated by applications to (co-)simulation, where numerical stability is a hard constraint, but should be attained by restricting as little as possible the allowed behaviours of the simulators. We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirements.Comment: Technical report complementing the following conference publication: Gomes, Cl\'audio, Beno\^it Legat, Rapha\"el Jungers, and Hans Vangheluwe. "Minimally Constrained Stable Switched Systems and Application to Co-Simulation." In IEEE Conference on Decision and Control. Miami Beach, FL, USA, 201

Actuator fault estimation based on a switched LPV extended state observer

article en cours de soumission à une revueActuator fault estimation problem is tackled in this paper. The actuator faults are modeled in the form of multiplicative faults by using effectiveness factors representing the loss of efficiency of the actuators. The main contribution of this paper lies in the capability of dealing with the presented problem by using a switched LPV observer approach. The LTI system in the presence of faulty actuators is rewritten as a switched LPV system by considering the control inputs as scheduling parameters. Then, the actuator faults and the system states are estimated using a switched LPV extended observer. The observer gain is derived, based on the LMIs solution for the switched LPV systems. The presented actuator fault estimation approach is validated by two illustrative examples, the first one about a damper fault estimation of a semi-active suspension system, and the second one concerned to fault estimations on a multiple actuators system

Strengthening QC relaxations of optimal power flow problems by exploiting various coordinate changes

Motivated by the potential for improvements in electric power system economics, this dissertation studies the AC optimal power flow (AC OPF) problem. An AC OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering limits. The difficulty of an AC OPF problem is strongly connected to its feasible space\u27s characteristics. This dissertation first investigates causes of nonconvexities in AC OPF problems. Understanding typical causes of nonconvexities is helpful for improving AC OPF solution methodologies. This dissertation next focuses on solution methods for AC OPF problems that are based on convex relaxations. The quadratic convex (QC) relaxation is one promising approach that constructs convex envelopes around the trigonometric and product terms in the polar representation of the power flow equations. This dissertation proposes several improvements to strengthen QC relaxations of OPF problems. The first group of improvements provides tighter envelopes for the trigonometric functions and product terms in the power flow equations. Methods for obtaining tighter envelopes includes implementing Meyer and Floudas envelopes that yield the convex hull of trilinear monomials. Furthermore, by leveraging a representation of line admittances in polar form, this dissertation proposes tighter envelopes for the trigonometric terms. Another proposed improvement exploits the ability to rotate the base power used in the per unit normalization in order to facilitate the application of tighter trigonometric envelopes. The second group of improvements propose additional constraints based on new variables that represent voltage magnitude differences between connected buses. Using \u27bound tightening\u27 techniques, the bounds on the voltage magnitude difference variables can be significantly tighter than the bounds on the voltage magnitudes themselves, so constraints based on voltage magnitude differences can improve the QC relaxation --Abstract, page iv