A Distributed Approach for the Optimal Power Flow Problem Based on ADMM and Sequential Convex Approximations

The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial, though their global optimality is not guaranteed. Existing semi-definite programming relaxation based approaches are restricted to OPF problems where zero duality holds. In this paper, an efficient novel method to address the general nonconvex OPF problem is investigated. The proposed method is based on alternating direction method of multipliers combined with sequential convex approximations. The global OPF problem is decomposed into smaller problems associated to each bus of the network, the solutions of which are coordinated via a light communication protocol. Therefore, the proposed method is highly scalable. The convergence properties of the proposed algorithm are mathematically substantiated. Finally, the proposed algorithm is evaluated on a number of test examples, where the convergence properties of the proposed algorithm are numerically substantiated and the performance is compared with a global optimal method.Comment: 14 page

Data-driven inversion-based control of nonlinear systems

In this paper, we introduce the Data-Driven Inversion-Based Control (D2-IBC) method for nonlinear control system design. The method relies on a two degree-of-freedom architecture, with a nonlinear controller and a linear controller running in parallel, and does not require any detailed physical knowledge of the plant to control. Specically, we use input/output data to synthesize the control action by employing convex optimization tools only. We show the eectiveness of the proposed approach on a simulation example, where the D2-IBC performance is also compared to that of the Direct FeedbacK (DFK) design approach, a benchmark method for nonlinear controller design from data

An asymptotically stable scheme for diffusive coagulation-fragmentation models

This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation with diffusion in space. A finite volume scheme is developed, based on a conservative formulation of the space nonhomogeneous coagulation-fragmentation model, it is shown that the scheme preserves positivity, total volume and global steady states. Finally, several numerical simulations are performed to investigate the long time behavior of the solution