Romain Bourdais

Integration of resource allocation coordination and branch-and-bound

In general, integer programming problems are computationally very hard to solve, which makes solving an integer programming problem with a large number of decision variables in a centralized way intractable. In this paper, we propose a novel integer optimization method for strategic planning by integrating the resource allocation coordination method into a branch-and-bound paradigm. Thanks to the distributed computation of the resource allocation coordination method and distributed evaluation of nodes in the branch-and-bound paradigm, our method is capable of solving an integer programming problem in a distributed way. Moreover, since in the branch-and-bound paradigm the size of solution space decreases monotonically as the iteration proceeds, it is guaranteed that the globally optimal solution to an integer programming problem is obtained by using our method. Finally, we apply our method to the optimal charging control problem of electric vehicles under constrained grid conditions in a simulation study.

Preservation of structural identifiability in expanded systems

Abstract The main result presented by this paper is that the structural identifiability of an original continues-linear time invariant (LTI) dynamic system can be preserved in expanded systems within the inclusion principle when using block structured complementary matrices. This preservation is ensured only for some selections of specific complementary matrices. Overlapping expansions of these systems are then discussed. An original system composed of two overlapped subsystems is used as a general prototype case. An illustrative example is given.

Multi-agent model predictive control based on resource allocation coordination for a class of hybrid systems with limited information sharing

We develop a multi-agent model predictive control method for a class of hybrid systems governed by discrete inputs and subject to global hard constraints. We assume that for each subsystem the local objective function is convex and the local constraint function is strictly increasing with respect to the local control variable. The proposed multi-agent control method is based on a distributed resource allocation coordination algorithm and it only requires limited information sharing among the local agents of the subsystems. Thanks to primal decomposition of the global constraints, the distributed algorithm can always guarantee global feasibility of the local control decisions, even in the case of premature termination. Moreover, since the control variables are discrete, a mechanism is developed to branch the overall solution space based on the outcome of the resource allocation coordination algorithm at each node of the search tree. Finally, the proposed multi-agent control method is applied to the charging control problem of electric vehicles under constrained grid conditions. This case study highlights the effectiveness of the proposed method.

A distributed algorithm to determine lower and upper bounds in branch and bound for hybrid Model Predictive Control

In this work, a class of model predictive control problems with mixed real-valued and binary control signals is considered. The optimization problem to be solved is a constrained Mixed Integer Quadratic Programming (MIQP) problem. The main objective is to derive a distributed algorithm for limiting the search space in branch and bound approaches by tightening the lower and upper bounds of objective function. To this aim, a distributed algorithm is proposed for the convex relaxation of the MIQP problem via dual decomposition. The effectiveness of the approach is illustrated with a case study.