Abstract-This paper considers the problem of solving Quadratic Programs (QP) arising in the context of distributed optimization and optimal control. A dual decomposition approach is used, where the QP subproblems are solved locally, while the constraints coupling the different subsystems in the time and space domains are enforced by performing a distributed non-smooth Newton iteration on the dual variables. The iterative linear algebra method Conjugate Gradient (CG) is used to compute the dual Newton step. In this context, it has been observed that the dual Hessian can be singular when a poor initial guess for the dual variables is used, hence leading to a failure of the linear algebra. This paper studies this effect and proposes a constraint relaxation strategy to address the problem. It is both formally and experimentally shown that the relaxation prevents the dual Hessian singularity. Moreover, numerical experiments suggest that the proposed relaxation improves significantly the convergence of the Distributed Dual Newton-CG.

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We propose a distributed algorithm for strictly convex quadratic programming (QP) problems with a generic coupling topology. The coupling constraints are dualized via Lagrangian relaxation. This allows for a distributed evaluation of the non-smooth dual function and its derivatives. We propose to use both the gradient and the curvature information within a non-smooth variant of Newton's method to find the optimal dual variables. Our novel approach is designed such that the large Newton system never needs to be formed. Instead, we employ an iterative method to solve the Newton system in a distributed manner. The effectiveness of the method is demonstrated on an academic optimal control problem. A comparison with state of-the-art first order dual methods is given.

SUMMARYIn this paper, we analyze and compare five distributed model predictive control (DMPC) schemes using a hydro-power plant benchmark. Besides being one of the most important sources of renewable power, hydropower plants present very interesting control challenges. The operation of a hydro-power valley involves the coordination of several subsystems over a large geographical area in order to produce the demanded energy while satisfying constraints on water levels and flows. In particular, we test the different DMPC algorithms using a 24-h power tracking scenario in which the hydro-power plant is simulated with an accurate nonlinear model. In this way, it is possible to provide qualitative and quantitative comparisons between different DMPC schemes implemented on a common benchmark, which is a type of assessment rare in the literature.

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