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In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems.Our algorithm is based on block coordinate descent updates in parallel and has a very simple iteration. We prove (sub)linear rate of convergence for the new algorithm under standard assumptions for smooth convex optimization.Further, our algorithm uses local information and thus is suitable for distributed implementations. Moreover, it has low iteration complexity, which makes it appropriate for embedded control. An MPC scheme based on this new parallel algorithm is derived, for which every subsystem in the network can compute feasible and stabilizing control inputs using distributed and cheap computations.For ensuring stability of the MPC scheme, we use a terminal cost formulation derived from a distributed synthesis. Preliminary numerical tests show better performance for our optimization algorithm than other existing methods.

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In this paper we investigate the problem of optimal real-time power dispatch of an interconnection of conventional power generation plants, renewable resources and energy storage systems. The objective is to minimize imbalance costs and maximize profits whilst satisfying user demand. The managing company is able to trade energy on an electricity market. Energy prices, demand and renewable generation are considered stochastic processes. We show that under certain assumptions, the stochastic power dispatch problem over a finite horizon can be recast into a stochastic optimization formulation but with deterministic constraints. We carry out a systematic study of stochastic optimization methods to solve this problem. We also show that this problem can be approximated by a proper deterministic optimization problem using the sample average approximation method, which can then be solved by standard means.