Rate Analysis of Inexact Dual Fast Gradient Method for Distributed MPC
In this chapter we propose a dual decomposition method based on inexact dual gradient information and constraint tightening for solving distributed model predictive control (MPC) problems for network systems with state-input constraints. The coupling constraints are tightened and moved in the cost using the Lagrange multipliers. The dual problem is solved by a fast gradient method based on approximate gradients for which we prove sublinear rate of convergence. We also provide estimates on the primal and dual suboptimality of the generated approximate primal and dual solutions and we show that primal feasibility is ensured by our method. Our analysis relies on the Lipschitz property of the dual MPC function and inexact dual gradients. We obtain a distributed control strategy that has the following features: state and input constraints are satisfied, stability of the plant is guaranteed, whilst the number of iterations for the suboptimal solution can be precisely determined.
The research leading to these results has received funding from: the European Union (FP7/2007–2013) under Grant agreement no 248940; CNCS (project TE-231, 19/11.08. 2010); ANCS (project PN II, 80EU/2010); POSDRU/89/1.5/S/62557.
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