by I. Necoara

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.