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.