Worst-case computational complexity analysis for embedded MPC based on dual gradient method

In this paper we analyze the computational complexity of a linear model predictive control (MPC) scheme for embedded systems based on the dual gradient algorithm. We recast our MPC problem as a linearly constrained convex problem. When it is difficult to project on the primal feasible set described by linear constraints, we use the Lagrangian relaxation to handle the complicated constraints and then we apply the dual gradient algorithm for solving the corresponding dual. We give a full convergence rate analysis for dual gradient algorithm: we provide sublinear or linear estimates on the primal suboptimality and feasibility violation of the generated approximate primal solutions. Our analysis relies on the Lipschitz property of the dual function or an error bound property. Furthermore, the iteration complexity analysis is based on an approximate primal solution given by the last primal iterate sequence. We also discuss implementation aspects of the proposed algorithm on constrained linear MPC for embedded systems.