Embedded Linear Model Predictive Control Through Mesh Adaptive Direct Search Algorithm In this paper we apply the derivativefree mesh adaptive direct search (MADS) algorithm to find the minimum of a constrained optimization problem, resulting from model predictive control (MPC). MPC requires indeed to solve an optimization problem online, at each sampling time of the system to regulate. A progressive barrier approach is used in MADS, in order to cope with the possibly infeasible initial point for the algorithm. Hardwareintheloop simulations are performed where the MADSbased MPC regulator is implemented on a microcontroller and a double integrator system is simulated on a PC. Control performances and circuit latency are assessed with respect to the number of MADS iterations.

Vertical hierarchical MPC for constrained linear systems Abstract   A hierarchical Model Predictive Control (MPC) formulation is presented for discretetime linear systems with state and input constraints. A vertical hierarchical controller, with one controller per level, reduces the computational burden associated with the solution of centralized MPC having long prediction horizons and short time steps. To guarantee satisfaction of state and input constraints in the presence of both known and unknown disturbances, a robust MPC formulation is used at each level while waysets are used as a novel coordination mechanism between controllers at different levels. These waysets are implemented as terminal state constraints on lowerlevel controllers and are computed online based on the optimal state trajectory of upperlevel controllers. To achieve the computational efficiency necessary for online calculation, waysets are represented as constrained zonotopes. State and input constraint satisfaction is proven for a hierarchical controller with an arbitrary number of levels and two numerical examples demonstrate the key features, performance, and scalability of the approach.