Romain Bourdais, Jean Buisson, Didier Dumur, Hervé Guéguen, Daniel Moroscan

In this chapter, we propose a distributed model predictive control scheme based on the Dantzig-Wolfe decomposition to control a collection of linear dynamical systems coupled by linear global constraints. The resulting structure is composed of one optimization agent for each system, and another one that has to ensure that the global constraints are fulfilled. The global solution of the problem is found in a finite number of iterations.

Matthias A. Müller and Frank Allgöwer

In this chapter, we describe a distributed MPC algorithm for cooperative control of a network of systems which are coupled by constraints and pursue a common, cooperative control objective. The proposed DMPC algorithm cannot only be used for classical control objectives such as set point stabilization, but also for more general cooperative control tasks such as consensus and synchronization problems. Possible application fields include teams of mobile robots, formation flight of aircrafts, as well as satellite control.

Eduardo Camponogara

This chapter presents existing models and distributed optimization algorithms for model predictive control (MPC) of linear dynamic networks (LDNs). The models consist of networks of subsystems with deterministic and uncertain dynamics subject to local and coupling constraints on the control and output signals. The distributed optimization algorithms are based on gradient-projection, subgradient, interior-point, and dual strategies that depend on the nature of the couplings and constraints of the underlying networks. The focus will be on a class of LDNs in which the dynamics of the subsystems are influenced by the control signals of the upstream subsystems with constraints on state and control variables. A distributed gradient-based algorithm is presented for implementing an interior-point method distributively with a network of agents, one for each subsystem.

Giulio Betti, Marcello Farina, Riccardo Scattolini

The Distributed Predictive Control (DPC) algorithm presented in this chapter has been designed for control of an overall system made by linear discrete time dynamically interconnected subsystems. The underlying rationale is that each subsystem knows in advance the future state and input trajectories of the other subsystems and guarantees that its actual trajectories lie within certain bounds in the neighborhood of the reference ones. This method enjoys the following properties: (i) state and input constraints can be considered; (ii) convergence is guaranteed; (iii) it is not necessary for each subsystem to know the dynamical models of the other subsystems; (iv) the transmission of information is limited.