Ralph Hermans, Mircea Lazar and Andrej Jokic

We provide an almost decentralized solution to the problem of stabilizing a network of discrete-time nonlinear systems with coupled dynamics that are subject to local state/input constraints. By “almost decentralized” we mean that each local controller is allowed to use the states of neighboring systems for feedback, whereas it is not permitted to employ iterations between the systems in the network to compute the control action. The controller synthesis method used in this work is Lyapunov-based model predictive control. The closed-loop stability conditions are decentralized via a set of structured control Lyapunov functions (CLFs) for which the maximum over all the functions in the set is a CLF for the global network of systems. However, this does not necessarily imply that each function is a CLF for its corresponding subsystem. Additionally, a solution is provided for relaxing the temporal monotonicity of the network-wide CLF. For infinity-norm based structured CLFs and input-affine dynamics, we show that the decentralized MPC algorithm can be implemented by solving a single linear program in each network node. Two application examples are provided to illustrate the effectiveness of the developed theory and to show that the proposed method can perform as well as more complex distributed, iteration-based MPC algorithms.

Alexandra Grancharova and Tor Arne Johansen

A suboptimal approach to distributed Nonlinear Model Predictive Control (NMPC) for systems consisting of nonlinear subsystems with nonlinearly coupled dynamics subject to both state and input constraints is proposed. The approach applies a dynamic dual decomposition method to reformulate the original centralized NMPC problem into a distributed quasi-NMPC problem by linearization of the nonlinear system dynamics and taking into account the couplings between the subsystems. The developed approach is based entirely on distributed on-line optimization (by gradient iterations) and can be applied to large-scale nonlinear systems. The theoretical results related to the application of the distributedMPC approach to both linear and nonlinear systems are outlined and some simulation results are provided.

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.