Cooperative control of dynamically decoupled systems via distributed model predictive control

Abstract

SUMMARY In this paper, we propose a general framework for distributed model predictive control of discrete‐time nonlinear systems with decoupled dynamics but subject to coupled constraints and a common cooperative task. To ensure recursive feasibility and convergence to the desired cooperative goal, the systems optimize a local cost function in a sequential order, whereas only neighbor‐to‐neighbor communication is allowed. In contrast to most of the existing distributed model predictive control schemes in the literature, we do not necessarily consider the stabilization of an a priori known set point. Instead, also other cooperative control tasks such as consensus and synchronization problems can be handled within the proposed framework. In particular, one of our main contributions is to show how for the latter case the terminal cost functions and the terminal region can be suitably defined and computed. Furthermore, we illustrate our results with simulation examples. Copyright © 2012 John Wiley & Sons, Ltd.

Feasible parallel-update distributed MPC for uncertain linear systems sharing convex constraints

“…The m th component of q c − t c − P cz * c (k + j) is equal to the slack remaining in constraint c, at prediction step j, in the direction p cm , given the known coupling outputsz * cr (k + j) of each r ∈ I c . Rewriting (16),…”

“…(i) Existence follows from Proposition 1: for all i ∈ I opt (k), and any The implication is that any subset of subsystems may optimize simultaneously, and (i) a feasible solution to each problem is guaranteed to exist, (ii) all coupled constraints remain satisfied, if the coupled constraint set in subsystems i's MDOCP is chosen as Z c q ci ( j) , withq ci ( j) satisfying (13) and (16). Theorem 1 assumes the existence and availability of suchq ci ( j), but the question remains of whether suchq ci ( j) can be found easily.…”

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Design Of Real-Time Implementable Distributed Suboptimal Control: An LQR Perspective

“…One popular approach is based on model predictive control (MPC) as presented in [12], [14], [15], [16], and [24]. In this approach, convergence to an optimal solution is guaranteed but at the expense of communication of entire trajectories among agents repeatedly.…”

A Distributed Framework for Real Time Path Planning in Practical Multi-agent Systems

“…However, only centralized solutions have been proposed based on these approaches (Earl and D'Andrea, 2007;Chasparis and Shamma, 2008). Another popular approach is based on model predictive control (MPC) in which each agent assumes a model for all the other dynamic agents in its environment over a finite prediction horizon and solves an optimization problem (see for example Dunbar and Murray (2002);FerrariTrecate et al (2009);Müller et al (2012)). However, these solutions typically require communication of entire trajectories among neighboring agents, which can result in excessive communication cost and latency in decision making.…”