Distributed model predictive control using a chain of tubes

Abstract

Abstract-A new distributed MPC algorithm for the regulation of dynamically coupled subsystems is presented in this paper. At each time instant, the control action is computed via two robust controllers working in a nested fashion. The inner controller provides local reference trajectories computed on a fully decentralized framework. The outer controller uses this information to take into account the effects of the dynamic coupling and implement a distributed control action. The tube-based approach to robustness is employed. A supplementary constraint is included in the outer optimization problem to provide recursive feasibility of the overall controller.

Distributed MPC: Guaranteeing Global Stability from Locally Designed Tubes

“…In order to achieve these global properties, many DMPC implementations employ synthesis procedures that are either centralized (Maestre et al, 2011;Lucia et al, 2015), or require the solution of problems that can be computationally expensive (Conte et al, 2016;Kern and Findeisen, 2013). In this context, and in particular with tube-based DMPC controllers, the following assumption is usually required (see for example Farina and Scattolini (2012); Riverso and Ferrari-Trecate (2012); Baldivieso and Trodden (2016); Hernandez and Trodden (2016)), Assumption 2. (Block-diagonal stabilizability).…”

“…The control objective is to steer the whole system towards an arbitrary equilibrium point using locally applied horizontal forces. This plant is used as a numerical example for various DMPC algorithms, see for example Riverso and Ferrari-Trecate (2012); Baldivieso and Trodden (2016); Hernandez and Trodden (2016); Trodden et al (2016).…”

“…The main aspect in which they differ is in which type of interaction is allowed between subsystems, and how this is treated. In recent years, robust MPC techniques such as tube MPC (TMPC) (Mayne et al, 2005) and others (for example Chisci et al (2001)), have inspired several DMPC approaches (Farina and Scattolini, 2012;Riverso and Ferrari-Trecate, 2012;Farina et al, 2014;Lucia et al, 2015;Trodden et al, 2016;Baldivieso and Trodden, 2016;Hernandez and Trodden, 2016). The main idea of such approaches is to treat the interactions between subsystems as local disturbances that may be handled (conservatively) by robust local controllers.…”

Online Trajectory Generation With Distributed Model Predictive Control for Multi-Robot Motion Planning

“…In [12], a probabilistic collision avoidance method was considered using a chance-constrained nonlinear MPC framework, and demonstrated successful experiments involving quadrotors sharing a workspace with a human. Other robust MPC frameworks such as tube MPC have been developed for distributed multi-agent systems, both with linear [13] and nonlinear [14] dynamics. Although both approaches provide proofs and simulation results, they are not real-time implementable with current hardware and solver capabilities.…”

Nested distributed MPC

“…In pursuit of iteration-free methods that still achieve desirable guarantees, a few authors (Farina and Scattolini, 2012;Riverso and Ferrari-Trecate, 2012;Trodden et al, 2016;Hernandez and Trodden, 2016) have exploited ideas from robust MPC, and particularly tube-based MPC (Mayne et al, 2005). The basic idea is-considering the mutual interactions as exogenous disturbances-to augment the conventional MPC control law with an ancillary, disturbance rejection term, computed off-line and based on the theory of disturbance-invariant sets.…”