Distributed synthesis and stability of cooperative distributed model predictive control for linear systems

Abstract

This paper presents a new formulation and synthesis approach for stabilizing cooperative distributed model predictive control (MPC) for networks of linear systems, which are coupled in their dynamics. The controller is defined by a network-wide constrained optimal control problem, which is solved online by distributed optimization. The main challenge is the definition of a global MPC problem, which both defines a stabilizing control law and is amenable to distributed optimization, i.e., can be split into a number of appropriately coupled subproblems. For such a combination of stability and structure, we propose the use of a separable terminal cost function, combined with novel time-varying local terminal sets. For synthesis, we introduce a method that allows for constructing these components in a completely distributed way, without central coordination. The paper covers the nominal case in detail and discusses the extension of the methodology to reference tracking. Closed-loop functionality of the controller is illustrated by a numerical example, which highlights the effectiveness of the proposed controller and its time-varying local terminal sets.

Distributed MPC: Guaranteeing Global Stability from Locally Designed Tubes * *Work supported by Doctoral Scholarship from CONICYT-PFCHA/ Concurso para Beca de Doctorado en el Extranjero{ 72150125, and the Harry Nicholson PhD Scholarship, Department of Automatic Control & Systems Engineering, University of Sheffild.

“…This collection forms what can be referred to as a square PI set, given that Z is defined by the cross product of subsets of the local dynamics state space. This is also pointed out in Maestre et al (2011);Lucia et al (2015); Nilsson and Ozay (2015); Conte et al (2016). Remark 17.…”

“…In order to find this feedback, a set of local LMIs is posed alongside with a single global LMI of dimension 4n × 4n (where n is the overall dimension of the plant). A similar problem is found in Conte et al (2016), where a distributed optimization approach is proposed to find the solution to the local LMIs, in the presence of a system-wide coupled LMI.…”

“…), from a possibly distributed design. 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.…”

“…These usually require the existence of a global linear feedback with a certain structure affine to the interaction pattern of the global system. This type of assumption is also present in DMPC techniques that are not based on robust approaches such as Conte et al (2016); Maestre et al (2011).…”

Data-driven process decomposition and robust online distributed modelling for large-scale processes

“…Networked distributed methods are the hotspot of many research fields of process automation, including distributed predictive control (Conte, Jones, Morari, & Zeilinger, 2016), networked control system (Baldea et al, 2013), distributed optimisation (Lin, Ren, & Song, 2016), distributed fault detection, etc. (Boem, Ferrari, Parisini, & Polycarpou, 2015).…”