Synthesis of separable controlled invariant sets for modular local control design

Abstract

Abstract-Many correct-by-construction control synthesis methods suffer from the curse of dimensionality. Motivated by this challenge, we seek to reduce a correct-by-construction control synthesis problem to subproblems of more modest dimension. As a step towards this goal, in this paper we consider the problem of synthesizing decoupled robustly controlled invariant sets for dynamically coupled linear subsystems with state and input constraints. Our approach, which gives sufficient conditions for decoupled invariance, is based on optimization over linear matrix inequalities which are obtained using slack variable identities. We illustrate the applicability of our method on several examples, including one where we solve local control synthesis problems in a compositional manner.

Distributed MPC: Guaranteeing Global Stability from Locally Designed Tubes

“…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.…”

“…The problem of finding separable PI sets is tackled in a similar way in Nilsson and Ozay (2015), where a set of LMIs is proposed to find simultaneously a set of local independent feedbacks K i that fulfil Assumption 2, and a corresponding collection of joint PI sets. This procedure is proposed to tackle disturbed local dynamics, but even when no disturbance is considered, the smaller LMI is of dimension 2n × 2n.…”

Compositional synthesis via a convex parameterization of assume-guarantee contracts

“…Linear systems. The closest works are [28] and [10]. In [28], the constrained set-invariance problem for discrete-time disturbed linear systems was considered.…”

“…The closest works are [28] and [10]. In [28], the constrained set-invariance problem for discrete-time disturbed linear systems was considered. However, the synthesis method was not compositional as the parameters of the controllers and the sets corresponding to assume-guarantee contracts, also characterized by zonotopes, were computed by solving a single large linear matrix inequality (LMI) problem.…”

“…However, the synthesis method was not compositional as the parameters of the controllers and the sets corresponding to assume-guarantee contracts, also characterized by zonotopes, were computed by solving a single large linear matrix inequality (LMI) problem. In [10], the same problem as in [28] was considered, the method was compositional, and was shown to scale well to 1000+ dimensions. However, there was no contract parameterization.…”