Sequential Synthesis of Distributed Controllers for Cascade Interconnected Systems

Abstract

We consider the problem of designing distributed controllers to ensure passivity of a large-scale interconnection of linear subsystems connected in a cascade topology. The control design process needs to be carried out at the subsystem-level with no direct knowledge of the dynamics of other subsystems in the interconnection. We present a distributed approach to solve this problem, where subsystem-level controllers are locally designed in a sequence starting at one end of the cascade using only the dynamics of the particular subsystem, coupling with the immediately preceding subsystem and limited information from the preceding subsystem in the cascade to ensure passivity of the interconnected system up to that point. We demonstrate that this design framework also allows for new subsystems to be compositionally added to the interconnection without requiring redesign of the pre-existing controllers.

A Decentralized Analysis and Control Synthesis Approach for Networked Systems with Arbitrary Interconnections

“…Emerging applications in infrastructure networks have renewed the attention towards analysis and control of largescale networked systems comprised of dynamically coupled subsystems [1], [2]. For example, in vehicular networks, a group of autonomous vehicles can co-ordinate with each other to maintain a particular formation that leads to saving energy as well as reducing congestion and improving safety in the transportation infrastructure [3], [4].…”

“…In such methods, controllers are derived locally at subsystems without explicit knowledge of the dynamics of the other subsystems. As pointed out in [1], distributed control synthesis approaches can be categorized into three groups: (i) Approaches that exploit/induce weak coupling between subsystems [10], [11]; (ii) Hierarchical approaches that compute (in a centralized manner) and enforce additional conditions on local control synthesis [12], [13]; (iii) Approaches that decompose the control synthesis process using numerical techniques such as methods of multipliers and Sylvester's criterion [1], [2], [14], [15]. In many networked systems of interest, assuming or enforcing weak coupling among subsystems is not practical [2].…”

Distributed Synthesis of Local Controllers for Networked Systems With Arbitrary Interconnection Topologies

“…In [34], we proposed a preliminary version of this approach to guarantee passivity for a limited class of networked systems with a cascade interconnection topology. In this paper, we consider arbitrary network topologies, as well as a more general quadratic dissipativity framework, which allows us to capture a variety of properties of interest, such as, L 2 stability, sector-boundedness, conicity, as well as passivity and its variants.…”

“…In this paper, we consider arbitrary network topologies, as well as a more general quadratic dissipativity framework, which allows us to capture a variety of properties of interest, such as, L 2 stability, sector-boundedness, conicity, as well as passivity and its variants. We further extend the approach to networks of switched systems, which were not considered in [34]. This paper is organized as follows.…”

Reinforcement Learning based Distributed Control of Dissipative Networked Systems

“…As a first step towards addressing this problem, we focus on a class of networked systems where each subsystem is dissipative [17] in open loop. Dissipativity is an input-output concept that can be used to guarantee a broad range of useful properties such as L 2 stability, robustness with respect to disturbances, and stability under time-delays [18]- [20] and has been widely used in traditional control theory for distributed controller synthesis [21]- [29]. In the context of RL, dissipativity has been used to enhance the convergence/performance of various learning schemes [30] and has been enforced as a system property for specific systems like Port-Hamiltonian systems [31], [32].…”