Decentralized H∞ Control of Interconnected Systems with Time-varying Delays

This paper focuses on the problem of delay dependent stability/stabilization of interconnected systems with time-varying delays. The approach is based on a new Lyapunov-Krasovskii functional. A decentralized delay-dependent stability analysis is performed to characterize linear matrix inequalities (LMIs) based on the conditions under which every local subsystem of the linear interconnected delay system is asymptotically stable. Then we design a decentralized state-feedback stabilization scheme such that the family of closedloop feedback subsystems enjoys the delay-dependent asymptotic stability for each subsystem. The decentralized feedback gains are determined by convex optimization over LMIs. All the developed results are tested on a representative example and compared with some recent previous ones

Decentralised delay-dependent static output feedback variable structure control

In this paper, an output feedback stabilisation problem is considered for a class of large scale interconnected time delay systems with uncertainties. The uncertainties appear in both isolated subsystems and interconnections. The bounds on the uncertainties are nonlinear and time delayed. It is not required that either the known interconnections or the uncertain interconnections are matched. Then, a decentralised delay-dependant static output feedback variable structure control is synthesised to stabilise the system globally uniformly asymptotically using the Lyapunov Razumikhin approach. A case study relating to a river pollution control problem is presented to illustrate the proposed approach

Distributed Design for Decentralized Control using Chordal Decomposition and ADMM

We propose a distributed design method for decentralized control by exploiting the underlying sparsity properties of the problem. Our method is based on chordal decomposition of sparse block matrices and the alternating direction method of multipliers (ADMM). We first apply a classical parameterization technique to restrict the optimal decentralized control into a convex problem that inherits the sparsity pattern of the original problem. The parameterization relies on a notion of strongly decentralized stabilization, and sufficient conditions are discussed to guarantee this notion. Then, chordal decomposition allows us to decompose the convex restriction into a problem with partially coupled constraints, and the framework of ADMM enables us to solve the decomposed problem in a distributed fashion. Consequently, the subsystems only need to share their model data with their direct neighbours, not needing a central computation. Numerical experiments demonstrate the effectiveness of the proposed method.Comment: 11 pages, 8 figures. Accepted for publication in the IEEE Transactions on Control of Network System

Decentralized pole assignment for interconnected systems

Given a general proper interconnected system, this paper aims to design a LTI decentralized controller to place the modes of the closed-loop system at pre-determined locations. To this end, it is first assumed that the structural graph of the system is strongly connected. Then, it is shown applying generic static local controllers to any number of subsystems will not introduce new decentralized fixed modes (DFM) in the resultant system, although it has fewer inputoutput stations compared to the original system. This means that if there are some subsystems whose control costs are highly dependent on the complexity of the control law, then generic static controllers can be applied to such subsystems, without changing the characteristics of the system in terms of the fixed modes. As a direct application of this result, in the case when the system has no DFMs, one can apply generic static controllers to all but one subsystem, and the resultant system will be controllable and observable through that subsystem. Now, a simple observer-based local controller corresponding to this subsystem can be designed to displace the modes of the entire system arbitrarily. Similar results can also be attained for a system whose structural graph is not strongly connected. It is worth mentioning that similar concepts are deployed in the literature for the special case of strictly proper systems, but as noted in the relevant papers, extension of the results to general proper systems is not trivial. This demonstrates the significance of the present work

Decentralized Implementation of Centralized Controllers for Interconnected Systems

Given a centralized controller associated with a linear time-invariant interconnected system, this paper is concerned with designing a parameterized decentralized controller such that the state and input of the system under the obtained decentralized controller can become arbitrarily close to those of the system under the given centralized controller, by tuning the controller's parameters. To this end, a two-level decentralized controller is designed, where the upper level captures the dynamics of the centralized closed-loop system, and the lower level is an observed-based sub-controller designed based on the new notion of structural initial value observability. The proposed method can decentralize every generic centralized controller, provided the interconnected system satisfies very mild conditions. The efficacy of this work is elucidated by some numerical examples

Delay-independent decentralised output feedback control for large-scale systems with nonlinear interconnections

In this paper, a stabilisation problem for a class of large-scale systems with nonlinear interconnections is considered. All the uncertainties are nonlinear and are subject to the effects of time delay. A decentralised static output feedback variable structure control is synthesised and the stability of the corresponding closed-loop system is analysed based on the Lyapunov Razumikhin approach. A set of conditions is developed to guarantee that the large-scale interconnected system is stabilised uniformly asymptotically. Further study shows that the conservatism can be reduced by employing additive controllers if the known interconnections are separated into matched and mismatched parts. It is not required that the subsystems are square. The designed controller is independent of time delay and thus it does not require memory. Simulation results show the effectiveness of the proposed approach

Time Complexity of Decentralized Fixed-Mode Verification

Given an interconnected system, this note is concerned with the time complexity of verifying whether an unrepeated mode of the system is a decentralized fixed mode (DFM). It is shown that checking the decentralized fixedness of any distinct mode is tantamount to testing the strong connectivity of a digraph formed based on the system. It is subsequently proved that the time complexity of this decision problem using the proposed approach is the same as the complexity of matrix multiplication. This work concludes that the identification of distinct DFMs (by means of a deterministic algorithm, rather than a randomized one) is computationally very easy, although the existing algorithms for solving this problem would wrongly imply that it is cumbersome. This note provides not only a complexity analysis, but also an efficient algorithm for tackling the underlying problem

Sequential Synthesis of Distributed Controllers for Cascade Interconnected Systems

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.Comment: Accepted to appear in the proceedings of the American Control Conference (ACC) 201