Pair-wise Subsystems Research Articles

Model decomposition-based fault-tolerant control for interconnected wave partial differential equation systems

The fault-tolerant control (FTC) issue for a class of interconnected wave-distributed parameter systems is addressed by using the inclusion principle. Both subsystem faults and coupling faults are considered. First, the original system is expanded into an equivalent decoupled system. The main structure of the expanded system consists of multiple pair-wise subsystems. Second, the pair-wise fault-tolerant controllers are designed to stabilise the pair-wise subsystems, which can compensate for the effects of subsystem faults and major coupling faults. Third, a coordinated fault-tolerant controller with a suitable coordinated compensator for the expanded system is constructed according to the pair-wise fault-tolerant controllers of all subsystems. The coordinated compensator is used to compensate for the effects of other minor interconnections and coupling faults, and the coordinated controller is designed for the expanded system. Furthermore, the fault-tolerant controller is obtained to guarantee asymptotical stability of the faulty interconnected wave system by satisfying the contraction condition. The numerical experiments are presented to illustrate the effectiveness of the FTC method.

A data‐driven fault detection and fault‐tolerant control scheme for large‐scale systems and its application on multi‐area interconnected power systems

Stimulated by the enhancing requirements for system safety as well as process reliability in complex industrial processes, this paper investigates a data-driven fault detection and fault-tolerant control scheme for large-scale systems. To this end, a pair-wise decomposition approach is first presented based on the inclusion principle, which expands the original large-scale system into a set of disjointed pair-wise subsystems. Then, for the pair-wise subsystems, the observer-based residual generators and observer-based state feedback controllers for fault detection and fault-tolerant control purpose are further developed in a decentralized way. On this basis, the fault-tolerant controller for the original large-scale system is obtained by the coordination and contraction of the decentralized observer-based state feedback controllers. Finally, the feasibility and effectiveness of the proposed scheme are demonstrated through the case study on a multi-area interconnected power system.

A common linear copositive Lyapunov function for switched positive linear systems with commutable subsystems

This article is concerned with the existence problem of a common linear copositive Lyapunov function (CLCLF) for switched positive linear systems with stable and pairwise commutable subsystems. Three families of such systems composed of only continuous-time subsystems, only discrete-time subsystems and mixed continuous- and discrete-time subsystems are considered, respectively. It is demonstrated that a CLCLF can always be constructed for the underlying system whenever its subsystems are continuous-time, discrete-time or the mixed type. The case when the number of subsystems is two is first considered, then the obtained result is extended to the general case. Three numerical examples are given to verify the validity of the developed results.

Coordinated Control for a Group of Interconnected Pairwise Subsystems

The implementation of pairwise decomposition is discussed on an interconnected system with uncertainties. Under the concept of system inclusion, two systems with the same expanded system achieved by the same expand transformation are considered as approximations. It is proven that a coordinated controller can be found to stabilize both the two systems. This controller is contracted from the coordinated controller of expanded system, with each pairwise subsystem having information structure constraint taken into consideration. At last, this controller design process is applied on a four-area power system treated as a group of subsystems with information structure constraints.

H∞Control of Pairwise Distributable Large-Scale TS Fuzzy Systems

The paper presents new conditions suitable in design of the stabilizing state controller for a class of continuous-time nonlinear systems, which are representable by pairwise distributable Takagi-Sugeno models. Taking into account the affine properties of the TS model structure and applying the pairwise subsystems fuzzy control scheme relating to the parallel distributed output compensators, the extended bounded real lemma form and the sufficient design conditions for pairwise decentralized control are outlined in terms of linear matrix inequalities. The proposed procedure decouples the Lyapunov matrix and the system parameter matrices in the LMIs and, using free tuning parameter, provides the way to obtain global stability of such large-scale TS systems and optimizes subsystems interactionH∞norm bounds.

Pair-wise decomposition and coordinated control of complex systems

Pair-wise decomposition and coordinated control for complex interconnected systems with any information structure constraints are proposed in this paper. Based on the inclusion principle, a permuted inclusion principle is presented to expand the system into an expanded space, from which a recurrent reverse order of pair-wise subsystems is extracted. By a standard LQ control, pair-wise controllers can be designed to stabilize and coordinate the pair-wise subsystems. According to these controllers, a coordinated compensator of subsystem interconnections is introduced in order to obtain a coordination-based controller for the expanded system. Therefore, a coordinated controller of the system can be contracted from the expanded space under the conditions of the inclusion principle. Moreover, a sufficient condition of connective stability for the system is also proved by the Lyapunov function and M-matrix. A main advantage of the proposed decomposition and control is that it allows any variation of information structure constraints of the system, especially the increase and decrease of subsystem numbers. Finally, the effectiveness of the proposed methodology is demonstrated by an application of automatic generation control to a four-area electric power system.

Decomposition and Stability Analysis for Complex Systems with Dynamic Interconnections

A method to decompose dynamic complex systems is proposed, that is, by using the dynamic inclusion principle and permutation transformation, complex system with information constrains of dynamic topology structure is decomposed as a group of pair-wise decoupled subsystems in the expanded space. Then according to the Lyapunov method, the connective stability of pair-wise subsystems is discussed by constructing Lyapunov functions in the case all isolated systems are stable, the conditions of connective stability for the expanded system are obtained, which are also adapt to the original system based on inclusion principle. Finally, the theorem and deduction of connective stability for the dynamic interconnnected complex system are given.

Modeling and decomposition of complex dynamic interconnected systems

Dynamic graphs and dynamic adjacency matrix are introduced to model for a class complex dynamic interconnected system in this paper. Three types of fundamental topology structures of the systems are described according to the multi-overlapping information structure constraints. By using the inclusion principle and permutation transformation, the system is decomposed as a group of pair-wise subsystems in the expanded space. In the framework of subsystems, the system appears as pair-wise decoupled, it provides convenience for us to design decentralized control scheme for such systems. Finally, the proposed modeling and decomposition methodology is applied to a four-subsystem dynamic interconnected system.

Overlapping decentralized approach to automation generation control of multi-area power systems

An overlapping decentralized control scheme is presented and applied to automatic generation control (AGC) for multi-area power systems. Based on the inclusion principle, the system is first decomposed in the expanded space as a group of pair-wise subsystems (areas). Then, the decentralized controllers designed, by standard linear quadratic (LQ) control laws are implemented in each pair-wise subsystem. Finally, the overlapping decentralized controller is obtained by coordinating and contracting the pair-wise decentralized controllers from the expanded space to the original space, preserving the inclusion conditions. When applied to AGC of a four-area power system, the proposed methodology not only guarantees AGC qualities, but also increases the system reliability with respect to a wide variety of structured perturbations. Simulation results illustrate the effectiveness of the presented approach both in the general case of information structure constraints and in the cases when some pairs of subsystems are disconnected by unpredicted faults.