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

Analysis and Design of Singular Markovian Jump Systems

This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H? control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, among other techniques. Features of the book include: · study of the stability problem for SMJSs with general transition rate matrices (TRMs); · stabilization for SMJSs by TRM design, noise control, proportional-derivative and partially mode-dependent control, in terms of LMIs with and without equation constraints; · mode-dependent and mode-independent H? control solutions with development of a type of disordered controller; · observer-based controllers of SMJSs in which both the designed observer and controller are either mode-dependent or mode-independent; · consideration of robust H? filtering in terms of uncertain TRM or filter parameters leading to a method for totally mode-independent filtering · development of LMI-based conditions for a class of adaptive state feedback controllers with almost-certainly-bounded estimated error and almost-certainly-asymptotically-stable corresponding closed-loop system states · applications of Markov process on singular systems with norm bounded uncertainties and time-varying delays Analysis and Design of Singular Markovian Jump Systems contains valuable reference material for academic researchers wishing to explore the area. The contents are also suitable for a one-semester graduate course

Stabilisation of descriptor Markovian jump systems with partially unknown transition probabilities

This paper is concerned with the stability and stabilisation problems for continuous-time descriptor Markovian jump systems with partially unknown transition probabilities. In terms of a set of coupled linear matrix inequalities (LMIs), a necessary and sufficient condition is firstly proposed, which ensures the systems to be regular, impulse-free and stochastically stable. Moreover, the corresponding necessary and sufficient condition on the existence of a mode-dependent state-feedback controller, which guarantees the closed-loop systems stochastically admissible by employing the LMI technique, is derived; the stabilizing state-feedback gain can also be expressed via solutions of the LMIs. Finally, numerical examples are given to demonstrate the validity of the proposed methods

Decentralised sliding mode control for a class of nonlinear interconnected systems

In this paper, a decentralised control strategy based on sliding mode techniques is proposed for a class of nonlinear interconnected systems. Both matched uncertainties in the isolated subsystems and mismatched uncertainties associated with the interconnections are considered. Under mild conditions, sliding mode controllers for each subsystem are designed in a decentralised manner by only employing local information. Conditions are determined which enable information on the interconnections to be employed in decentralised controller design to reduce conservatism. The developed results are applied to an automated highway system. Simulation results pertaining to a high-speed following system are presented to demonstrate the effectiveness of the approach

Positivity of Continuous-Time Descriptor Systems With Time Delays

This technical note is concerned with positivity characteristic of continuous-time descriptor systems with time delays. First, a set of necessary and sufficient conditions is presented to check the property. Then, considering a descriptor time-delay system with two assumptions, a new time-delay system is established whose positivity is equivalent to that of the original system. Furthermore, a set of necessary and sufficient conditions is provided to check the positivity of the new system. Finally, a numerical example is given to illustrate the validity of the results obtained

H ? filtering for stochastic singular fuzzy systems with time-varying delay

This paper considers the H? filtering problem for stochastic singular fuzzy systems with timevarying delay. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito-type stochastic differential equations. Based on an auxiliary vector and an integral inequality, a set of delay-dependent sufficient conditions is established, which ensures that the filtering error system is e?t - weighted integral input-to-state stable in mean (iISSiM). A fuzzy filter is designed such that the filtering error system is impulse-free, e?t -weighted iISSiM and the H? attenuation level from disturbance to estimation error is belowa prescribed scalar.Aset of sufficient conditions for the solvability of the H? filtering problem is obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities. Simulation examples are provided to illustrate the effectiveness of the proposed filtering approach developed in this paper

Adaptive and Robust Fault-Tolerant Tracking Control of Contact force of Pantograph-Catenary for High-Speed Trains

Abstract This paper presents a modified multi-body dynamic model and a linear time-invariant model with actuator faults (loss of effectiveness faults, bias faults) and matched and unmatched uncertainties. Based on the fault model, a class of adaptive and robust tracking controllers are proposed which are adjusted online to tolerate the time-varying loss of effectiveness faults and bias faults, and compensate matched disturbances without the knowledge of bounds. For unmatched uncertainties, optimal control theory is added to the controller design processes. Simulations on a pantograph are shown to verify the efficiency of the proposed fault-tolerant design approach

Robust holographic control of complex interconnected systems with similar structure

With development of scientific technology, the scale of engineering systems is more and more large. It is required that people must deal with some complicated systems and finish complicated tasks under complicated surroundings. Theorefore, we must face complicated systems seriously. In recent years, some new research methods such as mordern geometric method and differential algebra method have been applied to the study of control theory according to the development of nonlinear science, and it is possible for us to solve complicated enginering systems with the development of computer science, which promotes the investigation of complicated control systems. Now, We must recognize clearly that investagations of complicated systems will be a long-term and arduous task, and it is not possible to find a valid method to deal with general complicated control systems in recent decads. But we think that to study some complicated systems with special structure at first, then, to study general complicated control systems may be a kind of valid method. In this paper, based on the thoughts above, a class of complicated nonlinear control systems with similar structure is considered, and problems of structural holographic control and robust control are studied It is shown that both the theoretic analyzes and systems engineering design are able to be simplified by using similar structure of systems, and holographic property is closely connected with similar structure. The paper may be summarized as follows: In the first chapter, fundmental characteristics of general complicated systems are introduced and similar structure of complicated control systems is described. Then, some practical examples are given to illustrate the wide existences of similar systems. Finally, controllers with holographic structure are presented. In the second chapter, state feedback centralized controllers with holographic structure are designed for some similar systems such as nonlinear time-varying composite systems, nonlinear uncertain composite systems with isolated subsystems which are singal input linear systems or input-state decoupling systems, and parametric matched uncertain composite systems with isolated systems possessing uniform relative degrees. Then, state feedback decentralized controllers with holographic structure are designed for nonlinear similar large-scale systems with unmatched uncertainties. Because the controllers designed in this chapter are similar to"Bang-Bang"control and of holographic structure, it is easy to be designed in practical engineering systems. In the third chapter, observer design of similar systems is considered. First, a kind of robust variable-structure observer is proposed for"matched"uncertain composite systems. Then, an asympototic observer is designed for composite systems with the isolated subsystems possessing general nonlinear systems by using mordern differential geometric method. It is shown that observer design can be simplified by using similar structure of systems. In chapter 4, observer-based stabilization for nonlinear similar composite systems is discussed. The obtained results are applied to disc-shift systems. Simulation shows that the resuts are effective. In chapter 5, output feedback controllers with holographic structure for nonlinear composite systems are given to be used to stabilize the systems. The advantages of this chapter are that uncertaities involved in the chapter are unmatched, and the controllers are not only decentralized but also holographic. So it's of great pratical value In chapter 6, some tracking problems are considered. A kind of iterative learning control problem is studied for a class of nonlinear similar composite systems in section 1, and robust variable structure controller is proposed for a class of similar large scale systems with matched uncertainties to track desired output in section 2. Some problems to be investigated late and good prospects of the study of similar systems are proposed to conclude the paper

Robust Holographic Control Theory and Design of Complex Composite Systems with Similarity (In Chinese)

This book is the first monograph in the area of control of similar composite systems. It systematically presented the authors recent research results in the area. The concept of the similar composite systems as well as the research background is given first. Then some results about Stabilization, decentralized stabilization using state feedback and output feedback are presented. The observer design and observer based stabilization schemes are proposed. Finally Iterative learning control for nonlinear composite system is considered. Several simulation examples are presented to demonstrate the developed theoretical results