Decentralized Observer Design for a Class of Nonlinear Uncertain Large Scale Systems with Lumped Perturbations

Many valuable properties of the state feedback method can not be applied to some class of control systems while some of the system states cannot be measured directly. An attractive alternative approach is to make good use of a state observer. In this paper, a new decentralized sliding mode observer (DSMO) is proposed for a class of nonlinear uncertain large‐scale systems (LSS) with lumped perturbations based on the sliding mode control (SMC) theory. Our main result presented here is that we introduce a new switching term to the traditional LSS observer design for a class of large‐scale system to generate a new decentralized sliding mode observer. The generalized matrix inverse concept is adopted to avoid using the un‐measurable state and the global reaching condition of the sliding mode for each error subsystem is guaranteed. The stability of each equivalent error subsystem is verified based on the strictly positive real concept. It also shows that the investigated uncertain large‐scale systems still possesses the property of insensitivity to the lumped perturbations as does the traditional linear system. Moreover, the state transformation approach is no longer needed as there is no longer concern about the problems of finding a suitable transformation or indirect estimated states, since the proposed DSMO is not based on the transformed system model. Finally, a numerical example with a series of computer simulations is given to demonstrate the validity of the proposed decentralized sliding mode observer.     

A novel ecological network‐based computation platform as a grid middleware system

Next‐generation grid systems where the emphasis shifts to distributed global collaboration, a service‐oriented approach, and information layer issues exhibit a strong sense of automation. Requirements for these systems resemble the self‐organizing and the self‐healing properties of natural ecosystems. Inspired by this resemblance, we introduce some key ecological concepts and mechanisms into the design for the third‐generation grid systems. In this article, a novel Ecological Network‐based Grid Middleware (ENGM), which is based on Ecological Network Computing Environment (ENCE), is proposed. First, we discuss how to design the ENCE by agent‐oriented approaches based on the key concepts and principles of ecosystems. ENCE provides a new computing and problem‐solving paradigm by combining natural ecosystem mechanisms with agent technologies. Then, we design the ENGM with built‐in mechanisms to support desirable requirements of new grid systems, namely scalability, adaptability, self‐organization, simplicity, and survivability. Based on Jeffery's conceptual model, we also present a corresponding grid‐computing prototype that embeds ENGM layers from the implementation point of view. The ENGM will be useful to address the challenges of the third‐generation grid systems. Finally, as a demonstration, we built an ENGM platform‐based commercial grid service environment and developed a prototype of enterprise supply chain management system. The experimental results demonstrate that the proposed ENGM satisfies the requirements of the next‐generation grid and is suitable for new generation grid applications. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 859–884, 2004.     

Adaptive decentralized finite‐time output tracking control for MIMO interconnected nonlinear systems with output constraints and actuator faults

In this work, we present a novel adaptive decentralized finite‐time fault‐tolerant control algorithm for a class of multi‐input–multi‐output interconnected nonlinear systems with output constraint requirements for each vertex. The actuator for each system can be subject to unknown multiplicative and additive faults. Parametric system uncertainties that model the system dynamics for each vertex can be effectively dealt with by the proposed control scheme. The control input gain functions of the nonlinear systems can be not fully known and state dependent. Backstepping design with a tan‐type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, with the use of graph theory, finite‐time convergence of the system output tracking error into a small set around zero is guaranteed for each vertex, while the time‐varying constraint requirement on the system output tracking error for each vertex will not be violated during operation. An illustrative example on 2 interacting 2‐degree‐of‐freedom robot manipulators is presented in the end to further demonstrate the effectiveness of the proposed control scheme.     

Arbitration (or how to merge knowledge bases)

Knowledge-based systems must be able to “intelligently” manage a large amount of information coming from different sources and at different moments in time. Intelligent systems must be able to cope with a changing world by adopting a “principled” strategy. Many formalisms have been put forward in the artificial intelligence (AI) and database (DB) literature to address this problem. Among them, belief revision is one of the most successful frameworks to deal with dynamically changing worlds. Formal properties of belief revision have been investigated by Alchourron, Gardenfors, and Makinson, who put forward a set of postulates stating the properties that a belief revision operator should satisfy. Among these properties, a basic assumption of revision is that the new piece of information is totally reliable and, therefore, must be in the revised knowledge base. Different principles must be applied when there are two different sources of information and each one has a different view of the situation-the two views contradicting each other. If we do not have any reason to consider any of the sources completely unreliable, the best we can do is to “merge” the two views in a new and consistent one, trying to preserve as much information as possible. We call this merging process arbitration. In this paper, we investigate the properties that any arbitration operator should satisfy. In the style of Alchourron, Gardenfors, and Makinson we propose a set of postulates, analyze their properties, and propose actual operators for arbitration     

Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction

In this paper we improve on the incomplete oblique projections (IOP) method introduced previously by the authors for solving inconsistent linear systems, when applied to image reconstruction problems. That method uses IOP onto the set of solutions of the augmented system Ax?r=b, and converges to a weighted least‐squares solution of the system Ax=b. In image reconstruction problems, systems are usually inconsistent and very often rank‐deficient because of the underlying discretized model. Here we have considered a regularized least‐squares objective function that can be used in many ways such as incorporating blobs or nearest‐neighbor interactions among adjacent pixels, aiming at smoothing the image. Thus, the oblique incomplete projections algorithm has been modified for solving this regularized model. The theoretical properties of the new algorithm are analyzed and numerical experiments are presented showing that the new approach improves the quality of the reconstructed images.     

A New Approach For Stability Analysis Of Time‐Dependent Switched Continuous‐Time Linear Systems

In this paper, a new approach for stability analysis of time‐dependent switched linear systems is proposed. System equivalence is the main idea in this new approach, which derives a switched discrete linear parameter‐varying system from the switched continuous‐time linear switched system with interval dwell time, and the stability properties of the two corresponding systems are proved to be equivalent. Then, by applying a quadratic Lyapunov function approach for the equivalent switched discrete system, the stability of the switched continuous‐time linear system can be established without checking any average dwell time condition. Finally the computation complexity is analyzed, and mode incidence matrix is introduced to reduce the computation cost.     

A general analysis and control framework for process systems with inventory recycling

In this work, we generalize our previous results concerning the impact of material recycling and energy recovery on plant dynamics and control. We define a generic class of integrated process systems, in which an extensive quantity that obeys conservation laws is recovered from the process output and recycled to the process feed; the operation of the system is assumed to be subject to time‐varying, measurable disturbances. We establish, in this general case, that integration is conducive to the emergence of a two‐time‐scale dynamic behavior and derive reduced‐order models for the dynamics in each time scale. Subsequently, we postulate a hierarchical control framework that exploits these dynamics results in the design of coordinated fast and slow feedback/feedforward controllers and formulate a stability result for the closed‐loop system. We demonstrate these concepts on a case study concerning an energy‐integrated process. Copyright © 2013 John Wiley & Sons, Ltd.     

Fractional‐order–dependent global stability analysis and observer‐based synthesis for a class of nonlinear fractional‐order systems

This paper focuses on proposing novel conditions for stability analysis and stabilization of the class of nonlinear fractional‐order systems. First, by considering the class of nonlinear fractional‐order systems as a feedback interconnection system and applying small‐gain theorem, a condition is proposed for L₂‐norm boundedness of the solutions of these systems. Then, by using the Mittag‐Leffler function properties, we show that satisfaction of the proposed condition proves the global asymptotic stability of the class of nonlinear fractional‐order systems with fractional order lying in (0.5, 1) or (1.5, 2). Unlike the Lyapunov‐based methods for stability analysis of fractional‐order systems, the new condition depends on the fractional order of the system. Moreover, it is related to the H_∞‐norm of the linear part of the system and it can be transformed to linear matrix inequalities (LMIs) using fractional‐order bounded‐real lemma. Furthermore, the proposed stability analysis method is extended to the state‐feedback and observer‐based controller design for the class of nonlinear fractional‐order systems based on solving some LMIs. In the observer‐based stabilization problem, we prove that the separation principle holds using our method and one can find the observer gain and pseudostate‐feedback gain in two separate steps. Finally, three numerical examples are provided to demonstrate the advantage of the novel proposed conditions with the previous results.     

Optimization of dependently controlled jump rates of JLQG problem

The Jump Linear Quadratic Gaussian (JLQG) model is well studied due to its wide applications. However, JLQG with controlled jump rates are rarely researched, while the existing studies usually impose an assumption that jump rates are independent and separately controlled. In practical systems, their jump rates may not be independent of each other. In this paper, we consider a continuous‐time JLQG model with dependently controlled jump rates and formulate it as a two‐level control problem. The low‐level problem is a standard JLQG problem, thus we focus on solution of high‐level problem. We propose a Markov decision process‐based approach to calculate performance gradient with respect to jump rates control variable and develop a gradient‐based optimization algorithm. We present an application of manufacturing system to illustrate the main results of this paper. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A simplification of a real‐time verification problem

We revisit the problem of real‐time verification with dense‐time dynamics using timeout and calendar‐based models and simplify this to a finite state verification problem. We introduce a specification formalism for these models and capture their behaviour in terms of semantics of timed transition systems. We discuss a technique, which reduces the problem of verification of qualitative temporal properties on infinite state space of a large fragment of these timeout and calender‐based transition systems into that on clock‐less finite state models through a two‐step process comprising of digitization and finitary reduction. This technique enables us to verify safety invariants for real‐time systems using finite state model checking avoiding the complexity of infinite state (bounded) model checking and scale up models without applying techniques from induction‐based proof methodology. In the same manner, we verify timeliness properties. Moreover, we can verify liveness for real‐time systems, which are not possible by using induction with infinite state model checkers. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive stabilization of nonlinear teleoperation systems: An SIIOS approach

In this paper, the adaptive control problem of nonlinear teleoperation system based on the point of view of state‐independent input‐to‐output stability is addressed. By intentionally introducing the switched filter systems, a new IOS‐based control framework based on subsystem decomposition is developed. By designing the proper nonlinear controller, the complete closed‐loop system is first modeled into two interconnected subsystems with some well‐defined auxiliary variables. Then utilizing the small gain theorem, the weakly state‐independent input‐to‐output stability of complete system can be derived by the stability of each subsystem. As an important extension, the proposed control scheme is also proved to be suitable for the control of the single‐master‐multi‐slave teleoperation systems. Finally, the numerical example is given to demonstrate the effectiveness. Copyright © 2016 John Wiley & Sons, Ltd.     

Generic properties and control of linear structured systems: a survey

In this survey paper, we consider linear structured systems in state space form, where a linear system is structured when each entry of its matrices, like A,B,C and D, is either a fixed zero or a free parameter. The location of the fixed zeros in these matrices constitutes the structure of the system. Indeed a lot of man-made physical systems which admit a linear model are structured. A structured system is representative of a class of linear systems in the usual sense. It is of interest to investigate properties of structured systems which are true for almost any value of the free parameters, therefore also called generic properties. Interestingly, a lot of classical properties of linear systems can be studied in terms of genericity. Moreover, these generic properties can, in general, be checked by means of directed graphs that can be associated to a structured system in a natural way. We review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms. By properties we mean here system-specific properties like controllability, the finite and infinite zero structure, and so on, as well as, solvability issues of certain classical control problems like disturbance rejection, input-output decoupling, and so on. In this paper, we do not try to be exhaustive but instead, by a selection of results, we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool. We emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only. Moreover, the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well-known polynomially bounded combinatorial techniques for larger systems.     

Extending the object model to provide explicit support for crosscutting concerns

Concurrent systems tend to have certain properties that are not localized in single modular units, but their implementations cut across functional components, increasing coupling and making modular units difficult to reuse and adapt. Example properties include concurrency, synchronization, and authentication. This problem is particularly apparent in systems with evolving requirements, as adapting code that is not localized in single modular units proves to be a tedious process. In this paper we discuss issues related to requirements of concurrent software systems to provide explicit support for these cross‐cutting concerns, and we present the Aspect Moderator, a framework extension to the object model that can ease the development of concurrent object‐oriented systems. Copyright © 2002 John Wiley & Sons, Ltd.     

Stabilization of fuzzy systems with quantization and packet dropout

The discrete‐time and continuous‐time fuzzy systems with quantization and packet dropout are considered in this paper. The quantizer used here is a uniform one with arbitrary quantization regions, and the packet dropout process is modeled as a time‐homogenous Markov process. Because of the properties of packet dropout process, the fuzzy systems considered here are seen as Markov jump fuzzy systems, and the theories of Markov jump system are used to discuss the mean square stability of the closed‐loop systems. On the basis of the zoom strategy and Lyapunov theory, for the given failure rate and recovery rate, sufficient conditions are given for the closed‐loop fuzzy systems to be mean square stable, and the feedback controllers are designed to ensure the stability of fuzzy systems. A single link direct joint driven manipulator model is presented to show the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd.     

Hierarchical Control of Linear Systems from the Abstraction Feedback Gain

In this paper, the problem of hierarchical control for a class of linear systems is addressed. Given a large‐scale linear system, we obtain a stabilizing feedback gain for it from that of an abstract system. And then, we employ this feedback gain to design a new interface between the original system and the abstraction. Furthermore, the synthesis of the new interface can be allowed by a new simulation function characterized by a low‐order matrix associated to the abstraction. Finally, an example is given to illustrate the proposed approach.     

Regulation of lower triangular and non‐triangular nonlinear systems with uncertain high‐order nonlinearities via dynamic gain control

In this paper, we consider a global regulation problem of a class of nonlinear systems that have uncertain high‐order nonlinear terms. In particular, we introduce new high‐order lower triangular and non‐triangular conditions and propose a controller with dynamic gains to regulate the system with uncertain high‐order nonlinearities. In designing our controller, the information of the growth rate is not required, and the forms of the high‐order nonlinearities are more relaxed. We verify that the proposed method is applicable to the system which cannot be regulated by the existing methods. Examples and simulation results are given for clear illustration. Copyright © 2016 John Wiley & Sons, Ltd.     

New results for the analysis of linear systems with time‐invariant delays

This paper presents a comparison system approach for the analysis of stability and ??_∞ performance of linear time‐invariant systems with unknown delays. The comparison system is developed by replacing the delay elements with certain parameter‐dependent Padé approximations. It is shown using the special properties of the Padé approximation to e^?s that the value sets of these approximations provide outer and inner coverings for that of each delay element and that the robust stability of the outer covering system is a sufficient condition for the stability of the original time delay system. The inner covering system, in turn, is used to provide an upper bound on the degree of conservatism of the delay margin established by the sufficient condition. This upper bound is dependent only upon the Padé approximation order and may be made arbitrarily small. In the single delay case, the delay margin can be calculated explicitly without incurring any additional conservatism. In the general case, this condition can be reduced with some (typically small) conservatism to finite‐dimensional LMIs. Finally, this approach is also extended to the analysis of ??_∞ performance for linear time‐delay systems with an exogenous disturbance. Copyright © 2003 John Wiley & Sons, Ltd.     

ON THE STABILITY AND STABILIZATION OF TIME‐VARYING NONLINEAR CONTROL SYSTEMS

Many stability and stabilization problems of nonlinear time‐varying systems lead to asymptotic behavior of (–K + L)‐type systems, which consist of a K‐function and an L‐function. The stability of these systems is of fundamental importance for a series of stabilization problems of time‐varying nonlinear control systems. Even though the asymptotical stability of such systems has been used widely and (in most cases) implicitly, we do not find a rigorous proof, in the literature, and the existing proof for a particular case is questionable. Under quite general conditions, we prove that the solution of these systems tends to 0 as t →. Some generalizations are also obtained. As an immediate consequence, a general theorem is obtained for the stabilization of time‐varying systems. Using the new framework, we examine several stability and stabilization problems. First of all, for cascade systems, two sets of sufficient conditions are obtained for uniformly asymptotical stability and globally asymptotical stability, respectively. Then we consider the stability of ISS and IISS systems. A new concept, namely, strong IISS, is proposed. Several stability properties for autonomous systems are extended to time‐varying systems. Finally, we consider stabilization via detection. A rigorous proof is given for a smooth state feedback time‐varying system with weak detectability to be stabilizable by means of an observer.