Observer‐based fault‐tolerant control for a class of hybrid impulsive systems

This paper investigates the fault‐tolerant control (FTC) problem for a class of hybrid nonlinear impulsive systems. Two kinds of faults are considered: continuous faults that affect each mode and discrete faults that affect the impulsive switching. The FTC strategy is based on the trade‐off between the frequency of switching and the decreasing rate of Lyapunov functions along the solution of the system, which maintains the stability of overall hybrid impulsive systems in spite of these two kinds of faults. A switched reluctance motor example is taken to illustrate the applicability of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Fault-tolerant control for a class of hybrid systems with uncontrollable switching

This article focuses on the fault-tolerant control (FTC) problem for a class of hybrid systems modelled by hybrid automata. An observer-based FTC framework is proposed for the hybrid system with uncontrollable state-dependent switching and without full continuous state measurements. Two kinds of faults are considered: continuous faults that affect each mode and discrete faults that affect the mode transition. Sufficient conditions are given such that the hybrid system can be stabilised in the sense of LaSalle invariance principle. Simulation results of example of CPU processing control show the efficiency of the proposed method.     

A fault tolerant control framework for periodic switched non-linear systems

An observer-based fault tolerant control (FTC) framework is proposed for a class of periodic switched non-linear systems (PSNS) without full state measurements. Two kinds of faults are considered: continuous faults that affect each mode during its dwell period; and discrete faults that affect the switching sequence. Under the average dwell time scheme, the proposed FTC framework can maintain the stability of overall PSNS in spite of these two kinds of fault. A switched reluctance motor example is taken to illustrate the efficiency of the proposed method.     

Fault tolerant control design via hybrid petri nets

This paper proposes a novel fault tolerant control (FTC) scheme for hybrid systems modeled by hybrid Petri nets (HPNs). The HPNs model consists of discrete and continuous PNs. The faults are represented by unobservable discrete transitions or the normal observable discrete transitions with abnormal firing time in discrete PNs. First, an observer‐based fault diagnosis method is proposed to estimate the marking in discrete places with unknown initial marking and diagnose the faulty behavior simultaneously. Then, an adaptive fault tolerant controller is designed to maintain the general mutual exclusion constraints (GMEC) of discrete PNs, and a scheme that adjusts firing speeds of continuous transitions is provided to maintain the optimality of continuous PNs. Finally, an example of an intelligent transportation system consisting of automated vehicles on a bridge is included to demonstrate the effectiveness of our developed techniques. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Optimal hold functions for MDCS sampled‐data problems

In this paper the H² and H^∞ sampled‐data problems with mixed discrete/continuous specifications (MDCS) are considered. The hold function is not fixed a priory but rather is the design parameter. The (sub)optimal controller obtained is of the form of a serial interconnection of a (sub)optimal digital controller and a (sub)optimal hold function. It is demonstrated that the incorporation of the hold function into the sampled‐data design with MDCS extends considerably the possibility to reach a required trade‐off between discrete and continuous specifications in comparison with designs with a fixed hold function. Copyright © 2003 John Wiley & Sons, Ltd.     

Fault‐tolerant control of singularly perturbed systems with actuator faults and disturbances

The article proposes several fault‐tolerant control (FTC) laws for singularly perturbed systems (SPS) with actuator faults and disturbances. One of the main challenges in this context is that the fast‐slow decomposition is not available for actuator faults and disturbances. In view of this, some conditions for the asymptotic stability of the closed‐loop dynamics are investigated by amending the composite Lyapunov approach. On top of this, a closed‐form expression of the upper bound of singular perturbation parameter (SPP) is provided. Moreover, we design several SPP‐independent composite FTC laws, which can be applied when this parameter is unknown. Finally, the chattering phenomenon is eliminated by using the continuous approximation technique. We also emphasize that, for linear SPSs, the FTC design can be formulated as a set of linear matrix inequalities, while the SPP upper bound can be obtained by solving a convex optimization problem. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.     

Assume–guarantee verification of nonlinear hybrid systems with Ariadne

In many applicative fields, there is the need to model and design complex systems having a mixed discrete and continuous behavior that cannot be characterized faithfully using either discrete or continuous models only. Such systems consist of a discrete control part that operates in a continuous environment and are named hybrid systems because of their mixed nature. Unfortunately, most of the verification problems for hybrid systems, like reachability analysis, turn out to be undecidable. Because of this, many approximation techniques and tools to estimate the reachable set have been proposed in the literature. However, most of the tools are unable to handle nonlinear dynamics and constraints and have restrictive licenses. To overcome these limitations, we recently proposed an open‐source framework for hybrid system verification, called Ariadne , which exploits approximation techniques based on the theory of computable analysis for implementing formal verification algorithms. In this paper, we will show how the approximation capabilities of Ariadne can be used to verify complex hybrid systems, adopting an assume–guarantee reasoning approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive logic‐based switching fault‐tolerant controller design for nonlinear uncertain systems

This paper deals with the problem of fault‐tolerant control (FTC) for a class of nonlinear uncertain systems against actuator faults using adaptive logic‐based switching control method. The uncertainties under consideration are assumed to be dominated by a bounding system which is linear in growth in the unmeasurable states but can be a continuous function of the system output, with unknown growth rates. Several types of common actuator faults, e.g., bias, loss‐of‐effectiveness, stuck and hard‐over faults are integrated by a unified fault model. By utilizing a novel adaptive logic‐based switching control scheme, the actuator faults can be detected and automatically accommodated by switching from the stuck actuator to the healthy or even partly losing‐effectiveness one with bias, in the presence of large parametric uncertainty. In particular, two switching logics for updating the gain in the output feedback controllers are designed to ensure the global stability of the nominal (fault‐free) system and the boundedness of all closed‐loop signals of the faulty system, respectively. Two simulation examples of an aircraft wing model and a single‐link flexible‐joint robot are given to show the effectiveness of the proposed FTC controller. Copyright © 2010 John Wiley & Sons, Ltd.     

Hybrid dynamical systems: robust control synthesis problems

The paper presents a new approach to robust control synthesis problems for hybrid dynamical systems. The hybrid system under consideration is a composite of a continuous plant and a discrete event controller. State and output feedback problems are considered. The main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a Riccati differential equation of the H^∞ filtering type. These results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control.     

Models,feedback control,and open problems of 3D bipedal robotic walking

The fields of control and robotics are working toward the development of bipedal robots that can realize walking motions with the stability and agility of a human being. Dynamic models for bipeds are hybrid in nature. They contain both continuous and discrete elements, with switching events that are governed by a combination of unilateral constraints and impulse-like forces that occur at foot touchdown. Control laws for these machines must be hybrid as well. The goals of this paper are fourfold: highlight certain properties of the models which greatly influence the control law design; overview the literature; present two control design approaches in depth; and indicate some of the many open problems.     

Design of a fault tolerant control system incorporating reliability analysis and dynamic behaviour constraints

In highly automated aerospace and industrial systems where maintenance and repair cannot be carried out immediately, it is crucial to design control systems capable of ensuring desired performance when taking into account the occurrence of faults/failures on a plant/process; such a control technique is referred to as fault tolerant control (FTC). The control system processing such fault tolerance capability is referred to as a fault tolerant control system (FTCS). The objective of FTC is to maintain system stability and current performance of the system close to the desired performance in the presence of system component and/or instrument faults; in certain circumstances a reduced performance may be acceptable. Various control design methods have been developed in the literature with the target to modify or accommodate baseline controllers which were originally designed for systems operating under fault-free conditions. The main objective of this article is to develop a novel FTCS design method, which incorporates both reliability and dynamic performance of the faulty system in the design of a FTCS. Once a fault has been detected and isolated, the reconfiguration strategy proposed in this article will find possible structures of the faulty system that best preserve pre-specified performances based on on-line calculated system reliability and associated costs. The new reconfigured controller gains will also be synthesised and finally the optimal structure that has the ‘best’ control performance with the highest reliability will be chosen for control reconfiguration. The effectiveness of this work is illustrated by a heating system benchmark used in a European project entitled intelligent Fault Tolerant Control in Integrated Systems (IFATIS EU-IST-2001-32122).     

Approximately bisimilar symbolic models for randomly switched stochastic systems

In the past few years there has been a growing interest in the use of symbolic models for control systems. The main reason is the possibility to leverage algorithmic techniques over symbolic models to synthesize controllers that are valid for the concrete control systems. Such controllers can enforce complex logical specifications that are otherwise hard (if not impossible) to establish on the concrete models with classical control techniques. Examples of such specifications include those expressible via linear temporal logic or as automata on infinite strings. A relevant goal in this research line is in the identification of classes of systems that admit symbolic models: in particular, continuous-time systems with stochastic or hybrid dynamics have been only recently considered, due to their rather general and complex dynamics. In this work we make progress in this direction by enlarging the class of stochastic hybrid systems admitting finite, symbolic models: specifically, we show that randomly switched stochastic systems, satisfying some incremental stability assumption, admit such models.     

The HybridUML profile for UML 2.0

In this article, a new UML extension for the specification of hybrid systems, where observables may consist of both discrete and time-continuous parameters, is presented. Whereas hybrid modeling constructs are not available in standard UML, several specification formalisms for this type of system have been elaborated and discussed, among them the CHARON language of Alur et al. which possesses already several attractive features for modeling embedded real-time systems with hybrid characteristics. Adopting this as a basis, the profile inherits formal semantics based on CHARON, so it offers the possibility for formal reasoning about hybrid UML specifications. Conversely, the CHARON framework is associated with a new syntactic representation within the UML 2.0 world, allowing to develop hybrid specifications with arbitrary CASE tools supporting UML 2.0 and its profiling mechanism. The “look-and-feel” of the profile is illustrated by means of a case study of an embedded system controlling the cabin illumination in an aircraft. The benefits and weaknesses of the constructed hybrid UML profile are discussed, resulting in feed-back for the improvement of both UML 2.0 and the CHARON formalism. The work presented in this article has been investigated by the authors in the context of the HYBRIS (Efficient Specification of Hybrid Systems) project supported by the Deutsche Forschungsgemeinschaft DFG as part of the priority programme on Software Specification - Integration of Software Specification Techniques for Applications in Engineering.     

Observability and observer design for hybrid multicell choppers

Multicell choppers are part of a class of hybrid systems in which the continuous state vector is always unobservable, in the sense that the observability matrix never has full rank. Due to their hybrid behaviour, the recent concept of Z(T _N )-observability can be applied and analysed in the context of multicell choppers, which allows to give conditions, in terms of the switching sequence, under which the voltage across each capacitor can be reconstructed, not instantly, but after some number of switchings. The case when a DC-motor is coupled to the multicell chopper is also considered. It is shown that, under certain admissible assumptions, the voltages across the capacitors and the motor speed can be acceptably estimated. Two observers, one based on the super-twisting algorithm and the other one based on an adaptive approach, are designed. Additionally, we design an observer for the partial state observation. Simulations are given where the proposed observers are compared and the effectiveness of both is shown.     

Adaptive fault‐tolerant control for a class of output‐constrained nonlinear systems

In this work, by incorporating a tan‐type barrier Lyapunov function into the Lyapunov function design, we present a novel adaptive fault‐tolerant control (FTC) scheme for a class of output‐constrained multi‐input single‐output nonlinear systems with actuator failures under the perturbation of both parametric and nonparametric system uncertainties. We show that under the proposed adaptive FTC scheme, exponential convergence of the output tracking error into a small set around zero is guaranteed, while the constraint requirement on the system output will not be violated during operation. In the end, two illustrative examples are presented to demonstrate the effectiveness of the proposed FTC scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Timed Petri Nets in Hybrid Systems: Stability and Supervisory Control

In this paper, timed Petri nets are used to model and control hybrid systems. Petri nets are used instead of finite automata primarily because of the advantages they offer in dealing with concurrency and complexity issues. A brief overview of existing results on hybrid systems that are based on Petri nets is first presented. A class of timed Petri nets named programmable timed Petri nets (PTPN) is then used to model hybrid systems. Using the PTPN, the stability and supervisory control of hybrid systems are addressed and efficient algorithms are introduced. In particular, we present sufficient conditions for the uniform ultimate boundness of hybrid systems composed of multiple linear time invariant plants which are switched between using a logical rule described by a Petri net. This paper also examines the supervisory control of a hybrid system in which the continuous state is transfered to a region of the state space in a way that respects safety specifications on the plant's discrete and continuous dynamics.     

互联系统容错控制的研究回顾与展望

互联系统的容错控制是近年来控制领域的研究热点,具有重要的理论价值和实际意义.本文阐述了互联系统容错控制的基本结构和主要思想,总结了带有机械互联、网络互联和模型虚拟互联的三类互联系统的容错控制最新研究成果,并对该研究方向进行了展望.     

On fluidization of discrete event models: observation and control of continuous Petri nets

As a preliminary overview, this work provides first a broad tutorial on the fluidization of discrete event dynamic models, an efficient technique for dealing with the classical state explosion problem. Even if named as continuous or fluid, the relaxed models obtained are frequently hybrid in a technical sense. Thus, there is plenty of room for using discrete, hybrid and continuous model techniques for logical verification, performance evaluation and control studies. Moreover, the possibilities for transferring concepts and techniques from one modeling paradigm to others are very significant, so there is much space for synergy. As a central modeling paradigm for parallel and synchronized discrete event systems, Petri nets (PNs) are then considered in much more detail. In this sense, this paper is somewhat complementary to David and Alla (2010). Our presentation of fluid views or approximations of PNs has sometimes a flavor of a survey, but also introduces some new ideas or techniques. Among the aspects that distinguish the adopted approach are: the focus on the relationships between discrete and continuous PN models, both for untimed, i.e., fully non-deterministic abstractions, and timed versions; the use of structure theory of (discrete) PNs, algebraic and graph based concepts and results; and the bridge to Automatic Control Theory. After discussing observability and controllability issues, the most technical part in this work, the paper concludes with some remarks and possible directions for future research.     

A formal mathematical framework for modeling probabilistic hybrid systems

The development of autonomous agents, such as mobile robots and software agents, has generated considerable research in recent years. Robotic systems, which are usually built from a mixture of continuous (analog) and discrete (digital) components, are often referred to as hybrid dynamical systems. Traditional approaches to real-time hybrid systems usually define behaviors purely in terms of determinism or sometimes non-determinism. However, this is insufficient as real-time dynamical systems very often exhibit uncertain behavior. To address this issue, we develop a semantic model, Probabilistic Constraint Nets (PCN), for probabilistic hybrid systems. PCN captures the most general structure of dynamic systems, allowing systems with discrete and continuous time/variables, synchronous as well as asynchronous event structures and uncertain dynamics to be modeled in a unitary framework. Based on a formal mathematical paradigm exploiting abstract algebra, topology and measure theory, PCN provides a rigorous formal programming semantics for the design of hybrid real-time embedded systems exhibiting uncertainty.