Parameter fault detection and estimation of a class of nonlinear systems using observers

The focus of this paper is on the detection and estimation of parameter faults in nonlinear systems with nonlinear fault distribution functions. The novelty of this contribution is that it handles the nonlinear fault distribution function; since such a fault distribution function depends not only on the inputs and outputs of the system but also on unmeasured states, it causes additional complexity in fault estimation. The proposed detection and estimation tool is based on the adaptive observer technique. Under the Lipschitz condition, a fault detection observer and adaptive diagnosis observer are proposed. Then, relaxation of the Lipschitz requirement is proposed and the necessary modification to the diagnostic tool is presented. Finally, the example of a one-wheel model with lumped friction is presented to illustrate the applicability of the proposed diagnosis method.     

EP-based adaptive tracker with observer and fault estimator for nonlinear time-varying sampled-data systems against actuator failures

An evolutionary programming-based adaptive observer is presented in this paper to improve the performance of state estimation of nonlinear time-varying sampled-data systems. Also, this paper presents a novel state-space adaptive tracker together with the proposed observer and estimation schemes for nonlinear time-varying sampled-data systems having actuator failures. For the class of slowly varying nonlinear time-varying systems, the proposed methodology is able to achieve the desired fault detection and performance recovery for the originally well-designed systems, as long as the controller having the high-gain property. For practical implementation, we utilize the advantages of digital redesign methodology to convert a well-designed high-gain analog controller/observer into its corresponding low-gain digital controller/observer. Illustrative examples are given to demonstrate the effectiveness of the proposed method. The developed digitally redesigned adaptive tracker with the proposed observer and estimator is suitable for implementation by using microprocessors.     

Design of fault diagnosis filters: A multi-objective approach

In this paper, fault detection and isolation (FDI) in linear uncertain dynamic systems is addressed. The main contributions consist of the formulation of the FDI problem as a filter-based multi-objective optimization problem and the study of the tools used for the solution. The design objectives are formulated in terms of H_∞, H_- and generalized H₂ performance specifications as well as regional constraints on filter poles. The problem is solved using linear matrix inequality (LMI) and generalized structured singular value (μ_g) techniques. Special design features are illustrated through a simulation example and experimental results from a controlled hydraulic process are provided to demonstrate the potential of the proposed procedure.     

Bicausal bond graphs for supervision: From fault detection and isolation to fault accommodation

Model-based fault detection and isolation (FDI) requires an analytical system model from which fault indicators can be derived by assigning proper computational causalities. Many bond graph (BG) model-based techniques for FDI have been developed in recent past. Furthermore, many other advances have been made in the field of control engineering applications of BG modelling. Supervision systems not only perform FDI, but also take the necessary steps for fault accommodation. Fault accommodation is done either through system reconfiguration or through fault tolerant control (FTC). In this paper, it is shown that bicausal BG modelling proves to be a unified approach for sensor placement from the FDI and FTC viewpoint, identification of hardware redundancies for system reconfiguration, generation of fault indicators, estimation of fault parameters for fault accommodation, inversion of systems and actuator sizing for FTC, etc. It is shown that the use of bicausalled BG helps to integrate many of the recently developed advances made in the field of control engineering into development of complex supervision systems.     

Design of observers for a class of discrete-time uncertain nonlinear systems with time delay

This paper is concerned with the problem of observer design for a class of discrete-time Lipschitz nonlinear state delayed systems with, or without parameter uncertainty. The nonlinearities are assumed to appear in both the state and measured output equations. For both the cases with and without norm-bounded time-varying parameter uncertainties, a design method is proposed, which involves solving a linear matrix inequality (LMI). When a certain LMI is satisfied, the explicit expression of a desired nonlinear observer is also presented. An example is provided to demonstrate the applicability of the proposed approach.     

Robust fault detection for a class of nonlinear time-delay systems

In this paper, the robust fault detection filter (RFDF) design problems are studied for nonlinear time-delay systems with unknown inputs. Firstly, a reference residual model is introduced to formulate the robust fault detection filter design problem as an H_∞ model-matching problem. Then appropriate input/output selection matrices are introduced to extend a performance index to the time-delay systems in time domain. The reference residual model designed according to the performance index is an optimal residual generator, which takes into account the robustness against disturbances and sensitivity to faults simultaneously. Applying robust H_∞ optimization control technique, the existence conditions of the robust fault detection filter for nonlinear time-delay systems with unknown inputs are presented in terms of linear matrix inequality (LMI) formulation, independently of time delay. An illustrative design example is used to demonstrate the validity and applicability of the proposed approach.     

A trust-region method for H2 model reduction of bilinear systems on the Stiefel manifold

This paper investigates the Riemannian trust-region method for H₂ model reduction of bilinear systems. The H₂ error norm is treated as a cost function on the Stiefel manifold such that the orthogonality constraint for the projection matrix is plainly satisfied. The property related to the Euclidean gradient is studied. Then, the inner product associated with the Riemannian Hessian is derived, which can simplify the expression of the trust-region subproblem. The trust-region method for H₂ model reduction is accordingly established and the convergence is further discussed. Finally, two numerical examples are employed to demonstrate the performance of the proposed method.     

Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems

In this paper, the observer-based sliding mode control (SMC) problem is investigated for a class of uncertain nonlinear neutral delay systems. A new robust stability condition is proposed first for the sliding mode dynamics, then a sliding mode observer is designed, based on which an observer-based controller is synthesized by using the SMC theory combined with the reaching law technique. Then, a sufficient condition of the asymptotic stability is proposed in terms of linear matrix inequality (LMI) for the overall closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability problem is also discussed. It is shown that the proposed SMC scheme guarantees the reachability of the sliding surfaces defined in both the state estimate space and the state estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility of the proposed design scheme.     

Observer based fault-tolerant control for a class of nonlinear networked control systems

In this paper, we present a fault-tolerant control (FTC) framework for a class of nonlinear networked control systems (NCSs). Firstly, the plant is transformed into two subsystems with one of them decoupled from the system fault. Then, the nonlinear observer is designed to provide the estimation of unmeasurable state and modelling uncertainty, which are used to construct fault estimation algorithm. Considering the sampling intervals occurred by net, a fault-tolerant control method is proposed for such nonlinear NCSs using the impulsive system techniques. The controller gain and the maximum sampling interval, which make the faulty system stable are given. An example is included to show the efficiency of the proposed method.     

Active fault diagnosis for a class of closed-loop systems via parameter estimation

This paper addresses an active fault diagnosis problem for a class of discrete-time closed-loop system with stochastic noise. By introducing the theories of system identification, a novel active fault diagnosis method is developed to detect and isolate the faults. An important advantage of the proposed method is that there is no need to cut off the original input signal, which is necessary in most active fault diagnosis methods. Firstly, due to the features of the faults, we transform the problem of fault diagnosis into a problem of model selection by estimating model parameters. Then, the sufficient condition for active fault diagnosability is analysed, and the property that auxiliary input signal can enhance the fault diagnosability is given. Finally, simulation studies are carried out to demonstrate the effectiveness and applicability of the proposed method.     

Distributed sensor fault diagnosis for a formation of multi-vehicle systems

In the paper, a distributed sensor fault detection and isolation scheme is presented for a network of second-order integrators. A new distributed control law is developed to achieve formation of the system. By using the integration information of distributed formation errors, the control law improves the robustness of the formation. A distributed observer is then designed in each vehicle based on the closed-loop dynamic model of the vehicle. Each vehicle updates the states of the distributed observer by employing the measurements of itself and the transmitted state estimations from its neighbors. Based on the distributed observer, a distributed fault detection observer and a distributed fault isolation observer are designed. The presented distributed fault detection observer in each vehicle is able to be sensitive to the faults of all vehicles in the system. By using the distributed fault isolation observers, each vehicle is able to be sensitive to the faults of itself, its neighbors and its neighbors’ neighbors and to be robust to the faults of other vehicles. Although the fault isolation of the proposed scheme is simple, computation loads of the scheme are lower than the current ones since only the model of the individual vehicle is used. Finally, the effectiveness of the control law and the fault diagnosis scheme is demonstrated by simulations and real-time experiments carried out based on a formation of three quadrotors.     

Observer-based sliding mode control for a class of discrete systems via delta operator approach

In this paper, an observer-based sliding mode control (SMC) problem is investigated for a class of uncertain delta operator systems with nonlinear exogenous disturbance. A novel robust stability condition is obtained for a sliding mode dynamics by using Lyapunov theory in delta domain. Based on a designed sliding mode observer, a sliding mode controller is synthesized by employing SMC theory combined with reaching law technique. The robust asymptotical stability problem is also discussed for the closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability of sliding surfaces is also investigated in state-estimate space and estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the developed method.     

Decentralized adaptive fault tolerant control for a class of interconnected systems with nonlinear multisource disturbances

In this paper, a decentralized adaptive backstepping control scheme is proposed for a class of interconnected systems with nonlinear multisource disturbances and actuator faults. The nonlinear multisource disturbances comprise of two parts: one is the time-varying parameterized uncertainty; the other is the dynamic unexpected signal formulated by a nonlinear exogenous system. For each subsystem, the disturbances are compensated by an adaptive controller based on several dynamic signals and the bound estimation approach. Moreover, the effect of the actuator faults is tackled in spite of the fact that the faults may change in different cases infinite times. Meanwhile, through several smooth functions, the interactions among the subsystems are successfully disposed. As a result, the tracking errors can converge to an arbitrarily small value by choosing the design parameters appropriately. The proof of the closed-loop system stability is completed. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.     

Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays

In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties. This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests. The developed results in this paper for the nominal system encompass available results on H_∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.     

Fuzzy adaptive command filtered backstepping fault-tolerant control for a class of nonlinear systems with actuator fault

This paper investigates a class of nonlinear systems with actuator fault. In particular, fuzzy logic systems have been used to approximate the unknown nonlinear functions, backstepping procedure is adopted to design controller for the system with mismatched condition, command filter is utilized to eliminate the explosion of complexity of the backstepping and also to compensate the output of a filter subjected to the derivative of the virtual control. The stability of the closed-loop system and the convergence of the tracking error are proved via Lyapunov Theorem. In addition, two numerical simulation examples are illustrated the effectiveness of the proposed approach.     

Robust adaptive tracking with an additional plant identifier for a class of nonlinear systems

In this paper, we develop two new model reference adaptive control (MRAC) schemes for a class of nonlinear dynamic systems that is robust with respect to an uncertain state (output) dependent nonlinear perturbations and/or external disturbances with unknown bounds. The design is based on a controller parametrization with an adaptive integral action. Two types of adaptive controllers are considered—the state feedback controller with a plant parameter identifier, and the output feedback controller with a linear observer.     

一类具有动态领导者和时滞的多主体系统的一致性

研究了一类具有动态领导者并且存在时变耦合时滞的多主体系统的一致性问题．在所考虑的模型中,领导者的速度不能被精确量测．为了跟踪这样一个领导者主体,将对每个跟随者主体构造分散式状态估计器以及设计基于邻居的控制器;同时,由于耦合时滞的存在,基于邻居的控制器和状态估计器均包含了时变时滞的作用．当多主体系统的耦合拓扑是固定的或切换的有向图时,跟随者与领导者之间的跟踪误差得到了估计．特别地,可以证明,当动态领导者的速度可以被精确量测时,每一个跟随者都能够跟踪上领导者．     

一类非线性不确定多时滞中立型系统的鲁棒自适应控制（英文）

针对一类不确定多时滞中立型非线性系统，在其非线性不确定项的范数有界，但其上界未知的情况下，论证了自适应鲁棒控制器存在的条件，并给出了能适应未知参数变化且使得最终闭环系统一致最终有界的鲁棒控制律的设计方法。最后，具体算例的仿真结果说明了此法的有效性。     

Matroid algorithm for monitorability analysis of bond graphs

The monitorability analysis (ability to detect and isolate faults) using a model is presented. A foundation of this structural property using bond-graph model is proposed. The present paper deals with independent residual generation based on binary matroid, especially chain groups over GF(2). The methodology is applied to bond-graph model, and from the structural point of view, for this task, a matroid intersection algorithm is used to compute the maximum matching.