Event‐triggered control design for nonlinear systems with actuator failures and uncertain disturbances

SummaryThis paper presents a retrofit fault‐tolerant tracking control (FTTC) design method with application to an unmanned quadrotor helicopter (UQH). The proposed retrofit fault‐tolerant tracking controller is developed to accommodate loss‐of‐effectiveness faults in the actuators of UQH. First, a state feedback tracking controller acting as the normal controller is designed to guarantee the stability and satisfactory performance of UQH in the absence of actuator faults, while actuator dynamics of UQH are also considered in the controller design. Then, a retrofit control mechanism with integration of an adaptive fault estimator and an adaptive fault compensator is devised against the adverse effects of actuator faults. Next, the proposed retrofit FTTC strategy, which is synthesized by the normal controller and an additional reconfigurable fault compensating mechanism, takes over the control of the faulty UQH to asymptotically stabilize the closed‐loop system with an acceptable performance degradation in the presence of actuator faults. Finally, both numerical simulations and practical experiments are conducted in order to demonstrate the effectiveness of the proposed FTTC methodology on the asymptotic convergence of tracking error for several combinations of loss‐of‐effectiveness faults in actuators.

Theproblem ofapproximatedecoupling of nonlinear systemsby outputfeedback is considered. The structure of the controller is high-gain proportional plus integral. Linearization of the nonlinear closed-loop equations results in the standard singular perturbation form. Based on the singular perturbation concept, a control law is found that accomplishes approximate decoupling with stability for nonlinear systems. Application oftheproposed design schemeto thefullsix-degree-of-freedomnonlinearaircraftdynamicsmodelispresented,demonstrating itsvalidity. I. Introduction A SYSTEM is said to be decoupled if each component of the output depends only on the corresponding component of the input. The problem of decoupling a multivariable system has been extensively treated in the literature in the past 30 years. The necessary and sufe cient conditions were developed for linear 1;2 and nonlinear 3i6 systems. However, no systematic procedures for the controller design were considered. Nonlinear system controller design is typically approached by linearizing the system about a nominal operating point and applying linear system design methods. This will provide a linear control law that yields approximate noninteracting control and satisfy design objectives in the neighborhood of the constant operating point. For the purpose of this work, the design objectives for this highly coupled system of e ight dynamics are to closely track individual desired outputs, with zero steady-state response from others. However, the problem of computing the decoupling feedback control laws for a nonlinear system is quite dife cult. Approximate decoupling control for nonlinear systems is based onsingularperturbationconcepts.Thestructureofcontrollerishighgain output feedback with proportional plus integral (PI) control.It will be shown that the linearization of nonlinear closed-loop system about the nominal operating point yields the standard singular perturbation equation form when a scalar gain weighting g ! 1. Then,thesingularperturbationconcept,i.e.,necessaryandsufe cient conditions, is utilized to e nd a decoupling control law. This approach is a new, conceptually simple, but practically useful design method for approximate noninteracting control law design with stability for nonlinear systems. The results developed are easy to follow and are easily applicable to aircraft control decoupling problems. This paper introduces the application of this design method to approximate noninteracting e ight control system design.

The work deals finite frequency H<sub>∞</sub> control design for continuous time nonlinear systems, we provide sufficient conditions, ensuring that the closed-loop model is stable. Simulations will be gifted to show level of attenuation that a H<sub>∞</sub> lower can be by our method obtained developed where further comparison.

Based on the Takagi-Sugeno (T-S) fuzzy model approach, this study discusses the robust fault-tolerant tracking controller design for non-linear systems affected by external disturbances, uncertainties, and actuator failures. In contrast to existing results, this study assumes the actuator fault model includes linear and nonlinear terms, and a state feedback controller is designed to improve the tracking and stability of the system when actuators fail. Using a non-quadratic Lyapunov function, new sufficient conditions for L_2-gain tracking performance analysis are derived to determine simultaneously the minimal level of the L_2-gain and controller gains. The robustness of the proposed approach is also investigated. An illustration of the theoretical developments is provided by a Duffing forced oscillation system.

This article presents a fault-tolerant tracking control strategy for Takagi–Sugeno fuzzy model-based nonlinear systems which combines integral sliding mode control with adaptive control technique. Two common actuator faults: 1) loss of effectiveness and 2) increased bias input, are considered simultaneously. The fuzzy tracking control system is first established by incorporating the integral term of the output tracking error. Then, an appropriate fuzzy integral switching surface is designed such that the corresponding sliding motion only suffers from the unamplified unmatched disturbance. The solution of the nominal tracking controller can be transformed into a to convex optimization problem. In particular, an adaptive fuzzy sliding mode tracking controller is synthesized to ensure the accessibility of the sliding motion despite the effect of actuator faults and unknown disturbances. Finally, the proposed tracking strategy is verified by applying it to the dynamic positioning control of unmanned marine vehicles.

Dynamic event-triggered composite anti-disturbance fault-tolerant tracking control for ships with disturbances and actuator faults

This paper proposes an adaptive sliding mode fault tolerant control design for lipschitz nonlinear system subject to simultaneous actuator and sensor faults. First, in order to estimate the system states, actuator and sensor faults, only one observer with an adaptive nonlinear gain is required where the minimum phase condition is relaxed to delectability and the matching condition is weakened to become a condition related to the system dimensions. Furthermore, our approach is applicable where there are faults greater than outputs. Next, a virtual sensor technique is developed to replace a failed, missing or corrupted sensor to provide a signal having the same effect of the nominal sensor. Then, this study provides an adaptive sliding mode fault tolerant control to achieve an optimal interaction between observer, virtual sensor and controller models. Thus, using the LMI technique with multiobjective optimization performance, sufficient conditions are derived to ensure the closed-loop Lipschitz nonlinear system stability and guarantee that the Lipschitz set of the adaptive sliding mode observer is a subset of the adaptive sliding mode control Lipschitz set. Two illustrative examples the first is the robotic manipulator model and the second is the longitudinal dynamics of the following vehicle system were performed to verify the effectiveness of the proposed approach.

Global fixed-time attitude tracking control for the rigid spacecraft with actuator saturation and faults

Acknowledging the potential of system‐based design approaches, most international design standards for steel structures include preliminary versions of such alternative design methods. The Direct Design Method (DDM) is one of these approaches, which allows designing steel structures directly using advanced numerical analyses without requiring further member checks. This paper presents the DDM design (and verification) procedure and summarizes the key aspects of the advanced finite element model necessary for the determination of the system strength, with an emphasis on cold‐formed stainless steel portal frames. Through the design of two frames, the DDM design procedure is illustrated and the resulting cross‐sections are compared with those derived using the traditional two‐step design approach in the Eurocode and ASCE design frameworks. The results demonstrate that the DDM verification process is simpler and more direct, and that lighter structures are obtained when designing using the DDM for strength considerations. Finally, this paper also highlights that allowing larger deformations in the ultimate limit state design for the DDM does not have additional negative effects on the serviceability requirements if compared to the traditional two‐step design approach.

Direct feedback control design for nonlinear systems

An H∞ tracking-based adaptive fuzzy sliding mode controller (H∞ AFSMC) is proposed for a class of nonlinear systems involving system uncertainties and external disturbances. The H∞ tracking control design method and the adaptive fuzzy sliding mode control technique are combined in the design of the H∞ AFSMC controller. By the Lyapunov theory, it is shown that the proposed controller has the following advantages: it can inhibit the chattering phenomenon and can guarantee the H∞ tracking performance to attenuate the lumped uncertainties caused by the unmodelled dynamics, the approximation error and the external disturbances. Subsequently, the problem of H∞ AFSMC design is characterised in terms of an eigenvalue problem, which can be efficiently solved by using convex optimisation techniques. Finally, an inverted pendulum system is simulated to demonstrate the validity and effectiveness of the proposed controller.

This article tackles the finite‐time global trajectory tracking control problem of the autonomous underwater vehicle (AUV) in presence of input saturation constraints, actuator faults, unknown dynamics, and external disturbances. First, we describe the orientation of the AUV by rotation matrix instead of classical Euler angle or unit quaternion such that the AUV's dynamics could be globally formulated without singularity and unwinding phenomenon. After that, a smooth dead zone‐based model is introduced here to linearize the actuator model, leaving that the adaptive laws could be suitable for the solution of input saturation and actuator faults. Considering that the difficulty of model dynamic acquirement, together with the complicity of rotation‐matrix‐based representation, would trouble deployment of the controller. The minimum learning parameter technology is thereby utilized to approximated the dynamic nonlinearity of the AUV. On the basis of these, a rotation‐matrix‐based sliding mode control scheme is technically proposed. It is proved that the tracking errors can be stabilized to a small neighborhood of origin within a settling time. Finally, several set numerical experiments are conducted to assess the effectiveness and show the advantages of the proposed control scheme.

The problem of robust reliable control with multi-objective requirements and static-output-feedback (SOF) form is studied for a class of uncertain nonlinear systems subject to vector-bounded nonlinear dynamics, norm-bounded disturbances and actuator faults or the loss of actuator effectiveness. Based on the Lyapunov stability theory and multi-objective optimization strategy, a sufficient condition for the reliable controller design with SOF-form is developed. It can guarantee the robust stability, the given magnitude constraints on control input and system output, the prescribed level on the disturbance attenuation and the optimized quadratic cost performance of the closed-loop system under all possible faults. Thus, the comprehensive performance of the post-fault system is ensured by the designed controller. Finally, a numerical example is provided to verify the effectiveness of our proposed design algorithm.

It has been a common consensus that general techniques for stabilization of nonlinear systems are available only for some special classes of nonlinear systems. Control design for nonlinear systems with uncertain components is usually carried out on a per system basis, especially when physical control constraints, and certain control performance measures such as optimum time control are imposed. Elegant adaptive control techniques are difficult to apply to this type of problems. A new neural network based control design is proposed and presented in this paper to deal with a special class of uncertain nonlinear systems with multiple inputs. The desired system dynamics are analyzed and utilized in the process of the proposed intelligent control design. The theoretical results are provided to justify the design procedures. The simulation study is conducted on a second-order bilinear system with two inputs and uncertainties on its parameters. The simulation results indicate that the proposed design approach is effective.

This paper focuses on the event-triggered guaranteed cost control design of nonlinear systems via a self-learning technique. In brief, an event-based guaranteed cost control strategy of nonlinear systems subjects to matched uncertainties is developed, thereby balancing the performance of guaranteed cost and the actuality of limited communication resource. The original control design is transformed into an optimal control problem with an event-based mechanism, where the relationship of guaranteed cost performance compared to the time-based formulation is discussed. A critic neural network is constructed for implementing the event-based optimal control design with stability guarantee. Simulation experiments are carried out to verify the theoretical results in detail.