Fault tolerant H ∞ control for a class of polynomial non-linear discrete-time systems

This paper studies the fault tolerant control (FTC) problem for a class of polynomial nonlinear discrete-time systems with guaranteed H _∞ performance in the presence of actuator faults. The concerned fault is considered as a multi-model of the typical aberration in actuators’ effectiveness. A quadratic-like polynomial Lyapunov function is presented for the H _∞ specification. The main contribution of this paper is that the effect of the nonlinear terms appear in FTC analysis is described as an index in order to transform the controller design into a semi-definite programming (SDP). A numerical example is given to verify the applicability of this new approach for the nonlinear FTC synthesis.     

LMI approach to reliable guaranteed cost control with multiple criteria constraints: The actuator faults case

Based on the multi‐objective optimization strategy and linear matrix inequality approach, the problem of reliable guaranteed cost control with multiple criteria constraints is investigated for a class of uncertain discrete‐time systems subject to actuator faults. A fault model in actuators, which considers outage or partial degradation in independent actuators, is adopted. The quadratic stability is proved to be independent of the disturbance and the upper bound of a quadratic cost index is improved. The reliable feedback controller is designed to minimize the upper bound of the quadratic cost index, place all the closed‐loop poles in a specified disk, constrain the H_∞ norm level of the disturbance attenuation into a given range and guarantee the magnitudes of control inputs less than the given bound, as well. Thus, the resulting closed‐loop system can provide satisfactory stability, transient behavior, disturbance rejection level and optimized upper bound of the quadratic cost performance despite possible actuator faults. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive fault tolerant control for a class of input and state constrained MIMO nonlinear systems

In this work, we present a novel adaptive fault tolerant control (FTC) scheme for a class of control input and system state constrained multi‐input multi‐output (MIMO) nonlinear systems with both multiplicative and additive actuator faults. The input constraints can be asymmetric, and the state constraints can be time‐varying. A novel tan‐type time‐varying Barrier Lyapunov Function (BLF) is proposed to deal with the state constraints, and an auxiliary system is designed to analyze the effect of the input constraints. We show that under the proposed adaptive FTC scheme, exponential convergence of the output tracking error into a small neighbourhood of zero is guaranteed, while the constraints on the system state will not be violated during operation. Estimation errors for actuator faults are bounded in the closed loop. An illustrative example on a two degree‐of‐freedom robotic manipulator is presented to demonstrate the effectiveness of the proposed FTC scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Integrated fault estimation and fault‐tolerant control for uncertain Lipschitz nonlinear systems

This paper proposes an integrated fault estimation and fault‐tolerant control (FTC) design for Lipschitz non‐linear systems subject to uncertainty, disturbance, and actuator/sensor faults. A non‐linear unknown input observer without rank requirement is developed to estimate the system state and fault simultaneously, and based on these estimates an adaptive sliding mode FTC system is constructed. The observer and controller gains are obtained together via H_∞ optimization with a single‐step linear matrix inequality (LMI) formulation so as to achieve overall optimal FTC system design. A single‐link manipulator example is given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Disturbance attenuation with fast global finite‐time convergence for generalized high‐order uncertain nonlinear systems

This paper focuses on the problem of disturbance attenuation with fast global finite‐time convergence (FTC) for a class of generalized high‐order uncertain nonlinear systems. Combining the fast finite‐time stabilization technique with a delicate manipulation of sign functions, a new control approach is proposed to attenuate the serious uncertainties substantially, including time‐varying control coefficients, nonlinear parameters, and external disturbances, while achieving the performance evaluated in terms of L₂‐L_2p gain. A notable feature of the control strategy is the fast FTC, which greatly shortens the convergent time when the initial state is far away from the origin. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

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.     

Distributed reliable H∞ consensus control for a class of multi‐agent systems under switching networks: A topology‐based average dwell time approach

This paper investigates the problem of distributed reliable H_∞ consensus control for high‐order networked agent systems with actuator faults and switching undirected topologies. The Lipschitz nonlinearities, several types of actuator faults, and exogenous disturbances are considered in subsystems. Suppose the communication network of the multi‐agent systems may switch among finite connected graphs. By utilizing the relative state information of neighbors, a new distributed adaptive reliable consensus protocol is presented for actuator failure compensations in individual nodes. Note that the Lyapunov function for error systems may not decrease as the communication network is time‐varying; as a result, the existing distributed adaptive control technique cannot be applied directly. To overcome this difficulty, the topology‐based average dwell time approach is introduced to deal with switching jumps. By applying topology‐based average dwell time approach and Lyapunov theory, the distributed controller design condition is given in terms of LMIs. It is shown that the proposed scheme can guarantee that the reliable H_∞ consensus problem is solvable in the presence actuator faults and external disturbance. Finally, two numerical examples are given the effectiveness of the proposed theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Reliable Robust Preview Tracking Control Against Actuator Faults

In this paper we provide a solution to the reliable robust preview tracking problem against actuator faults for discrete LTI systems with polytopic uncertainties. This solution is in terms of the solvability of linear matrix inequalities (LMIs). The method is based on multi‐objective optimization and LQ tracking performance indices. To avoid the conservativeness problem associated with using a common LMI solution for the normal case and the fault cases, different LMI solutions are used in the proposed method. Two iterative algorithms are proposed and compared. Numerical examples are used to show the effectiveness of the algorithms.     

Further results on finite‐time consensus of second‐order multi‐agent systems without velocity measurements

This paper investigates the problem of finite‐time consensus (FTC) for second‐order nonlinear multi‐agent systems when the velocity information is unavailable. Based on the global finite‐time stability theory and homogeneity with dilation, a class of novel finite‐time consensus protocols are proposed for the multi‐agent systems. The protocol design is divided into two parts. First, when all the state information of the agents are measurable, a new continuous state feedback is designed to achieve FTC. Then, when the velocity information is unmeasurable, two finite‐time convergent discontinuous observers are presented to estimate the velocities of the followers and the leader, respectively, which further ensure the final FTC for the multi‐agent systems. Finally, one example is given to demonstrate the efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Time domain constrained H∞‐synthesis

Structured H_∞‐synthesis subject to time domain performance specifications is introduced. Our method allows to control trajectories of the linearized system and the underlying nonlinear dynamics simultaneously. A non‐smooth bundle optimization method for this class of programs is proposed and discussed. Our approach is tested against two benchmark studies: control of a rotational actuator to attenuate vibration noise, and control of a continuous crystallizer. Our algorithm gives a local convergence certificate and is suited for systems with large state dimension. Copyright © 2010 John Wiley & Sons, Ltd.     

H∞ control of memristive neural networks with aperiodic sampling and actuator saturation

The H_∞ control problem for memristive neural networks with aperiodic sampling and actuator saturation is considered in this paper. A novel approach that is combined with the discrete‐time Lyapunov theorem and sampled‐data system is proposed to cope with the aperiodic sampling problem. On the basis of such method and choosing a polyhedral set, sufficient conditions to determine the ellipsoidal region of asymptotic stability and exponential stability for the estimation error system are obtained through a saturating sampled‐data control. Furthermore, H_∞ performance index of memristive neural networks with disturbance is also analyzed, whereas the observer and controller gains are calculated from stability conditions of linear matrix inequalities. Finally, the effectiveness of the theoretical results is illustrated through the numerical examples.     

Robust non‐fragile H ∞ ∕ L2 − L ∞ control of uncertain linear system with time‐delay and application to vehicle active suspension

This paper presents an approach to design robust non‐fragile H _∞ ∕ L₂ ? L _∞ static output feedback controller, considering actuator time‐delay and the controller gain variations, and it is applied to design vehicle active suspension. According to suspension design requirements, the H _∞ and L₂ ? L _∞ norms are used, respectively, to reflect ride comfort and time‐domain hard constraints. By employing a delay‐dependent Lyapunov function, existence conditions of delay‐dependent robust non‐fragile static output feedback H _∞ controller and L₂ ? L _∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities. Then, a new procedure based on LMI optimization and a hybrid algorithm of the particle swarm optimization and differential evolution is used to solve an optimization problem with bilinear matrix inequality constraints. Simulation results show that the designed active suspension system still can guarantee their own performance in spite of the existence of the model uncertainties, the actuator time‐delay and the controller gain variations. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust adaptive fault‐tolerant control of uncertain linear systems via sliding‐mode output feedback

This paper is concerned with the robust adaptive fault‐tolerant compensation control problem via sliding‐mode output feedback for uncertain linear systems with actuator faults and exogenous disturbances. Mismatched disturbance attenuation is performed via H_∞ norm minimization. By incorporating the matrix full‐rank factorization technique with sliding surface design successfully, the total failure of certain actuators can be coped with, under the assumption that redundancy is available in the system. Without the need for a fault detection and isolation mechanism, an adaptive sliding mode controller, where the gain of the nonlinear unit vector term is updated automatically to compensate the effects of actuator faults, is designed to guarantee the asymptotic stability and adaptive H_∞ performance of closed‐loop systems. The effectiveness of the proposed design method is illustrated via a B747‐100/200 aircraft model. Copyright © 2014 John Wiley & Sons, Ltd.     

H ∞ observer design for uncertain nonlinear discrete‐time systems with time‐delay: LMI optimization approach

We present a robust H _∞ observer for a class of nonlinear discrete‐time systems. The class under study includes an unknown time‐varying delay limited by upper and lower bounds, as well as time‐varying parametric uncertainties. We design a nonlinear H _∞ observer, by using the upper and lower bounds of the delay, that guarantees asymptotic stability of the estimation error dynamics and is also robust against time‐varying parametric uncertainties. The described problem is converted to a standard optimization problem, which can be solved in terms of linear matrix inequalities (LMIs). Then, we expand the problem to a multi‐objective optimization problem in which the maximum admissible Lipschitz constant and the minimum disturbance attenuation level are the problem objectives. Finally, the proposed observer is illustrated with two examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust global stabilization of linear systems with input saturation via gain scheduling

The problem of robust global stabilization of linear systems subject to input saturation and input‐additive uncertainties is revisited in this paper. By taking advantages of the recently developed parametric Lyapunov equation‐based low gain feedback design method and an existing dynamic gain scheduling technique, a new gain scheduling controller is proposed to solve the problem. In comparison with the existing ?₂‐type gain scheduling controller, which requires the online solution of a state‐dependent nonlinear optimization problem and a state‐dependent ?₂ algebraic Riccati equation (ARE), all the parameters in the proposed controller are determined a priori. In the absence of the input‐additive uncertainties, the proposed controller also partially recovers Teel's ?_∞‐type scheduling approach by solving the problem of global stabilization of linear systems with actuator saturation. The ?_∞‐type scheduling approach achieves robustness not only with non‐input‐additive uncertainties but also requires the closed‐form solution to an ?_∞ ARE. Thus, the proposed scheduling method also addresses the implementation issues of the ?_∞‐type scheduling approach in the absence of non‐input‐additive uncertainties. Copyright © 2009 John Wiley & Sons, Ltd.     

Trajectory planning/re-planning for satellite systems in rendezvous mission in the presence of actuator faults based on attainable efforts analysis

The objective of fault-tolerant control (FTC) is to minimise the effect of faults on system performance (stability, trajectory tracking, etc.). However, the majority of the existing FTC methods continue to force the system to follow the pre-fault trajectories without considering the reduction in available control resources caused by actuator faults. Forcing the system to follow the same trajectories as before fault occurrence may result in actuator saturation and system's instability. Thus, pre-fault objectives should be redefined in function of the remaining resources to avoid potential saturation. The main contribution of this paper is a flatness-based trajectory planning/re-planning method that can be combined with any active FTC approach. The work considers the case of over-actuated systems where a new idea is proposed to evaluate the severity of faults occurred. In addition, the trajectory planning/re-planning approach is formulated as an optimisation problem based on the analysis of attainable efforts domain in fault-free and fault cases. The proposed approach is applied to two satellite systems in rendezvous mission.     

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.     

Adaptive fault‐tolerant control for feedback linearizable systems with an aircraft application

This paper investigates fault‐tolerant control (FTC) for feedback linearizable systems (FLSs) and its applications. The dynamic effects caused by the actuator faults on the feedback linearized model are firstly analyzed, which reveals that under actuator faults, the control input in the linearized model is affected by uncertain terms. In the framework of model reference control, the first FTC strategy is proposed as a robust controller, which achieves asymptotic tracking control of the FLS under actuator faults. A disadvantage of this strategy is that it relies on explicit information about several parameters in the actuator faults. This requirement is later relaxed by combining the robust FTC strategy with an adaptive technique to generate the adaptive FTC law, which is then improved to alleviate possible chattering of the actuator and estimation drifting of the adaptive parameter. Finally, the proposed FTC strategies are evaluated by reference command tracking control of a pendulum and an air‐breathing hypersonic vehicle under actuator faults. Simulation results demonstrate good tracking performance, which confirms effectiveness of the proposed strategies. Copyright © 2014 John Wiley & Sons, Ltd.     

Consensus problem of high‐order multi‐agent systems with external disturbances: An H∞ analysis approach

This paper is devoted to the output consensus problem of directed networks of multiple high‐order agents with external disturbances, and proposes a distributed protocol using the neighbors' measured outputs. By defining an appropriate controlled output and conducting a model transformation in two steps, consensus performance analysis of the multi‐agent system under the proposed protocol is transformed into a normal H_∞ problem. Then using H_∞ theory of linear systems, conditions are derived to ensure the consensus performance with a prescribed H_∞ index for networks with fixed and switching topologies, respectively. A numerical example of the formation control application is included to validate the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.