Static output feedback reliable controller design of nonlinear systems with multiple constraints

ABSTRACTThis paper is concerned with the problem of observer-based reliable passive control for uncertain Takagi–Sugeno (T–S) fuzzy systems with time-delay and actuator faults. By employing Lyapunov stability theory, fault treatment method and linear matrix inequalities (LMIs), a sufficient condition on the existence of an observer-based reliable passive controller is given. Further, the LMI conditions are proposed for the observer-based reliable passive controller design. The gain of reliable controller and observer can be obtained by solving the proposed LMIs. Using the reliable passive controller, the closed-loop system is not only internally stable but also strictly passive even though some actuator components fail and system state fails to be measured completely. Finally, a truck-trailer system example is given to verify the effectiveness and advantages of the designed approach.

This paper is focused on the static output feedback (SOF) control problem for a class of switched nonlinear systems with actuator faults. By means of the Takagi-Sugeno fuzzy model, the switched nonlinear plant is described by a family of switched fuzzy systems. Considering transmission failures may occur between controller and actuator, a reliable SOF controller against actuator faults is designed. Sufficient conditions are developed to guarantee the existence of the reliable SOF controller. Furthermore, an iterative algorithm is designed to determine the controller gains, which avoids the conservatism brought by the traditional singular value decomposition method. To validate the effectiveness of the proposed approach, a numerical example is exploited and simulation results are also presented.

This paper considers the problem of adaptive reliable guaranteed cost controller design for linear time-delay systems against actuator faults via dynamic output feedback. Based on indirect adaptive method, a new reliable dynamic output feedback controller is established. The controller gains are affinely dependent on the estimations of fault parameters, which are updating automatically according to the proposed adaptive laws. New delay-dependent sufficient conditions for the existence of the reliable guaranteed cost dynamic output feedback controller are derived in terms of linear matrix inequalities, which have less conservativeness than the corresponding reliable dynamic output feedback controller with fixed gains. An example is presented to show the effectiveness of the proposed method.

This paper develops some new reliable controller design methods for finite and infinite horizon cases with nonzero initial conditions using an H/sub /spl infin//-like performance measure with weightings on initial and final states. For the state-feedback case, it gives necessary and sufficient conditions for the existence of the reliable controller for outages in a prespecified subset of actuators. For the output-feedback case, it gives sufficient conditions for reliable controller design for outages in preselected subsets of actuators or sensors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This article investigates the reliable output feedback control problem for networked nonlinear semi-Markov jump systems, in which a control strategy with redundant channels is established to reduce the adverse effect caused by packet dropouts. The actuator faults are fully considered in the setup. On the basis of stochastic analysis theory and fuzzy-model-based method, some criteria are established to guarantee the σ -error mean-square stability for the considered systems. As a consequence, the reliable output feedback controller design method is proposed, which can be utilized to deal with the actuator failures problem effectively. Finally, two illustrative examples are employed to explain the availability of the presented design approach, where the single-link robot arm system model is contained.

This article presents a singular system approach to the reliable $$\mathscr {H}_{\infty }$$ static output feedback (SOF) control for continuous-time nonlinear systems with Markovian jumping actuator faults. The approximation of nonlinear plants is carried out in a Takagi–Sugeno fuzzy-affine (FA) environment, and the Markov chain is adopted to characterize the actuator failure phenomenon. Specifically, by utilizing a singular model transformation strategy, the traditional closed-loop system is converted into a singular FA system. With the construction of a mode-dependent Lyapunov function, and invoking S-procedure and some convexifying techniques, the reliable piecewise SOF controller design is then carried out for the underlying systems via a convex program. An illustrative example is finally given to show the efficacy of the developed method.

In this paper, we propose an adaptive sliding mode-based fault tolerant control for mobile robots. While a mobile robot is tracking a given trajectory, several fault cases may occur, such as sensor model and controller faults, changes in the dynamic equation due to robot body shape or weight changes, and loss of actuator effectiveness. Disturbance signals are caused by the actuator faults and, for various reasons, can be considered the primary issue for the robots. In real-time applications, the Sliding Mode Controller (SMC) is insufficient if the robot parameters are unknown, the robot model is non-linear, and the overall system is subject to disturbances. An adaptive law is used to support the SMC to maintain the sliding surface and solve the problems of unknown system parameters, actuator faults, and disturbances. Besides SMC, the kinematic controller is also used, and its gain values are optimized using a neural network and a kinematic controller. The stability of the overall system is proven by using the Lyapunov theory. Besides actuator faults, the system is disturbed by defining a disturbance signal, which is added to the control signals. To show the effectiveness of the proposed controller, it is compared with traditional SMC and PID.

Reliable control for networked control systems with probabilistic actuator fault and random delays

This study is concerned with the reliable controller design for networked control systems (NCS) against both probabilistic sensors faults and actuators faults. The faults of each sensor or actuator occur randomly and their failure rates are governed by two sets of unrelated random variables satisfying certain probabilistic distribution. In terms of the probabilistic failures of every sensor or actuator, new type of distribution-based NCS fault model is proposed. Based on the new built model, reliable controller is designed and sufficient conditions for the exponentially mean square stability (EMSS) of NCS are obtained by using Lyapunov functional method. The main contribution of the proposed fault model and methods lies with its practicality and generalisation, which contains many realistic problems in the NCS, such as probabilistic sensors or actuators failures, partial degradation, data distortion, packet dropout, network-induced delay and so on. Moreover, some existing models in the open literatures are deemed as special cases of the proposed fault model. To illustrate the implementation procedure, a vertical take-off and landing (VTOL) aircraft system is given to show the effectiveness and application of the proposed method.

Exploiting the stochastic Hamiltonian structure, this paper investigates the robust fault-tolerant control (FTC) for stochastic port-Hamiltonian systems (SPHSs) with actuator faults. First, an energy-based robust FT controller is developed for SPHSs against the loss of actuator effectiveness. Then, an alternative condition, as well as its corresponding controller are given to extend the application of the proposed controller. Unlike the existing FT controllers, they are continuous, and there is no need to solve the Lyapunov function and Hamilton–Jacobi–Isaacs (HJI) inequalities associated with the nominal systems. Finally, an energy-based robust adaptive FT controller is presented for the faulty SPHSs to deal with parameter perturbations, and an alternative condition with its corresponding controller is also given. Both the adaptive controllers preserve the main stochastic Hamiltonian structure of the faulty systems. Compared to the existing adaptive controller, simulations on synchronous generators show the effectiveness of the proposed methods.

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.

Reliable control for positive switched systems with random nonlinearities

In this paper, the reliable control problem is studied for a class of discrete linear Markovian jump singular systems with actuator failures. A more practical model of actuator failures than outage is considered. It is important that the transition probabilities of the jumping process are assumed to be partly unknown. The failures of actuator are quantified by a variable taking values in a given interval. The purpose of the addressed reliable control problem is to design a reliable controller based on the state feedback method such that the closed-loop systems are asymptotically mean-square stable disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures. The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the effectiveness of the proposed design approach.

SummaryTraditional adaptive event‐triggered design methods compensated for the event‐triggered error are not direct, and the stability analysis of resulting close‐loop systems is rather complicated. To alleviate the above restrictions, we propose a direct and simple event‐triggered co‐design method to solve the tracking control problem for parameter strict‐feedback systems with actuator faults and uncertain disturbances. By introducing a compensating terms in a smooth function form of a conventional control law and certain positive integrable functions, the effects of actuator faults and event‐triggered error can be compensated completely. Such a direct design method has the following features: (i) a direct compensation of the event‐triggered error is achieved without introducing any extra design parameters; (ii) it is not necessary to know any bound information on the parameters of event‐triggered threshold, and global asymptotic tracking control of the overall closed‐loop system is achieved; and (iii) the resulting stability criteria of the proposed event‐triggered control design are much simpler and easier to fulfill by virtue of the introduced co‐design method. Simulations are then carried out to validate the proposed schemes.

A fault-alarm based hybrid controller design approach for Markovian jump system with actuator fault is investigated in this paper. By using linear matrix inequality (LMI) technology, both robust and reliable controllers are presented, which ensure that the normal systems and the fault systems are robustly stable. Then, in order to reduce the conservativeness of reliable controller design algorithm, a fault alarm-based switching method is given via choosing an adaptive threshold. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.