Dynamic Output Feedback Robust Fault-Tolerant Control for Time-Delay Systems

This paper is concerned with analyzing a novel model transformation of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new auxiliary model is proposed by employing a new approximation for time-varying delay state, and then delay partitioning method is used to analyze the scaled small gain of this auxiliary model. A sufficient condition on discrete-time T-S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced l 2 disturbance attenuation performance, is derived by employing the scaled small gain theorem. Then the solvability condition for the induced l 2 DOF control is also established, by which the DOF controller can be found by solving a set of linear matrix inequalities (LMIs).

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This paper investigates the problem of event-triggered dynamic output feedback control for networked Takagi-Sugeno (T-S) fuzzy systems with asynchronous premise variables. Our attention is focused on the design of an event-triggered fuzzy dynamic output feedback controller that guarantees that the closed-loop system is asymptotically stable. First, with consideration of the limited bandwidth and restricted network resource, an event-triggered communication scheme is proposed to save the limited network resource. Second, different from the existing results in the literature, a fuzzy dynamic output feedback controller with asynchronous premise variables is constructed such that the premise membership functions are not necessarily the same as the networked T-S fuzzy systems. Then, by using the Wirtinger inequality and some slack matrices, a less conservative stability and stabilization conditions for the existence of fuzzy dynamic output feedback controller are derived in the form of linear matrix inequalities, which can be solved by the standard MATLAB toolbox. Finally, an example is given to demonstrate the effectiveness of the designed event-triggered fuzzy dynamic output feedback controller.

In this paper, the $\boldsymbol{L}_{\infty}$ control synthesis problem for linear systems subject to actuator saturation and persistent bounded disturbance is studied. An $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator are simultaneously designed. First, by using the quadratic Lyapunov function technique, a sufficient condition on the existence of the $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator is established via linear matrix inequalities (LMIs). Such an integrated controller is able to guarantee the regional stabilization and the $\boldsymbol{L}_{\infty}$ performance of linear systems with actuator saturation and external persistent bounded disturbance. Second, novel algorithms are developed to optimize the upper bound on the $\boldsymbol{L}_{\infty}$ performance, the event-triggered threshold and the domain of attraction. Moreover, an output-based event-triggered mechanism applying to the anti-windup dynamic output feedback control design is provided, which reduces the number of control actuation updates and information transmission with respect to the traditional time-triggered control scheme.

In this paper, we address a synthesis problem of the parameter-dependent output feedback H∞ control for linear parameter-varying systems with time-delay. The scheme adopts the parameter-dependent past state information to construct the dynamic output feedback controller. In this case, on basis of the quadratic Lyapunov functional with parameter-dependence, we analyze the parameter-dependent H∞ stability conditions for the closed-loop time-delayed linear parameter-varying system in terms of linear matrix inequalities. However, this stability condition is of an infinite-dimension. To derive computationally tractable criteria for the dynamic output feedback controller, several slack variables and a convex relaxation technique are employed to have the infinite-dimensional condition of linear matrix inequalities cast into a finite dimensional convex optimization problem. By solving the convex optimization problem, we harvest the dynamic output feedback controller with memory for the time-delayed linear parameter-varying system. Finally, two examples are included to illustrate the effectiveness of the proposed approach.

A robust dynamic output feedback controller synthesis algorithm considering H∞/H2performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.

The goal of this paper is to describe an active decentralized fault-tolerant control (ADFTC) strategy based on dynamic output feedback for reconfigurable manipulators with concurrent actuator and sensor failures. Consider each joint module of the reconfigurable manipulator as a subsystem, and treat the fault as the unknown input of the subsystem. Firstly, by virtue of linear matrix inequality (LMI) technique, the decentralized proportional-integral observer (DPIO) is designed to estimate and compensate the sensor fault online; hereafter, the compensated system model could be derived. Then, the actuator fault is estimated similarly by another DPIO using LMI as well, and the sufficient condition of the existence ofH∞fault-tolerant controller in the dynamic output feedback is presented for the compensated system model. Furthermore, the dynamic output feedback controller is presented based on the estimation of actuator fault to realize active fault-tolerant control. Finally, two 3-DOF reconfigurable manipulators with different configurations are employed to verify the effectiveness of the proposed scheme in simulation. The main advantages of the proposed scheme lie in that it can handle the concurrent faults act on the actuator and sensor on the same joint module, as well as there is no requirement of fault detection and isolation process; moreover, it is more feasible to the modularity of the reconfigurable manipulator.

This paper considers the design problem of dynamic output feedback control for fractional-order (FO) Takagi-Sugeno fuzzy systems with uncertain parameters. Via the application of FO system stability theory, robust control method and the linear matrix inequality techniques, sufficient conditions are given for the stability analysis and the existence of the dynamic fuzzy output feedback controllers. The dynamic output feedback controller designed here guarantees the robust stability of the closed-loop system. Finally, a fractional order chaotic system simulation example is given to illustrate the effectiveness of the design approach here.

The design of delay-dependent wide-area DOFC with prescribed degree of stability α for damping inter-area low-frequency oscillations in power system

ABSTRACTThis paper investigates the robust control of discrete‐time switched systems in the presence of parametric uncertainty and time‐varying delays. To accommodate a more general model, nonlinear Lipschitz functions are incorporated. Additionally, the system is modeled with constraints on both control inputs and outputs. To achieve the control objectives, static and dynamic output feedback controllers are designed using the robust model predictive control (RMPC) framework. The underlying optimization problem is formulated and solved, leveraging Lyapunov‐Krasovskii functionals (LKF) and switched Lyapunov functions (SLF). The asymptotic stability of the closed‐loop system under arbitrary switching signals is ensured by satisfying sufficient conditions expressed as linear matrix inequalities (LMIs). A key advantage of the proposed method lies in its low conservatism. Moreover, the time delay and state variables are assumed unknown, and they ensure an acceptable transient response of the closed‐loop system. To demonstrate the effectiveness of the designed controllers, simulation results are provided and compared against prior related works, highlighting the improvements achieved.

This note investigates the problem of output feedback H∞ control for linear discrete-time systems. Three types of H∞ controllers are considered, namely, static output feedback controllers, dynamic output feedback controllers, and observer-based output feedback controllers. New design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality (LMI) representations, which guarantee the prescribed H∞ performances of the closed-loop systems. In contrast to the existing LMI conditions for designing the output feedback H∞ controllers, the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example.

Dynamic output-feedback control for nonlinear continuous-time systems based on parametric uncertain subsystem and interval type-2 fuzzy model

This paper is devoted to the problems of non-fragile H∞ and L2–L∞ control for a class of linear systems with time-varying state delay. The purpose is to design a dynamic output feedback controller with additive gain variations such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ (or L2–L∞) performance level. By using linear matrix inequality approach, a delay-dependent stability criterion is obtained by introducing a new type of Lyapunov–Krasovskii functional. Based on the obtained criterion, sufficient conditions for the existence of desired controllers are derived, and the corresponding stabilisation dynamic output feedback controller design algorithm is proposed. Numerical examples are included to illustrate the benefit and effectiveness of the proposed method.

An LMI Method to Robust Iterative Learning Fault-tolerant Guaranteed Cost Control for Batch Processes