An applied optimization-based gain-scheduled fuzzy control

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.

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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).

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.

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 presents a systematic approach to design observer-based output feedback controllers for hybrid dynamical systems arising from bipedal walking. We consider a class of parameterized observer-based output feedback controllers for local exponential stabilization of hybrid periodic orbits. The properties of the Poincare map are investigated to show that the Jacobian linearization of the Poincare map takes a triangular form. This demonstrates the nonlinear separation principle for periodic orbits. In particular, the exponential stabilization of hybrid periodic orbits under dynamic output feedback control can be achieved by solving separate eigenvalue placement problems for the nonlinear state feedback and the observer. The paper then solves the state feedback and observer design problems by employing an iterative algorithm based on a sequence of optimization problems involving bilinear and linear matrix inequalities. The theoretical results are confirmed by designing a nonlinear observer-based output feedback controller for underactuated walking of a 3D humanoid model with 18 state variables, 54 state feedback parameters, and 271 observer parameters.

In this paper, we study stability analysis and stabilization problems for a class of nonlinear two-dimensional (2-D) discrete systems with time-varying state delays, described by local state-space (LSS) Fornasini-Marchesini (FM) second model. The upper and lower bounds of time-varying state delays are positive integers and the nonlinearity satisfies Lipschitz condition. First, a stability criteria is proposed through introducing a new Lyapunov function. Then a dynamic output feedback controller is designed to assure the stability of nonlinear 2-D time-varying systems. Moreover, the output feedback system matrices can be obtained by solving linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of our results.

The problem of robust stabilisation is considered for uncertain systems using linear static output feedback (SOF) controllers and linear dynamical output feedback (DOF) controllers with fixed order. The existence conditions of output feedback controllers are given by matrix inequalities and result in some nonlinear optimisation problems. A class of uncertain plants whose nominal systems are minimal phase with a full row rank can be robustly stabilised by an SOF controller and DOF controller with any order, and controllers can be obtained by solving some linear matrix inequalities (LMIs). The method is demonstrated by two numerical examples

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

This paper presents a dynamic output feedback controller with determined order for the stabilization of a class of fractional-order system with nonlinear uncertain parameters with fractional order . Using stability theories of fractional-order systems and linear matrix inequalities (LMIs), some sufficient conditions in the LMI form are deduced to guarantee the robustness and asymptotic stabilization of the system. Designing a dynamic robust controller, along with all its useful features, leads to more unknown parameters in comparison with a static controller and makes controller design procedure more difficult due to more complex constraints that must be solved. In this paper, using proper lemmas and theorems, LMI techniques, and suitable solvers and parsers the difficulty of designing such controllers has been overcome. Simulation results of three different numerical examples illustrate that the proposed sufficient theoretical results are applicable and effective for tackling robust stabilization problems.

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.

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.

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

This paper deals with the problem of robust fault-tolerant dynamic output feedback controllers design for time-delay systems. The system under consideration involves parameter uncertainties and time-delay. The purpose is to design the dynamic output feedback controller such that, for all admissible uncertainties as well as actuator failures, the system remains stable. The sufficient condition is given in the form of linear matrix inequalities (LMIs) to maintain the stability of the closed-loop system for the time-delay system against actuator failures, and the design of the dynamic output feedback controller is proposed. Finally, an illustrative example and simulation results are given to demonstrate the effectiveness of the proposed method.

This paper proposes dynamic output-feedback networked control with actuator saturation and sensor failure for Markovian jump descriptor systems (MJDS). First, the mode-dependent dynamic output-feedback controller is described as a quasi-linear parameter varying system. Then, the stochastic admissibility criterion for the closed-loop system with sensor failure and actuator saturation is obtained as matrix inequalities. To obtain the feasible solution of the non-convex condition, this paper successfully obtains the equivalent condition in terms of strict linear matrix inequalities (LMIs) and the controller gains. A numerical example shows the validity of the proposed result.