Robust Finite-time Research Articles

Robust Finite-Time Control for Autonomous Operation of an Inverter-Based Microgrid

Recently, more and more small-scale renewable generation sources based distributed generators are integrated to the existing power network through power electronic-based converters. Microgrid has been proposed as a solution to meet the challenges posed by highly intermittent renewable generations. To address the fast response and complex operating conditions of various inverters in an autonomous microgrid, this paper proposes a robust finite-time control algorithm for frequency/voltage regulation and active/reactive power control. The major advantages of the proposed control algorithm include, being robust and stable against various load disturbances, unmodeled dynamics and system parameter perturbations; enabling flexible convergence time according to user preferences and different operating conditions' requirements. The finite-time convergence of the robust control algorithm is guaranteed through rigorous analysis and the balance between control accuracy and chattering suppression is investigated. Simulation results demonstrate the effectiveness of the proposed robust finite-time control algorithm.

Robust finite-time control for neutral systems with time-varying delays via sliding mode observer

This paper is concerned with the problem of robust finite-time sliding mode control (SMC) for a class of continuous-time uncertain neutral systems with time-varying delays. Firstly, based on the constructed sliding mode observer, an integral sliding surface is put forward on the estimation space. Secondly, the synthesized SMC law guarantees the finite-time reachability of the predefined sliding surface. Thirdly, through finite-time stability analysis, sufficient conditions are established to guarantee the required performance of the system during both reaching phase and sliding motion phase. Finally, a practical example is provided to verify the effectiveness of the proposed method.

Distributed Robust Finite-Time Secondary Voltage and Frequency Control of Islanded Microgrids

This paper presents a distributed, robust, finite-time secondary control for both voltage and frequency restoration of an islanded microgrid with droop-controlled inverter-based distributed generators (DGs). The distributed cooperative secondary control is fully distributed (i.e., uses only the information of neighboring DGs that can communicate with one another through a sparse communication network). In contrast to existing distributed methods that require a detailed model of the system (such as line impedances, loads, other DG units parameters, and even the microgrid configuration, which are practically unknown), the proposed protocols are synthesized by considering the unmodeled dynamics, unknown disturbances, and uncertainties in their models. The other novel idea in this paper is that the consensus-based distributed controllers restore the islanded microgrid's voltage magnitudes and frequency to their reference values for all DGs within finite time, irrespective of parametric uncertainties, unmodeled dynamics, and disturbances, while providing accurate real-power sharing. Moreover, the proposed method considers the coupling between the frequency and voltage of the islanded microgrid. Unlike conventional distributed controllers, the proposed approach quickly reaches consensus and exhibits a more accurate robust performance. Finally, we verify the proposed control strategy's performance using the MATLAB/SimPowerSystems toolbox.

Robust Finite-Time Stabilization for Networked Control Systems via Static Output-Feedback Control: Markovian Jump Systems Approach

The problems of robust finite-time stochastic stability and stabilization of uncertain networked control systems (NCSs) in the presence of random delays are considered in this paper. First, network-induced random delays are modeled as a Markov chain, and the resulting closed-loop system is transformed into a Markovian jump linear system (MJLS). Since the accurate access to the transition probabilities (TPs) is hard or even impossible, some of the elements in the transition probability matrix (TPM) are considered as unknown parameters. Based on this model, the sufficient conditions for the robust finite-time stochastic stability and stabilization of the uncertain NCS are proposed. Moreover, a new linear matrix inequality (LMI) approach is employed to calculate the static output-feedback controllers. Additionally, the results of the proposed scheme are verified by two examples and simulations, which include a practical example.

Sliding-Mode-Control-Based Robust Finite-Time Antisway Tracking Control of 3-D Overhead Cranes

In this paper, a robust finite-time antisway (i.e., antiswing and antiskew) tracking control method is developed for three-dimensional (3-D) overhead crane systems using a sliding-mode control (SMC) method. In order to control the overhead cranes, various tracking controllers have been developed to achieve satisfactory position tracking and swing suppression. However, along with the trolley and girder positions, both sway angles (i.e., swing and skew angles) should be controlled using the forces driving the trolley and girder for satisfactory transient response and safety enhancement through the suppression of sway angles even in the presence of uncertainties in 3-D cranes that have not been a major consideration in previous works. By introducing the sliding surface dependent on position tracking errors and the finite-time stabilization method for the skew angular rate, the proposed SMC-based robust finite-time antisway tracking control method is designed using the terms, each of which achieves position tracking control, antiswing control, and antiskew control. Accordingly, the proposed method can effectively suppress the sway motion of the 3-D crane and work well even with the variation in payload weight, the initial sway angles, and parameter uncertainties due to the payload weight uncertainty. The validity of the proposed method is supported by stability analysis and simulation and experimental results.

Criteria for robust finite‐time stabilisation of linear singular systems with interval time‐varying delay

Finite-time stabilisation involves finding state feedback controllers which stabilise the closed-loop system in a finite-time interval. This paper deals with robust finite-time stabilisation of linear singular systems with interval time-varying delay. Based on singular value decomposition method and a generalised Jensen inequality, we provide sufficient conditions for the design of such controllers guaranteeing the finite-time stability of the closed-loop system. The proposed conditions are expressed in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed methods.

Adaptive RBFNN finite-time control of normal forms for underactuated mechanical systems

This paper presents a constructive design of a continuous finite-time controller for a class of mechanical systems known as underactuated systems that satisfy the symmetry properties. An adaptive radial basis function neural network (RBFNN) finite-time control scheme is proposed to stabilize the underactuated system at a given equilibrium, regardless of the various uncertainties and disturbances that the system contains. First, a coordinate transformation is introduced to decouple the control input so that an n-th order underactuated system can be represented into a special cascade form. Next, an adaptive robust finite-time controller is derived from adding a power integrator technique and the RBFNN to approximate the nonlinear unknown dynamics in the new space, whose bounds are supposedly unknown. The stability and finite-time convergence of the closed-loop system are established by using Lyapunov theory. To show the effectiveness of the proposed method, simulations are carried out on the rotary inverted pendulum, a typical example of an underactuated mechanical system.

Robust control of post-stall pitching maneuver based on finite-time observer

This article presents a robust finite-time maneuver control scheme for the longitudinal attitude dynamic of the aircraft with unsteady aerodynamic disturbances and input saturation. To efficiently eliminate the influence of unsteady aerodynamic disturbances, nonlinear finite-time observers are developed. Despite the existence of the nonlinearity and the coupling between aircraft states and unsteady aerodynamic disturbances, the proposed observers can still precisely estimate the unmeasurable unsteady aerodynamic disturbances in finite time. To attenuate the effect caused by input saturation, a finite-time auxiliary system is constructed. With the error between the desired control input and saturation input as the input of the auxiliary system, the additional signals are generated to compensate for the effect of input saturation. Combined with the finite-time observers and the finite-time auxiliary system, a robust finite-time backstepping attitude control design is developed. The finite-time convergence of all closed-loop system signals is rigorously proved via Lyapunov analysis method under the developed robust attitude control schemes. Finally, simulation results are presented to illustrate the effectiveness of the proposed attitude control approaches.

Robust finite time control algorithm for satellite attitude control

Finite time controllers robust to inertia matrix uncertainty for satellite attitude stabilization control and attitude tracking control are developed in this paper. A three-stage finite sliding mode is constructed to improve system convergence rate. The singularity issue is solved by using the property of Euler Axis when it's paralleled to angular velocity. Based on this finite time sliding mode, finite time controller is developed to ensure the system state could reach the sliding mode in finite time. System inertia matrix uncertainty and disturbance torque is considered in this paper. The control torque constraint is also considered to ensure the norm of control torque does not exceed system upper bound. Finite time stability of the controller is proved and the controller performance is demonstrated by simulation results.

Robust finite-time stability of discrete time systems with interval time-varying delay and nonlinear perturbations

The problem of finite-time stability (FTS) for discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties is considered in this paper. In order to obtain less conservative stability criteria, a finite sum inequality with delayed states is proposed. Some sufficient conditions of FTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii-like functional (LKLF) with power function and single/double summation terms. More precisely estimations of the upper bound of the initial value of LKLF and the lower bound of LKLF are proposed. As special cases, the FTS of nominal discrete-time systems with constant or time-varying delay is considered. The numerical examples are presented to illustrate the effectiveness of the results and their improvement over the existing literature.

Robust Finite-time H∞ Control of Linear Time-varying Delay Systems with Bounded Control via Riccati Equations

In this paper, we will present new results on robust finite-time H∞ control for linear time-varying systems with both time-varying delay and bounded control. Delay-dependent sufficient conditions for robust finite-time stabilization and H∞ control are first established to guarantee finite-time stability of the closed-loop system via solving Riccati differential equations. Applications to finite-time H∞ control to a class of linear autonomous time-delay systems with bounded control are also discussed in this paper. Numerical examples are given to illustrate the effectiveness of the proposed method.

Robust finite time second-order sliding mode stabilization control for floated inertial platform

High precision inertial navigation system is one of the main ways to improve the accuracy of the satellite orbit and to prolong life. In order to solve the suspension stabilization problem of the floated inertial navigation platform (or the floated platform), a robust finite time second-order sliding mode control scheme is proposed. This control method can guarantee the stability and rapidity of the system under the complex disturbances. Then, focusing on the design problem of the observer, the nonlinear extended state observer is designed to enhance the adaptability for random uncertainty and to improve the robust performance and the stabilization accuracy of the controller. Finally, the stability and convergence of the control system are proven by the homogeneous theory. The simulation results demonstrate that the proposed method can eliminate the input chattering of the sliding mode control efficiently and the high precision inertial stabilization of the floated inertial platform is realized with the accuracy higher than [Formula: see text].

Robust Finite-Time Stabilization of Fractional-Order Neural Networks With Discontinuous and Continuous Activation Functions Under Uncertainty.

This paper is concerned with robust finite-time stabilization for a class of fractional-order neural networks (FNNs) with two types of activation functions (i.e., discontinuous and continuous activation function) under uncertainty. It is worth noting that there exist few results about FNNs with discontinuous activation functions, which is mainly because classical solutions and theories of differential equations cannot be applied in this case. Especially, there is no relevant finite-time stabilization research for such system, and this paper makes up for the gap. The existence of global solution under the framework of Filippov for such system is guaranteed by limiting discontinuous activation functions. According to set-valued analysis and Kakutani's fixed point theorem, we obtain the existence of equilibrium point. In particular, based on differential inclusion theory and fractional Lyapunov stability theory, several new sufficient conditions are given to ensure finite-time stabilization via a novel discontinuous controller, and the upper bound of the settling time for stabilization is estimated. In addition, we analyze the finite-time stabilization of FNNs with Lipschitz-continuous activation functions under uncertainty. The results of this paper improve corresponding ones of integer-order neural networks with discontinuous and continuous activation functions. Finally, three numerical examples are given to show the effectiveness of the theoretical results.

Resilient and robust finite-time H∞ control for uncertain discrete-time jump nonlinear systems

• Investigating the resilient and robust finite-time H ∞ control for DMJNSs. • Designing a controller to ensure that DMJNSs are SFTS, SFTB or SH ∞ FTB for DMJNSs. • Presentation of LMI-based conditions to deal with the feasibility issues. • The effectiveness of proposed approaches is illustrated by numerical examples. This paper studies the robust and resilient finite-time H ∞ control problem for uncertain discrete-time nonlinear systems with Markovian jump parameters. With the help of linear matrix inequalities and stochastic analysis techniques, the criteria concerning stochastic finite-time boundedness and stochastic H ∞ finite-time boundedness are initially established for the nonlinear stochastic model. We then turn to stochastic finite-time controller analysis and design to guarantee that the stochastic model is stochastically H ∞ finite-time bounded by employing matrix decomposition method. Applying resilient control schemes, the resilient and robust finite-time controllers are further designed to ensure stochastic H ∞ finite-time boundedness of the derived stochastic nonlinear systems. Moreover, the results concerning stochastic finite-time stability and stochastic finite-time boundedness are addressed. All derived criteria are expressed in terms of linear matrix inequalities, which can be solved by utilizing the available convex optimal method. Finally, the validity of obtained methods is illustrated by numerical examples.

Finite time coordinated formation control for spacecraft formation flying under directed communication topology

This paper investigates the finite time coordinated formation control problem for spacecraft formation flying (SFF) under the assumption of directed communication topology. By using the neighborhood state measurements, a robust finite time coordinated formation controller is firstly designed based on the nonsingular terminal sliding mode surface. To address the special case that the desired trajectory of the formation is only accessible to a subset of spacecraft in the formation, an adaptive finite time coordinated formation controller is also proposed by designing a novel sliding mode surface. In both cases, the external disturbances are explicitly taken into account. Rigorous theoretical analysis proves that the proposed control schemes ensure that the closed-loop system can track the desired time-varying trajectory in finite time. Numerical simulations are presented that not only highlights the closed-loop performance benefits from the proposed control algorithms, but also illustrates the effectiveness in the presence of external disturbances when compared with the existing coordinated formation control schemes.

An improved robust finite-time dissipative control for uncertain fuzzy descriptor systems with disturbance

ABSTRACTIn this paper, finite-time robust control problems are investigated for Takagi– Sugeno fuzzy descriptor systems. We provide a novel sufficient condition for robust finite-time admissibility of Takagi– Sugeno fuzzy descriptor systems, involving a group of coupled linear matrix inequalities (LMIs), which guarantee dissipative performance, reduce conservativeness and improve LMIs forms. Second, corresponding controllers are developed based on both parallel distributed compensation and non-parallel distributed compensation. Simulations demonstrate the effectiveness of the proposed control approach.

Robust finite-time estimation of biased sinusoidal signals: A volterra operators approach

A novel finite-time convergent estimation technique is proposed for identifying the amplitude, frequency and phase of a biased sinusoidal signal. Resorting to Volterra integral operators with suitably designed kernels, the measured signal is processed yielding a set of auxiliary signals in which the influence of the unknown initial conditions is removed. A second-order sliding mode-based adaptation law–fed by the aforementioned auxiliary signals–is designed for finite-time estimation of the frequency, amplitude, and phase. The worst case behavior of the proposed algorithm in presence of the bounded additive disturbances is fully characterized by Input-to-State Stability arguments. The effectiveness of the estimation technique is evaluated and compared with other existing tools via extensive numerical simulations.

Finite time control of robotic manipulators with position output feedback

SummaryThis paper deals with the robust finite time tracking of desired trajectories for a wide group of robotic manipulators in spite of unknown disturbances, uncertainties, and saturations of actuators while only manipulator's positions are available and its velocities are not measurable physically. A new form of chattering‐free second order fast nonsingular terminal sliding mode control scheme is introduced to design input torques for fulfilling the determined tracking objective in the adjustable total finite settling time. The proposed control algorithm is incorporated with two nonlinear observers to estimate disturbances and velocities of joints within finite settling times. The global finite time stability of the closed‐loop manipulator is analytically proved. Finally, a numerical simulation is carried out to verify the effectiveness of the designed input torques. Copyright © 2017 John Wiley & Sons, Ltd.

Robust finite-time guaranteed cost control for impulsive switched systems with time-varying delay

This paper is concerned with the problem of robust finite-time guaranteed cost control for a class of impulsive switched systems with time-varying delay. Firstly, the definitions of finite-time boundedness, finite-time stabilization, and robust finite-time guaranteed cost control are presented. Next, based on the average dwell-time approach, sufficient conditions on robust finite-time guaranteed cost control are obtained for the uncertain impulsive switched systems. Then, by using multiple Lyapunov-like functional method and linear matrix equality (LMI) technique, the state feedback controller is designed to guarantee that the uncertain impulsive switched system is finite-time stabilized. Furthermore, a finite-time guaranteed cost bound is given. Finally, a numerical example is shown to illustrate the effectiveness of the proposed results.

Robust finite-time chaos synchronization of time-delay chaotic systems and its application in secure communication

This paper presents finite-time chaos synchronization of time-delay chaotic systems with uncertain parameters. According to the proposed method, a lot of coupled items can be treated as zero items. Thus, the whole system can be simplified greatly. Based on robust chaotic synchronization, secure communication can be realized with a wide range of parameter disturbance and time-delay. Numerical simulations are provided to illustrate the effectiveness of the proposed method.