Robust Finite-time Control Research Articles

Robust finite-time control design for attitude stabilization of spacecraft under measurement uncertainties

This paper investigates the finite-time attitude stabilization of spacecraft under multiple uncertainties. Besides inertia uncertainties, external disturbances, and actuator faults, the measurement uncertainties are particularly considered. When including the measurement uncertainties, the spacecraft attitude control system becomes a mismatching system, which brings a great challenge to the control design. To resolve this problem, a novel robust finite-time attitude control approach is proposed by using a dual-disturbance-observer-based structure. First, two finite-time disturbance observers are developed to estimate the mismatched and matched lumped disturbances in the spacecraft attitude kinematics and dynamics, respectively. Then, the robust finite-time attitude controller is synthesized by incorporating the two finite-time disturbance observers into the adding a power integrator technique. It is strictly proved that the proposed robust finite-time attitude controller can ensure the actual attitude and angular velocity stabilize to the small neighborhoods around the origin in finite time even subject to multiple uncertainties. Benefiting from the feedforward disturbance compensation, the proposed controller is not only robust against inertia uncertainties, external disturbances, and actuator faults, but also insensitive to measurement uncertainties. Lastly, the effectiveness and advantages of the proposed control approach are validated through simulations and comparisons.

Robust finite-time PID control for discrete-time large-scale interconnected uncertain system with discrete-delay

In this paper, we investigate the decentralized proportional–integral–derivative (PID) output-feedback control problem for a class of discrete-time uncertain large-scale systems with delayed interconnections. The robust finite time stabilization of the addressed uncertain large-scale system is attained via the feedback control with the prescribed extended passive performance index. Specifically, by using an appropriate Lyapunov–Krasovskii functional, a new set of sufficient conditions is derived on the basis of linear matrix inequality which ensures the finite-time boundedness of the augmented closed-loop uncertain large-scale systems. Furthermore, cone complementarity linearization (CCL) algorithm is developed to obtain the control gain parameters. Finally, a numerical example is provided to illustrate the effectiveness of proposed control design.

Robust finite-time cooperative formation control of UGV-UAV with model uncertainties and actuator faults

This paper investigates the finite-time cooperative formation control problem for a heterogeneous system consisting of an unmanned ground vehicle (UGV) - the leader and an unmanned aerial vehicle (UAV) - the follower. The UAV system under consideration is subject to modeling uncertainties, external disturbance as well as actuator faults simultaneously, which is associated with aerodynamic and gyroscopic effects, payload mass, and other external forces. First, a backstepping controller is developed to stabilize the leader system to track the desired trajectory. Second, a robust nonsingular fast terminal sliding mode surface is designed for UAV and finite-time position control is achieved using terminal sliding mode technique, which ensures the formation error converges to zero in finite time in the presence of actuator faults and other uncertainties. Furthermore, by combining the radial basis function neural networks (NNs) with adaptive virtual parameter technology, a novel NN-based adaptive nonsingular fast terminal sliding formation controller (NN-ANFTSMFC) is developed. By means of the proposed adaptive control strategy, both uncertainties and actuator faults can be compensated without the prior knowledges of the uncertainty bounds and fault information. By using the proposed control schemes, larger actuator faults can be tolerated while eliminating control chattering. In order to realize fast coordinated formation, the expected position trajectory of UAV is composed of the leader position information and the desired relative distance with UGV, based on local distributed theory, in the three-dimensional space. The tracking and formation controllers are proved to be stable by the Lyapunov theory and the simulation results demonstrate the effectiveness of proposed algorithms.

Variable structure robust controller design for blood glucose regulation for type 1 diabetic patients: A backstepping approach

Diabetes mellitus type 1 occurs when β‐cells in the pancreas are destroyed by the immune system. As a result, the pancreas cannot produce adequate insulin, and the glucose enters the cells to produce energy. To elevate the glycaemic concentration, sufficient amount of insulin should be taken orally or injected into the human body. Artificial pancreas is a device that automatically regulates the level of body insulin by injecting the requisite amount of insulin into the human body. A finite‐time robust feedback controller based on the Extended Bergman Minimal Model is designed here. The controller is designed utilizing the backstepping approach and is robust against the unknown external disturbance and parametric uncertainties. The stability of the system is proved using the Lyapunov theorem. The controller is exponentially stable and hence provides the finite‐time convergence of the blood glucose concentration to its desired magnitude. The effectiveness of the proposed control method is shown through simulation in MATLAB/Simulink environment via comparisons with previous studies.

Synchronization control of externally disturbed chaotic spacecraft in pre-assigned settling time

This article reports the design of a novel finite-time robust nonlinear controller for the synchronization of two identical chaotic spacecraft. The proposed controller does not cancel nonlinear terms appearing in the chaotic spacecraft dynamics. Avoiding the cancelation of the nonlinear terms of the plant by the controller makes the closed-loop robust stable in the presence of uncertainties in the chaotic spacecraft parameters; this concept blooms base for the design of computationally efficient simple control law. The proposed finite-time robust nonlinear controller (1) synchronizes two nearly identical chaotic spacecraft in finite-time duration, (2) expedites the convergence of errors vector to zero without oscillation, and (3) eradicates the effects of external disturbances. Analysis based on the Lyapunov second theorem proves that the synchronization error converges fast and verifying the closed-loop’s robust global stability. The finite-time stability technique affirms the convergence of the synchronization error to zero in settling time. This research article also studies the effects of the exogenous disturbances and the controller parameter’s slowly smooth variations on the closed-loop performance. The controller parameter variation analysis sets the procedure for tuning the controller parameters. The computer-based simulation results validate the theoretical findings and provide a comparative performance analysis with the other recently proposed synchronization feedback controllers. This article uses Mathematica 12.0 version in the Microsoft 10 environment for all the simulations.

Robust finite-Time control and reachable set estimation for uncertain switched neutral systems with time delays and input constraints

This work focuses on robust finite-time fault-tolerant control and reachable set estimation for uncertain switched neutral systems subject to time delays as well as input constraints. There are few attempts to investigate robust finite-time boundedness and reachable set estimation for uncertain switched neutral systems. At the same time, input-output finite-time stability is also investigated. Compared with the existing studies, this system has wider application. A dynamic output feedback nonlinear controller is researched. An augmented closed-loop system is provided. Moreover, the sufficient conditions of finite-time boundedness, reachable set estimation and input-output finite-time stability for the closed-loop system are obtained in the framework of linear matrix inequalities via piecewise Lyapunov function. Ultimately, two examples are provided to demonstrate this validity of this approach in this paper.

Finite-time controller design with adaptive fixed-time anti-saturation compensator for hypersonic vehicle

An adaptive anti-saturation robust finite-time control algorithm (AARFTC) is designed for flexible air-breathing hypersonic vehicle (FAHV) under actuator saturations. Firstly, an adaptive fixed-time anti-saturation compensator (AFAC) is presented to drive system to faster leave the saturated region Compared to traditional anti-saturation compensators, the auxiliary variable of AFAC is able to realize faster and more accurate convergence when saturation disappears, which avoids the influence on convergent characteristics of tracking error. In addition, the novel adaptive law in AFAC can further shorten the duration of saturation and improve the convergent speed of tracking error via adjusting gain in AFAC according to saturation of actuator. Then, dynamic inversion control is combined with AFAC to establish anti-saturation controller for velocity subsystem. Secondly, differentiator-based backstepping control is combined with AFAC for height subsystem. Two recursive fixed settling time differentiators are utilized to approximate derivatives of virtual control signals exactly in fixed time, which avoids the complex computational burden residing in traditional backstepping control and improves convergent accuracy compared to command filtered backstepping control. Meanwhile, AFAC is utilized to suppress the influence of elevator saturation. Ultimately, multiple sets of simulations on FAHV subject to external disturbances, parametric uncertainties and actuator saturations are carried out to show the superiorities of AFAC and AARFTC.

Robust finite-time trajectory tracking control for a space manipulator with parametric uncertainties and external disturbances

Space manipulator is considered as one of the most promising technologies for future space activities owing to its important role in various on-orbit serving missions. In this study, a robust finite-time tracking control method is proposed for the rapid and accurate trajectory tracking control of an attitude-controlled free-flying space manipulator in the presence of parametric uncertainties and external disturbances. First, a baseline finite-time tracking controller is designed to track the desired position of the space manipulator based on the homogeneous method. Then, a finite-time disturbance observer is designed to accurately estimate the lumped uncertainties. Finally, a robust finite-time tracking controller is developed by integrating the baseline finite-time tracking controller with the finite-time disturbance observer. Rigorous theoretical analysis for the global finite-time stability of the whole closed-loop system is provided. The proposed robust finite-time tracking controller has a relatively simple structure and can guarantee the position and velocity tracking errors converge to zero in finite time even subject to lumped uncertainties. To the best of the authors’ knowledge, there are really limited existing controllers can achieve such excellent performance under the same conditions. Numerical simulations illustrate the effectiveness and superiority of the proposed control method.

Continuous Terminal Sliding-Mode Control for FJR Subject to Matched/Mismatched Disturbances.

A robust finite-time control (FTC) framework using continuous terminal sliding-mode control (SMC) and high-order sliding-mode observer (HOSMO) is discussed to realize the trajectory tracking of flexible-joint robots in this article. Control performances of the robots always suffer from unknown matched and mismatched time-varying disturbances. Traditional SMC exists with a chattering phenomenon and cannot cope with mismatched time-varying disturbances due to its inherent structure property. For this reason, two HOSMOs are devised to estimate the time-varying disturbances on the link and motor side, respectively. Then, by fusing the states and disturbance estimations into a novel terminal sliding-mode surface, a continuous robust FTC scheme is developed. The proposed control strategy can not only handle both matched and mismatched time-varying disturbances but also obtain a finite-time convergence performance. The rigorous finite-time stability analysis of the closed-loop system under the proposed control method is guaranteed. The results are illustrated to verify the effectiveness and robustness of the proposed design approach.

Robust Control of a PMSG-Based Wind Turbine Generator Using Lyapunov Function

This paper proposes a robust finite-time controller (FTC) for a permanent magnet synchronous generator (PMSG)-based wind turbine generator (WTG). An adaptive observer is used for the rotor angle, rotor speed, and turbine torque estimations of the PMSG, thus eliminating the use of anemometers. The robustness of the proposed FTC regarding parameter uncertainty and the external weak power grid is analyzed. The impacts of the power grid short-circuit ratio (SCR) at the point of common coupling (PCC) on the conventional proportional-integral (PI) controller and the proposed FTC are discussed. Case studies illustrate that the proposed observer-based FTC is able to estimate the mechanical variables accurately and provides robust control for WTGs with parameter uncertainty and weak power grids.

A novel robust finite-time tracking control of uncertain robotic manipulators with disturbances

In this article, an innovative technique to design a robust finite-time state feedback controller for a class of uncertain robotic manipulators is proposed. This controller aims to converge the state variables of the system to a small bound around the origin in a finite time. The main innovation of this article is transforming the model of an uncertain robotic manipulator into a new time-varying form to achieve the finite-time boundedness criteria using asymptotic stability methods. First, based on prior knowledge about the upper bound of uncertainties and disturbances, an innovative finite-time sliding mode controller is designed. Then, the innovative finite-time sliding mode controller is developed for finite-time tracking of time-varying reference signals by the outputs of the system. Finally, the efficiency of the proposed control laws is illustrated for serial robotic manipulators with any number of links through numerical simulations, and it is compared with the nonsingular terminal sliding mode control method as one of the most powerful finite-time techniques.

Robust Output Feedback Tracking Control for Flexible-Joint Robots Based on CTSMC Technique

This brief considers a robust finite-time output feedback control scheme for the tracking problem of flexible-joint (FJ) robotic systems subject to unknown matched and mismatched time-varying disturbances. For this purpose, a novel dynamic terminal sliding mode surface is firstly constructed base on a sliding mode observer. Then, a continuous finite-time control scheme is developed to cope with these disturbances. Besides, the proposed controller guarantees the finite-time convergence of the closed-loop system and requires only the measurements of link positions. Finally, a two-link FJ robot as an example is provided to illustrate the effectiveness of the proposed control scheme.

Observer-based finite-time robust control of nonlinear time-delay systems via Hamiltonian function method

ABSTRACT This paper investigates the observer-based finite-time robust control problem of a general class of nonlinear time-delay systems via Hamiltonian function method, and proposes some new finite-time robust stabilisation results. First, by applying Hamiltonian realisation method, the paper develops an equivalent Hamiltonian form of original system. Then, based on the equivalent Hamiltonian form, we design the corresponding observer system, study the observer-based finite-time robust stabilisation problem and present some new observer-based robust stabilisation results by constructing some suitable Lyapunov functionals. Finally, the study of an illustrative example shows that the results obtained of the paper work well in the observer-based finite-time robust stabilisation the system.

Robust finite-time controller for damping of subsynchronous resonance in doubly fed induction generator wind farm

To alleviate subsynchronous resonance in doubly fed induction generator–based wind farm, this study devises a robust nonlinear control for a rotor-side converter based on a fractional-order sliding mode controller. The designed fractional-order sliding mode controller is able to realize finite-time control and reduce the control time compared with terminal sliding mode control, which contributes to the faster mitigation of subsynchronous resonance. Impedance-based analysis and transient simulation are carried out to evaluate the performance of the fractional-order sliding mode controller compared with terminal sliding mode control and subsynchronous damping control. Simulation results verify that the fractional-order sliding mode controller is able to damp SSR within shorter time and effectively reduce the fluctuation range of a system’s transient responses under various working conditions of compensation degrees and wind speeds. Furthermore, the fractional-order sliding mode controller enhances the robustness under external disturbance and parametric uncertainty, ensuring safe operation of the practical wind farm.

Robust Finite-Time Control of Linear System with Non-Differentiable Time-Varying Delay

Practical systems such as hybrid power systems are currently implemented around the world. In order to get the system to work properly, the systems usually require their behavior to be maintained or state values to stay within a certain threshold. However, it is difficult to form a perfect mathematical model for describing behavior of the practical systems since there may be some information (uncertainties) that is not observed. Thus, in this article, we studied the stability of an uncertain linear system with a non-differentiable time-varying delay. We constructed Lyapunov-Krasovskii functionals (LKFs) containing several symmetric positive definite matrices to obtain robust finite-time stability (RFTS) and stabilization (RFTU) of the uncertain linear system. With the controller and uncertainties in the considered system, there exist nonlinear terms occurring in the formulation process. Past research handled these nonlinear terms as new variables but this led to some difficulty from a computation point of view. Instead, we applied a novel approach via Cauchy-like matrix inequalities to handle these difficulties. In the end, we present three numerical simulations to show the effectiveness of our proposed theory.

Robust finite-time fault-tolerant control for networked control systems with random delays: A Markovian jump system approach

In this paper, the problems of robust finite-time fault-tolerant stochastic stability and stabilization of networked control systems (NCSs) in the presence of random delays and actuator faults are investigated. First, sensor-to-controller and controller-to-actuator random delays are modeled as a Markov chain. Since in the network environment, the accurate access to the transition probabilities (TPs) of Markov chain is hard or even impossible, TPs information is limited. Then, by considering actuator fault indicator matrix and employing the state augmentation technique, the resulting closed-loop system is transformed into a Markovian jump system (MJS). Based on this model, the sufficient conditions are developed to ensure the finite-time fault-tolerant stochastic stability of the faulty NCS, and the fault-tolerant controllers are designed by solving a feasibility problem in terms of linear matrix inequalities (LMIs). The effectiveness of the proposed approach is illustrated during the simulation of a numerical example. Moreover, the faulty behavior of a continuous-stirred tank reactor (CSTR) is investigated and the applicability of the proposed method is demonstrated.

Robust Finite-Time Tracking for Uncertain Linear Systems with Actuator Faults

In this paper, a robust finite-time fault-tolerant control (FTC) scheme is developed for uncertain linear systems in the presence of actuator faults. Since the system uncertainties and actuator faults are unknown, the controller parameters are updated online by the adaptive laws without the need for fault detection and isolation. It is proved that the proposed state-feedback model reference adaptive finite-time FTC scheme can guarantee that the tracking error converges to a small neighborhood of the origin in finite time. An application example for an aircraft lateral-directional dynamic system is presented to show the effectiveness of the proposed control scheme.

Robust finite-time control of impulsive positive systems under ℒ1-gain performance

This paper is concerned with robust finite-time ℒ1-gain control problem for impulsive positive systems (IPSs). By adopting the average impulsive interval technique, sufficient conditions ensuring the finite-time boundedness of IPSs under ℒ1-gain characterization are formulated. The design of a feedback controller is also addressed to make the closed-loop system be positive, finite-time bounded (FTB), and have ℒ1-gain characterization. Results are presented in the form of linear programming (LP) inequalities. Finally, a numerical example is given to demonstrate the efficiency of the proposed design.

Attitude Tracking Control for Rigid Spacecraft With Parameter Uncertainties

In this paper, the attitude tracking control problem for rigid spacecraft is investigated in the presence of parameter uncertainties and external disturbances. An extended state observer is designed to estimate the parameter uncertainties and external disturbances. Then, by using the obtained estimation, a robust finite-time controller is proposed to achieve attitude tracking for the rigid spacecraft via the backstepping technique. The practical finite-time stability of the closed-loop system under the presented controller is proven by the Lyapunov stability theory. Finally, some simulation results are provided to illustrate the effectiveness and superiority of the proposed controller compared with some existing control schemes.

Finite-Time Trajectory Tracking Control of Output-Constrained Uncertain Quadrotor

In this article, a finite-time robust tracking control of output constrained multirotor unmanned aerial vehicle (UAV) is proposed. A finite-time sliding mode control (SMC) technique with barrier Lyapunov function (BLF) is used to assure robustness of the derived control laws while maintaining the output in specified constraints. A comparison of the proposed controller is carried out with conventional SMC to manifest the effectiveness of the output-constrained tracking control. Numerical simulations of quadrotor UAV with exogenous disturbances and time-invariant output constraints demonstrate the efficacy of the proposed controller regarding robustness, finite-time convergence, and chattering reduction.