Finite-time Output Feedback Control Research Articles

Observer-Based Output Feedback Attitude Stabilization for Spacecraft With Finite-Time Convergence

This brief investigates the problem of finite-time output feedback control for spacecraft attitude stabilization without angular velocity measurement. First, two new sufficient conditions for finite-time ultimate boundedness and local finite-time stability are derived, which reduce the conservativeness of the traditional conditions. Then, based on the two new sufficient conditions of the finite-time stability, a finite-time observer is proposed to estimate the unknown angular velocity by using the quadratic Lyapunov function method. Next, a finite-time attitude controller is designed based on the estimate of the angular velocity. The finite-time stability of the entire closed-loop system is analyzed through the Lyapunov approach. The rigorous proof shows that the observation errors and the spacecraft attitude will converge to a residual set of zero in finite time. Numerical simulation results illustrate the effectiveness of the proposed strategy.

Reduced-order observer-based saturated finite-time stabilization of high-order feedforward nonlinear systems by output feedback

This paper is concerned with the problem of global finite-time stabilization by output feedback for a class of feedforward (upper-triangular) nonlinear systems in p-normal form. Remarkably, both the high order powers and the saturated input are involved in the system under consideration, that renders the existing output feedback control methods are inapplicable. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a reduced order observer-based saturated finite-time output feedback control scheme is successfully developed. With choosing appropriate design parameters, the proposed controller ensures that the states of the closed-loop system are regulated to zero in a finite time without violation of the input constraint. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed method.

Continuous finite-time output torque control approach for series elastic actuator

Series elastic actuator (SEA) is widely used in robots that intelligently interact with humans, but unavoidably suffer from the influences brought by interactions, such as variations of the payload parameters and external disturbances. In order to address these challenges, this paper proposes a practical finite-time output feedback controller (FT-OFC) along with a finite-time extended state observers (FT-ESO) to generate the desired torque for SEA. Specifically, the dynamics of SEA system is analyzed and transformed firstly, through several coordinate transformations, into an integral-chain form. Based on this, we construct a new FT-ESO to estimate the uncertainties as well as the states of SEA system. Subsequently, a continuous terminal sliding-mode control scheme is introduced to synthesize the control law. Lyapunov-based analysis is provided to demonstrate that the equilibrium point of the closed-loop system is finite-time stable. The validity and superior performance of the proposed method are verified by a series of experiments carried out on a self-built SEA platform.

A Finite-Time Output Feedback Control Scheme for Dynamic Positioning System of Ships

This paper develops a finite-time output feedback control scheme for dynamic positioning (DP) system of ships in the presence of unmeasured states of ships, unknown dynamic model parameters and unknown time-varying environment disturbances. A novel finite-time extended state observer (FTESO) is first proposed to simultaneously and precisely estimate the unmeasured states of ships, unknown dynamic model parameters, and unknown time-varying environment disturbances in finite time. Second, based on the outputs of FTESO, the terminal sliding mode (TSM) controller is designed to guarantee that the DP system can track the position and heading at desired values in finite time with precise performance. Then, it is proved that all error signals of the closed-loop DP control system can converge to zero in finite time by utilizing the homogeneous method and the Lyapunov stability theory. Finally, the numerical simulations on a supply ship are carried out to illustrate the effectiveness of the proposed finite-time output feedback control scheme.

Further synchronization in finite time analysis for time-varying delayed fractional order memristive competitive neural networks with leakage delay

Abstract This article mainly concerns the synchronization in finite-time to the time-varying delay fractional order memristive competitive neural networks (TMFCNNs) with leakage delay. By means of Fillipov’s theory, Gronwall–Bellman integral inequality, H o ¨ lder’s inequality, and the Caputo derivative properties, the novel algebraic sufficient conditions are proposed to guarantee the synchronization in finite time of addressing TMFCNNs with non-integer order: 0 p 1 2 and 1 2 ≤ p 1 via finite-time output feedback controller. Up to now, there are no relevant results in fractional order competitive-type neural networks, and this article makes filling up for this gap. The obtained results are improved to some existing results on integer-order memristive competitive neural networks. Finally, two numerical examples with simulations are also designed to confirm the merits of the proposed theoretical results, while we estimate the upper bound of the settling time for the synchronization errors.

Finite-Time Output Feedback Control for a Rigid Hydraulic Manipulator System

The position tracking control problem of a hydraulic manipulator system is investigated. By utilizing homogeneity theory, a finite-time output feedback controller is designed. Firstly, a finite-time state feedback controller is developed based on homogeneity theory. Secondly, a nonlinear state observer is designed to estimate the manipulator’s velocity. A rigorous analysis process is presented to demonstrate the observer’s finite-time stability. Finally, the corresponding output feedback tracking controller is derived, which stabilizes the tracking error system in finite time. Simulations demonstrate the effectiveness of the designed finite-time output feedback controller.

Finite-time stability control of an electric vehicle under tyre blowout

In this paper, the authors consider the problem of tyre blowout control via output feedback for an electric vehicle (EV) driven by four in-wheel motors to reduce fatal damage. First, an EV dynamic model in the case of a tyre blowout is established. The model considers the unmeasurable state, unknown added front wheel steering angle generated by a tyre blowout and uncertain external disturbances. Second, to address the difficulties in estimating the unmeasurable state, unknown parameters and disturbances for the EV, a finite-time observer is introduced. Then, by introducing a coordinate transformation, the state-space model of an EV with tyre blowout is converted into a simple form for which a state feedback control law is constructed by adding a power integrator method. Combining the finite-time observer with the finite-time control law, an output feedback controller is designed to stabilize the EV when a tyre bursts. A torque allocation method is also given to operate every wheel except the burst tyre to stabilize and stop the EV. Finally, computer simulations are given to validate the proposed finite-time output feedback controller for the EV tyre blowout control.

Finite-time output feedback control for discrete-time switched linear systems with mode-dependent persistent dwell-time

This paper is concerned with finite-time output feedback control for a class of discrete-time switched linear systems. The mode-dependent persistent dwell-time (MDPDT) switching is considered, which is more general than dwell-time switching and average dwell-time switching. By using the MDPDT approach and multiple Lyapunov functions technique, sufficient conditions are proposed so that the closed-loop system is finite-time bounded with a guaranteed H∞ performance. Furthermore, the corresponding criterion is proposed to design a set of dynamic output feedback (DOF) controllers for the switched system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

Finite-time output feedback control of uncertain switched systems via sliding mode design

ABSTRACTThe problem of sliding mode control (SMC) is investigated for a class of uncertain switched systems subject to unmeasurable state and assigned finite (possible short) time constraint. A key issue is how to ensure the finite-time boundedness (FTB) of system state during reaching phase and sliding motion phase. To this end, a state observer is constructed to estimate the unmeasured states. And then, a state estimate-based SMC law is designed such that the state trajectories can be driven onto the specified integral sliding surface during the assigned finite time interval. By means of partitioning strategy, the corresponding FTB over reaching phase and sliding motion phase are guaranteed and the sufficient conditions are derived via average dwell time technique. Finally, an illustrative example is given to illustrate the proposed method.

Design finite-time output feedback controller for nonlinear discrete-time systems with time-delay and exogenous disturbances

ABSTRACTThis paper considers the finite-time output feedback controller design for nonlinear discrete-time systems with time-delay and time-varying exogenous disturbances. The exogenous disturbances are unknown bounded signals. In this regard, a theorem is given and the sufficient conditions are extracted which guarantees the finite-time boundedness of the time-delay closed-loop system via selecting the appropriate Lyapunov-Krasovskii functional. Furthermore, the gain of output feedback is achieved through the feasibility testing of the derived linear matrix inequalities (LMIs). Finally, a numerical example is given to verify the effectiveness of the developed technique.

A Continuous Finite-Time Output Feedback Control Scheme and Its Application in Quadrotor UAVs

A continuous output feedback control scheme is presented for double integrator systems subject to non-vanishing perturbation. In the method, no explicit state observer or disturbance observer is designed. The geometric homogeneity technique and Lyapunov stability theory are utilized to ensure the global finite-time stability of the closed-loop system. The extension of the algorithm to multi-input multi-output is developed, and its application in quadrotor unmanned aerial vehicles is investigated. Finally, the numerical simulation results are provided to validate the efficiency of the proposed method.

A Robust Finite-Time Output Feedback Control Scheme for Marine Surface Vehicles Formation

In view of the marine surface vehicles are subject to unknown time-varying external disturbance and its velocities are not available for feedback, a robust finite-time output feedback control scheme is presented for multiple marine surface vehicles to achieve precise formation control in this paper. Without neglecting the first time derivative of disturbance, a novel finite-time extended state observer (FTESO) is proposed to precisely estimate the external disturbance and velocity information in finite time. Based on the outputs of FTESO, the distributed formation controller is designed to guarantee that a group of marine surface vehicles can track the time-varying virtual leader in finite time with precise tracking performance. The errors of the proposed FTESO and formation controller can be guaranteed to converge to zero in finite time by using the homogeneous method and the Lyapunov theory. Numerical simulations are presented to illustrate the effectiveness of the proposed finite-time output feedback formation control scheme.

Multivariable Finite-Time Control of 5 DOF Upper-Limb Exoskeleton Based on Linear Extended Observer

An output feedback finite-time control strategy for five degree of freedoms (DOF) upper-limb exoskeleton is investigated in this paper. First, a multivariable second-order sliding mode control is proposed to improve the response speed and stability of the exoskeleton system with parameter uncertainties and external disturbances. Furthermore, for the sake of high control precision with limited information, a finite-time linear extended state observer is constructed to estimate both the unmeasured states and the lumped perturbations. Finally, by utilizing the 5-DOF upper-limb model, simulation results are presented to demonstrate the effectiveness of the control strategy.

Global output-feedback finite-time stabilization for a class of stochastic nonlinear cascaded systems

In this paper, the problem of global finite-time stabilization via output-feedback is investigated for a class of stochastic nonlinear cascaded systems (SNCSs). First, based on the adding a power integrator technique and the homogeneous domination approach, a global output-feedback finite-time control law is constructed for the driving subsystem. Then, based on homogeneous systems theory, it is shown that under some mild conditions the global finite- time stability in probability of the driving subsystem implies the global finite-time stability in probability of the whole SNCS. Finally, a simulation example is given to illustrate the effectiveness of the proposed control design approach.

Reliable spacecraft rendezvous without velocity measurement

This paper investigates the problem of finite-time velocity-free autonomous rendezvous for spacecraft in the presence of external disturbances during the terminal phase. First of all, to address the problem of lack of relative velocity measurement, a robust observer is proposed to estimate the unknown relative velocity information in a finite time. It is shown that the effect of external disturbances on the estimation precision can be suppressed to a relatively low level. With the reconstructed velocity information, a finite-time output feedback control law is then formulated to stabilize the rendezvous system. Theoretical analysis and rigorous proof show that the relative position and its rate can converge to a small compacted region in finite time. Numerical simulations are performed to evaluate the performance of the proposed approach in the presence of external disturbances and actuator faults.

Finite-Time Attitude Trajectory Tracking Control of Rigid Spacecraft

In this paper, we investigate the finite-time attitude tracking control problem for a rigid spacecraft on the special orthogonal group ( $SO(3)$ ). The exponential coordinates, derived from the exponential and logarithmic maps of Lie group, are utilized to describe the attitude tracking error on $SO(3)$ almost globally unique except for a zero measure set on which the logarithmic map is double valued. To avoid this issue, a novel nonsingular sliding surface is designed to guarantee that the attitude tracking error will never reach the zero measure set and provide fixed-time stability during the sliding phase. Then, a novel continuous second-order sliding mode control scheme is developed to force the system state to reach the desired sliding surface in finite time. The salient feature of the proposed control scheme is that it significantly suppresses the chattering phenomenon. In addition, to address the lack of angular velocity measurements, a finite-time observer is proposed to recover the unknown angular velocity information in finite time. Then, an observer-based finite-time output feedback control strategy is obtained. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed control scheme.

Finite-Time Output Feedback Control for PWM-Based DC–DC Buck Power Converters of Current Sensorless Mode

This paper investigates the finite-time output feedback control problem for dc–dc buck switched power converters of the current sensorless mode. A finite-time state-feedback controller is first built by using a recursive design method, and then a novel reduced-order observer, rather than the conventional full-order observer, is derived to estimate the unmeasurable state of the dc–dc buck system with a finite-time convergence rate. The output feedback control law built by combining the state-feedback control law and the measured system state from the observer is proved to be effective with an explicit stability analysis. Compared with the asymptotic stability control method, not only a faster convergence rate around the equilibrium is obtained but also a better suppression ability against resistance, inductance, and input voltage variation can be achieved for the closed-loop system. Moreover, the sensorless control strategy will be more reliable and cost reducible than its state-feedback control counter-case. Simulations and experimental comparison results verify the effectiveness of the proposed control method.

Output Feedback Stabilization of Inertial Stabilized Platform with Unmatched Disturbances Using Sliding Mode Approach

Inertial stabilized platforms are extensively used to keep the light of sight free from the effects of vehicle motion or vibration. In order to reduce the assembly difficulty and cost as well as achieve an accurate pointing in the presence of disturbances, a finite-time output feedback control strategy is proposed. On the basis of the dynamic model with both matched and unmatched uncertainties, two high-order sliding mode observers are designed to estimate the newly defined virtual state and the lumped uncertainty, respectively. Combing with the nonsingular terminal sliding mode technique, an output feedback control based on the estimates and the output is developed. The proposed method can achieve not only stability and robustness against uncertainties but also the finite-time convergence to the desired angular rate without control chattering. Finally, the comparative simulations are performed to show the effectiveness of the proposed method.

Adaptive Neural Network Finite-Time Output Feedback Control of Quantized Nonlinear Systems.

This paper addresses the finite-time tracking issue for nonlinear quantized systems with unmeasurable states. Compared with the existing researches, the finite-time quantized feedback control is considered for the first time. By proposing a new finite-time stability criterion and designing a state observer, a novel adaptive neural output-feedback control strategy is raised by backstepping technique. Under the presented control scheme, the finite-time quantized feedback control problem is coped with without limiting assumption for nonlinear functions.

Finite-time output-feedback synchronization control for bilateral teleoperation system via neural networks

The finite-time control problem is considered for bilateral teleoperation system via output feedback approach. A new observer is designed for the velocity estimation and the resulting velocity error system is proved to be semi-globally stable. The observer based output feedback finite-time controller is developed by employing a novel nonsingular fast integral terminal sliding mode. The closed-loop system is proved to be stable based on Lyapunov stability theory. It is shown that the master-slave synchronization error converges to zero in finite time. The merit of the proposed method is that the designed controller only uses the position information which renders that the master-slave synchronization error reaches zero in the prescribed time. Simulation and experiment are performed and the results demonstrate the effectiveness of the proposed method.