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This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integ...
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The active disturbance rejection control (ADRC) for uncertain systems with non-affine control input is studied in the paper. Considering a wide class of uncertainties, the necessary and sufficient condition of the nominal model for the stability of the ADRC based closed-loop system is explicitly presented, which illustrates the basic selection crit...
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... The DOB estimates and compensates for external disturbances to enhance performance, while the RTOB focuses on measuring reaction torques to maintain system stability and control [54,55]. These observers work in tandem to estimate the interaction forces between the master and slave manipulators without direct force measurement, thus improving the system's accuracy and responsiveness in force control [56,57]. The RTOB, essentially a modified DOB, estimates real-time external torque reactions from the slave manipulator, using the system's internal disturbances to calculate reaction torque [58]. ...
Pedicle screw fixation is an essential surgical technique for addressing various spinal pathologies, including degenerative diseases, trauma, tumors, neoplasms, and infections. Despite its efficacy, the procedure poses significant challenges, notably the limited visibility of spinal anatomical landmarks and the consequent reliance on surgeon's hand-eye coordination. These challenges often result in inaccuracies and high radiation exposure due to the frequent use of fluoroscopy X-ray guidance. Addressing these concerns, this study introduces a novel approach to pedicle screw insertion by utilizing a robot-assisted system that incorporates sensorless based haptics incorporated 5-DOF surgical manipulation. This innovative system aims to minimize radiation exposure and reduce operating time while improving the surgeon's hand posture capabilities. The developed prototype, expected to be implemented using bilateral control, was tested through preliminary cadaveric experiments focused on the insertion of both percutaneous and open pedicle screws at the L4-L5 level of the lumbar spine. Validation of the Sensorless Haptic Feedback feature was an integral part of this study, aiming to enhance precision and safety. The results, confirmed by fluoroscopic x-ray images, demonstrated the successful placement of two percutaneous and two open pedicle screws, with average position and torque errors of 0.011 radians and 0.054 Nm for percutaneous screws, and 0.0116 radians and 0.0057 Nm for open screws, respectively. These findings underscore the potential of the sensorless haptic feedback in a robot-assisted pedicle screw insertion system to significantly reduce radiation exposure and improve surgical outcomes, marking a significant advancement in spinal surgery technology.
... For fixed-time stability, its settling time bound is a constant even if the initial condition tends to infinity and the constant is only relevant to design parameters, which helps to estimate the settling time and design controller to meet the requirement of the stringent settling time constraint. Since fixed-time stability has this attractive feature, it has been applied to missile tracking [9]; spacecraft attitude synchronization [10]; power system control [11], [12]; disturbed nonlinear system control [13]; and dispersion of mobile robots [14]. Recently, a large number of fixed-time consensus protocols have been developed (see [15]- [20]). ...
... Lemma 7 [13]: ...
This article is concerned with fixed-time leader-follower consensus problem for multiagent systems (MASs) with output constraints, unknown control direction, unknown system dynamics, unknown external disturbance, and dead-zone control input. First, a fixed-time distributed observer is presented for each follower to estimate the leader's states. Next, using a modified nonlinear mapping, an output-constrained system is transformed into an unconstrained system. Then, by adopting adding a power integrator technique, radial basis function neural network (RBFNN) approximation, and adaptive method, the ideal fixed-time stable virtual control protocol is derived and the issues of unknown control direction, unknown system dynamics, and unknown external disturbance are addressed. Finally, the actual control protocol is developed using the bound of dead-zone parameters. It is shown that the proposed control scheme achieves fixed-time leader-follower consensus of the studied MAS. The presented control protocol is applied to the leader-follower consensus of inverted pendulums and simulation results verify its effectiveness.
... In recent years, the output tracking problem for uncertain nonlinear systems has attracted much attention in the control theory community. Many modern nonlinear control techniques have been employed to handle this problem, such as sliding mode control [1]- [3], the observed-based control [3], [4], the dynamic surface control [5], [6], et al. A main limitation in these works is that the states of the uncertain nonlinear systems are compelled to be unconstrained. ...
This paper studies the prescribed performance tracking control problem for pure-feedback nonlinear system with full-state constraints. By incorporating the asymmetric barrier Lyapunov functions (BLFs) into the dynamic surface control, we develop an adaptive prescribed performance control scheme, which can ensure that all closed-loop signals remain bounded and the full-state constraints are not violated. Furthermore, we explore the event-triggered adaptive prescribed performance control problem for nonlinear systems with full-state constraints, which can save the limited computing and communication resources. Numerical simulations are provided to illustrate the performances of the designed adaptive controller and the event-triggered adaptive controller.
... An alternative characterization based on homogeneity theory was proposed in [2,3]. These results have been widely exploited for the design of online di↵erentiators [4,5], stabilizing controllers [6,7], state observers [8,9], multi-agent consensus [10,11] and multi-agent coordination [12] with fixed-time convergence property, to name a few. ...
A methodology, based on timescale transformations and Lyapunov analysis, for designing autonomous and non-autonomous dynamical systems exhibiting the predefined-time stability property is provided in this paper. Thus, the current proposal allows characterizing a broad class of predefined-time stable systems, placing them under a common framework with existing methods which use time-varying gains based on time-base generators. What follows from this construction is that the bound of the convergence time for this class of systems is the lowest possible. Moreover, it is independent of the initial conditions and is set a priori through a tuning parameter. This design procedure is a relevant contribution when compared to traditional fixed-time convergent algorithms since the current convergence time bounds are conservative. Finally, we analyze several existing and novel algorithms for autonomous and non-autonomous systems showing the effectiveness of the method.
... From the analysis of proof procedure, we can see that the convergence time T of SGFTUUB stabilization is finite and dependent on the state value X (t m ). In recent works (Ni et al., 2016(Ni et al., , 2017a, a special finite-time control problem called 'fixed-time control' was investigated. The convergence time of fixed-time control is independent of initial conditions and bounded by a constant. ...
... However, in order to realize bounded time stabilization, the control laws of fixedtime control schemes are usually more complex than those of finite-time (non-fixed-time) control schemes. Unlike the results in Ni et al. (2016Ni et al. ( , 2017a, model uncertainties and input constraints are considered in this paper, and thus the proposed results cannot be directly extended to the case of fixed-time control. In the future, the fixed-time control of system (1) with uncertainties and input constraints will be an important research issue. ...
This paper addresses the problem of robust adaptive finite-time tracking control for a class of mechanical systems in the presence of model uncertainties, unknown external disturbances, and input nonlinearities containing saturation and deadzone. Without imposing any conditions on the model uncertainties, radial basis function neural networks are used to approximate unknown nonlinear continuous functions, and an adaptive tracking control scheme is proposed by exploiting the recursive design method. It is shown that the input saturation and deadzone model can be expressed as a simple linear system with a time-varying gain and bounded disturbance. An adaptive compensation term for the upper bound of the lumped disturbance is introduced. The semi-global finite-time uniform ultimate boundedness of the corresponding closed-loop tracking error system is proved with the help of the finite-time Lyapunov stability theory. Finally, an example is given to demonstrate the effectiveness of the proposed method.
... Finite time control method is another effective strategy to improve disturbance rejection performance. [22][23][24]. In [25], fixed-time leader-following lag consensus problem of second-order multiagent systems with input delay is discussed by a novel nonsingular terminal sliding mode protocol. ...
... Ã randn (1,1)] is considered as external disturbance. When we adopt adaptive Super-Twisting sliding mode control, the Super-Twisting sliding mode controller parameters of Eq (22) are selected as k 1 = 15, k 2 = 5. However when the conventional adaptive sliding mode control is simulated, the sliding controller parameter of Eq (6) is selected as k = 6. ...
This paper proposes a novel adaptive Super-Twisting sliding mode control for a microgyroscope under unknown model uncertainties and external disturbances. In order to improve the convergence rate of reaching the sliding surface and the accuracy of regulating and trajectory tracking, a high order Super-Twisting sliding mode control strategy is employed, which not only can combine the advantages of the traditional sliding mode control with the Super-Twisting sliding mode control, but also guarantee that the designed control system can reach the sliding surface and equilibrium point in a shorter finite time from any initial state and avoid chattering problems. In consideration of unknown parameters of micro gyroscope system, an adaptive algorithm based on Lyapunov stability theory is designed to estimate the unknown parameters and angular velocity of microgyroscope. Finally, the effectiveness of the proposed scheme is demonstrated by simulation results. The comparative study between adaptive Super-Twisting sliding mode control and conventional sliding mode control demonstrate the superiority of the proposed method.
A fixed-time trajectory tracking control of autonomous surface vessels (ASVs) subject to unmeasured speed is studied in this work. By using the homogeneity-based Lyapunov method, the unknown system states, including the unmeasured speed and lumped disturbances, are estimated by using a novel extended state observer (ESO) within fixed time. Subsequently, using the estimated states, the task of fixed-time tracking is completed with the aid of a newly proposed output-constrained power integrator method, which makes the vessel position and heading strictly within the predefined output constraints, and the tracking errors can be reduced to a range of zero under the continuous control action. The practical fixed-time stability (FTS) of the closed-loop system is analyzed in the sense of Lyapunov, while the output constraints can be well maintained during maneuvering. Finally, the ascendancy of the designed scheme is exhibited by simulation comparisons.
This paper addresses the fixed-time trajectory tracking control problem of a fully actuated marine surface
vehicle with full state constraints and system uncertainties. A continuous fixed-time convergence tracking controller
is proposed based on fixed-time control and adding a power integrator methods, which achieves system stabilization
within a finite time independent of system initial conditions. Moreover, a novel barrier Lyapunov function with a
power integrator is designed to ensure the full state tracking error within the constraints. To accurately estimate the
lumped disturbances of the vehicle system, a fixed-time disturbance observer is designed to guarantee the settling
time of the disturbance observer bounded by a time constant independent of initial estimation errors. Finally,
the proposed control scheme is proved to be fixed-time stable via fixed-time Lyapunov stability theorem and the
full state constraints can never be violated. A numerical simulation is provided to illustrate the effectiveness and
superiority of the proposed control scheme.
This paper presents a novel fixed-time sliding mode disturbance observer (SMDO)-based robust backstepping cruise tracking control scheme with closed-loop finite-time convergence for flexible air-breathing hypersonic vehicles (FAHVs). In order to enhance the control system's robustness, a fixed-time SMDO is designed to compensate for the flexibility effects, model uncertainties, and external disturbances in FAHVs. In consequence, fixed convergence time of disturbance observation is achieved independently of initial estimation errors. Furthermore, velocity and altitude continuous finite-time tracking controllers are constructed by incorporating the SMDO and nonsmooth backstepping technique. To solve the problem of "explosion of complexity" in the conventional backstepping approach, nonsmooth filters are specifically constructed to generate the derivatives of virtual control laws. A Lyapunov-based stability analysis is conducted to show the finite-time convergence of the closed-loop FAHV control system. Finally, several representative numerical simulations are given to illustrate the effectiveness and superiority of the proposed control strategy.
