Prescribing Performance Research Articles

Broad learning control of a two-link flexible manipulator with prescribed performance and actuator faults

AbstractIn this paper, we present a broad learning control method for a two-link flexible manipulator with prescribed performance (PP) and actuator faults. The trajectory tracking errors are processed through two consecutive error transformations to achieve the constraints in terms of the overshoot, transient error, and steady-state error. And the barrier Lyapunov function is employed to implement constraints on the transition state variable. Then, the improved radial basis function neural networks combined with broad learning theory are constructed to approximate the unknown model dynamics of flexible robotic manipulator. The proposed fault-tolerant PP control cannot only ensure tracking errors converge into a small region near zero within the preset finite time but also address the problem caused by actuator faults. All the closed-loop error signals are uniformly ultimately bounded via the Lyapunov stability theory. Finally, the feasibility of the proposed control is verified by the simulation results.

Safety flight envelope calculation and protection control of UAV based on disturbance observer

In this paper, as for the unmanned air vehicle (UAV) under external disturbance, an attainable-equilibrium-set-based safety fight envelope (SFE) calculation method is proposed, based on which a prescribed performance protection control scheme is presented. Firstly, the existing definition of the SFE based on attainable equilibrium set (AES) is extended to make it consistent and suitable for the UAV system under disturbance. Secondly, a higher-order disturbance observer (HODO) is developed to estimate the disturbances and the disturbance estimation is applied in the computation of the SFE. Thirdly, by using the calculated SFE, a desired safety trajectory based on the time-varying safety margin function and first-order filter is developed to prevent the states of the UAV system from exceeding the SFE. Moreover, an SFE protection controller is proposed by combining the desired safety trajectory, backstepping method, HODO design, and prescribed performance (PP) control technique. In particular, the closed-loop system is established on the basis of disturbance estimation error, filter error, and tracking error. Finally, the stability of the closed-loop system is verified by the Lyapunov stability theory, and the simulations are presented to illustrate the effectiveness of the proposed control scheme.

Switching mechanism-based event-triggered fuzzy adaptive control with prescribed performance for MIMO nonlinear systems

<p style='text-indent:20px;'>This paper investigates the switching mechanism-based event-trig-gered fuzzy adaptive control issue of multi-input and multi-output (MIMO) nonlinear systems with prescribed performance (PP). Utilizing fuzzy logic systems (FLSs) to approximate unknown nonlinear functions. By using the switching threshold strategy, the system has more flexibility in strategy selection. The proposed control scheme can better solve the communication resource limitation. On account of the Lyapunov stability theory, the stability of the controlled system is proved. And all signals of the controlled system are bounded. Moreover, the tracking errors are controlled in a diminutive realm of the origin within the PP bounded. Simultaneously, the Zeno behavior is avoided. Finally, illustrate the effectiveness of the control scheme that has been proposed by demonstrating some simulation consequences.</p>

Adaptive fuzzy output regulation of uncertain pure‐feedback non‐linear systems with prescribed performance

The output regulation problem for pure-feedback non-linear systems with prescribed performance (PP) driven by an external linear system with unknown parameter are investigated. First, an observer with a disturbance signal is designed to observe unmeasured system states. Secondly, fuzzy logic systems (FLS) are used to approximate unknown non-linear non-affine functions. Thirdly, a fuzzy internal model is obtained to reject disturbance, and an adaptive fuzzy output feedback algorithm is proposed based on dynamic surface control (DSC) technique and backstepping method. Simultaneously, an L function is constructed so that the overall property (steady-state property and dynamic property) of the tracking error are constrained by PP functions. The results explain that the proposed control algorithm can make sure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded (SUUB), and the tracking error is semi-globally PP uniformly ultimately bounded (SPPUUB). Finally, two examples are given to show the validity of the results.

RISE-based prescribed performance control of Euler–Lagrange systems

In this study, we addressed the problem of design of high-performance tracking controller for uncertain systems described by the Euler–Lagrange formulation. The main objective was to combine the advantages of the robust integral of the sign of the error (RISE) controller with those of the prescribed performance (PP) controller. In particular, we aimed to obtain asymptotic tracking for the uncertain systems through a continuous control command while ensuring the transient performance. Two controllers were developed. First, the PP property was injected into the RISE controller assuming no constraint on the actuation amplitude existed, and then this property was incorporated into the saturated RISE controller. The performance of the proposed controllers was validated through experimental and simulation tests.

Bounded‐input prescribed performance control of uncertain Euler–Lagrange systems

This study proposes a novel saturated prescribed performance (PP) controller for Euler–Lagrange dynamic systems. The design of bounded-input controller is facilitated by means of introduction of auxiliary dynamics in the closed-loop system. The controller takes advantages of using an adaptive multilayer neural network and a robust term to deal with uncertainties of the system. Through the stability analysis, it is shown that PPwith saturated control command is feasible having certain constraints on initial conditions and external disturbances. The proposed controller is validated through experimental and simulation studies conducted on a lower-limb robotic exoskeleton.

Prescribed performance synchronization controller design of fractional-order chaotic systems: An adaptive neural network control approach

In this study, an adaptive neural network synchronization (NNS) approach, capable of guaranteeing prescribed performance (PP), is designed for non-identical fractional-order chaotic systems (FOCSs). For PP synchronization, we mean that the synchronization error converges to an arbitrary small region of the origin with convergence rate greater than some function given in advance. Neural networks are utilized to estimate unknown nonlinear functions in the closed-loop system. Based on the integer-order Lyapunov stability theorem, a fractional-order adaptive NNS controller is designed, and the PP can be guaranteed. Finally, simulation results are presented to confirm our results.

Adaptive Jacobian force/position tracking for space free-flying robots with prescribed transient performance

This paper presents a tracking control with guaranteed prescribed performance (PP) for space free-flying robots with uncertain kinematics (Jacobian matrix) and dynamics, uncertain normal force parameter, and bounded disturbances in a compliant contact with a planar surface. Given the orientation of the surface and a nonlinear model of the elastic force, a controller is designed requiring no information on the robot parameters and the disturbances. This controller will guarantee that the tracking errors satisfy PP indexes such as the maximum steady-state errors and overshoots, and the minimum convergence rates. Thus, contact maintenance can be ensured as prescribed. An approximation of the Jacobian is utilized in the presence of uncertain robot kinematics, and PP position/attitude tracking of the free-flying base is achieved in addition to the PP force/position tracking of the manipulator’s fingertip. The proposed controller is based on an error transformation technique, and a directly tunable gain for the transformed error feedback is introduced in the control to trade off between the tracking performance and control effort. Numerical simulations and comparisons demonstrate the effectiveness and superiority of the proposed controller.