Adaptive Prescribed Performance Control Research Articles

Expansive Errors-Based Fuzzy Adaptive Prescribed Performance Control by Residual Approximation

This article is concerned with an expansive errors (EE)-based fuzzy adaptive prescribed performance control of a class of multiple-input and multiple-output nonlinear systems in the presence of unknown interconnection nonlinearities using fuzzy residual approximation technique. Based on an newly defined expansive error, residual nonlinearities’ fuzzy approximation scheme is proposed. The merits of designed control can be presented as twofold: 1) by incorporating an EE-based technique into pioneering prescribed performance control methodology, the defined intermediate and output tracking errors are kept within the regions represented by preassigned functions and control parameters simultaneously and 2) expansive errors-related residual nonlinearity is approximated by fuzzy logic systems, which further ameliorates the output tracking performance by compensating the affects raised by composite inner and interconnection nonlinearities among subsystems. With the designed expansive errors-based fuzzy adaptive prescribed performance control, all the closed-loop signals are kept bounded in the sense of Lyapunov stability theorem. Comparative simulation studies are presented to verify the effectiveness and advantages of theoretical findings.

Observer-based Finite-time Adaptive Prescribed Performance Control for Nonlinear Systems with Input Delay

Observer-based Finite-time Adaptive Prescribed Performance Control for Nonlinear Systems with Input Delay

Prescribed Performance Adaptive Control for a Nonlinear Aeroelastic System with Input Constraint

A constrained prescribed performance compensation controller is proposed for a nonlinear aeroelastic system in the presence of wind gust, system uncertainties, and input saturation. To deal with the effects of the nonsmooth saturation nonlinearity, an approximate saturation function is introduced into the controller design, which can smoothly approximate the real saturation with arbitrarily prescribed precision. Specifically, by designing the prescribed performance function, a fixed-time control framework is designed to ensure that the closed-loop system has the prescribed tracking performance. The designed control algorithm can not only compensate the adverse effect caused by disturbances and uncertainties but also restrain the excessive amplitude of control input. Finally, the stability analysis shows that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded via the Lyapunov stability analysis method, and simulation results are presented to demonstrate the feasibility and effectiveness of the proposed method.

Adaptive finite-time prescribed performance attitude tracking control for reusable launch vehicle during reentry phase: An event-triggered case

This paper is devoted to address the attitude tracking problem for reusable launch vehicle (RLV) with uncertain aerodynamic parameters, input saturation and limited transmission resources. Based on the framework of the backstepping technique, a novel event-triggered adaptive prescribed performance control protocol is presented. Firstly, an extended state observer is used to provide the estimation for the whole system uncertainties. Then, an event-triggered mechanism is applied to exactly determine when control signals should be updated, which successfully eliminates the unnecessary periodic/continuous sampling in time-triggered researches and creates less waste of transmission resources. To compensate the negative effects induced by the aperiodic updating of control signals in event-triggered mechanism, an appointed-time prescribed performance controller is devised. In this way, the stability and tracking performance for the attitude system of the RLV can be guaranteed simultaneously. Moreover, the detailed theoretical analysis confirms that Zeno-free triggering is completely guaranteed along with stability. Finally, extensive simulations are carried out to validate the effectiveness of the proposed control protocol.

Barrier Lyapunov function-based adaptive prescribed performance control of the PMSM used in robots with full-state and input constraints

The permanent magnet synchronous motor is extensively used in robots due to its superior performances. However, robots mostly operate in unstructured and dynamically changing environments. Therefore, it is urgent and challenging to achieve high-performance control with high security and reliability. This paper investigates an accelerated adaptive fuzzy neural prescribed performance controller for the PMSM to solve chaotic oscillations, prescribed output performance constraint, full-state constraints, input constraints, uncertain time delays, and unknown external disturbances. First, for ensuring the permanent magnet synchronous motor with higher security, faster response speed, and lower tracking error simultaneously, a novel unified prescribed performance log-type barrier Lyapunov function is proposed to handle both prescribed output performance constraint and full-state constraints. Subsequently, a continuous differentiable constraint function-based model is introduced for solving input constraints nonlinearity. The Lyapunov–Krasovskii functions are utilized to compensate the uncertain time delays. Besides, a type-2 sequential fuzzy neural network is exploited to approximate unknown nonlinearities and unknown gain. For the “explosion of complexity” associated with backstepping, a tracking differentiator is integrated into this controller. Furthermore, a speed function is introduced in the backstepping technique for accelerated convergence. On the basis of above works, the accelerated adaptive backstepping controller is achieved. And the presented controller can ensure that all the closed-loop signals are ultimate boundedness, and all state variables are restricted in the prespecified regions and the permanent magnet synchronous motor successfully escapes from chaotic oscillations. Finally, the simulation results verify the effectiveness of the proposed controller.

A Modified Adaptive Prescribed Performance Control Method for Motion Control Problems of Robotic Manipulato

A Modified Adaptive Prescribed Performance Control Method for Motion Control Problems of Robotic Manipulato

Adaptive prescribed performance control with selected transient response for a class of nonlinear systems with uncertainties

SummaryThis article proposes a novel adaptive prescribed performance control method. Featured with a selected transient performance, the proposed control method can achieve prescribed performance control by a new error transformation method. With the proposed control strategy, the closed‐loop system can follow the prescribed performance with a predefined curve. An adaptive controller is constructed based on the adaptive backstepping technique. By utilizing the Lyapunov stability, asymptotic stability is achieved for the closed‐loop system. Two examples with simulation results are provided to illustrate the proficiency of the proposed control strategy. To make comparisons, the same second‐order transient response is adopted as the performance function for both examples. The selection of gains and parameters are investigated by tests. The expected prescribed performance and the asymptotic stability are achieved in both examples, which verifies the proposed control strategy. Some discussions and comparisons are made accordingly as well.

Adaptive prescribed performance control of nonlinear asymmetric input saturated systems with application to AUVs

In this paper, the adaptive prescribed performance tracking control of nonlinear asymmetric input saturated systems in strict-feedback form is addressed under the consideration of model uncertainties and external disturbances. A radial basis function neural network (RBF-NN) is utilized to handle the model uncertainties. By prescribed performance functions, the transient performance of the system can be guaranteed. The continuous Gaussian error function is represented as an approximation of asymmetric saturation nonlinearity such that the backstepping technique can be leveraged in the control design. Based on the Lyapunov synthesis, residual function approximation inaccuracies and external disturbances are compensated by constructed adaptive control laws. As a consequence, all the signals in the closed-loop system are uniformly ultimately bounded and the tracking errors bounded by prescribed functions converge to a small neighbourhood of zero. The proposed method is applied to the autonomous underwater vehicles (AUVs) with extensive simulation results demonstrating the effectiveness of the proposed method.

Prescribed performance adaptive control for an uncertain robotic manipulator with input compensation updating law

This paper investigates an adaptive prescribed performance control strategy with specific time planning for trajectory tracking of robotic manipulator subject to input constraint and external disturbances. By constructing an accumulated error vector embedded with a performance enhancement function and introducing an input auxiliary function, a specified-time control framework with built-in prescribed performance is further designed to ensure that the trajectory tracking performance. More particularly, the proposed control law is compatible with the control input saturation suppression algorithm, which is capable of improving the robustness of closed loop system. Under the framework of the proposed control strategy, it is proved by theory that all the signals in the closed-loop system are bounded, and moreover the tracking error can reach the exact convergence domain in a given time. At last, a numerical example is presented to indicate the feasibility and effectiveness of the proposed method.

Observer-Based Autopilot Heading Finite-Time Control Design for Intelligent Ship with Prescribed Performance

Traffic engineering control is a major challenge in marine transportation. Cost efficiency and high performance demand advanced technologies for the ship control systems. This paper develops an autopilot heading control scheme based on a fuzzy state observer for an intelligent ship on this subject to track the prescribed function while calling for performance limitation and order execution time. A fuzzy logic system (FLS) is adopted to approximate the unknown uncertainties caused by the changes in water depth, wind, wave, ship loading, and speed in navigation. State observer is required to obtain unknown yaw rate. By adopting performance function and tracking error transformation techniques, the heading tracking error can converge to prescribed performance bounds. Taking settling time into account, the finite-time adaptive prescribed performance control algorithm can save more resources effectively. Based on the Lyapunov stability theory, the observer-based adaptive fuzzy control approach does not cause any unbounded signal, the system remains stable. Meanwhile, the autopilot heading control system with an unknown yaw rate and constraint state can benefit from the given design.

Extended state observer-based adaptive prescribed performance control for a class of nonlinear systems with full-state constraints and uncertainties

Extended state observer-based adaptive prescribed performance control for a class of nonlinear systems with full-state constraints and uncertainties

Adaptive prescribed performance control for hydraulic system with disturbance compensation

SummaryIn this article, an adaptive prescribed performance controller is developed for hydraulic system with uncertainties. An extraordinary feature is that better prescribed performance control can be achieved by compensating the uncertainties including parameter uncertainties and disturbances. For this reason, the transformation of system output error is realized by a prescribed performance function, which is employed to constrain the boundary of tracking error and convergence rate, then the tracking error of the original system with a priori prescribed performance can be realized by stabilizing the transformed system. Adaptive control is employed to solve the system parametric uncertainties; extended state observers are built to estimate the multiple disturbances. Based on the backstepping method, they are integrated into the design of the novel controller to guarantee prescribed tracking error performance. The stability analysis of the proposed controller is carried out via the Lyapunov theory. Finally, experimental results indicate good performance of the proposed algorithm.

Adaptive Prescribed Performance Control for Torsional Vibration of Cold Rolling Mill with Disturbance Uncertainties

Adaptive Prescribed Performance Control for Torsional Vibration of Cold Rolling Mill with Disturbance Uncertainties

Adaptive prescribed performance control for nonlinear pure-feedback systems: a scalarly virtual parameter adaptation approach

In this paper, an adaptive prescribed performance controller, consisting of a novel scalarly virtual parameter adaptation (SVPA) technique, is developed for a class of single-input and single-output high-order nonlinear pure-feedback systems in the presence of model uncertain yet locally Lipschitz nonlinearities. The objective of this work is to improve the transient and steady performance of pioneering prescribed performance control (PPC) by incorporating a single SVPA mechanism into the virtual and actual controllers, therein, the unknown yet bounded parameters are defined with respect to proper composite system and virtual functions, bringing the gap between pioneering PPC and linearly parameterized approximator-based PPC schemes (including neural networks, fuzzy logic systems, etc.), that is, the computational complexity of proposed method exceeds PPC with one level (caused by introduced single adaptive law) yet maintains low level with comparison to linearly parametrized approximator-based PPC. It is guaranteed that both virtual and actual tracking errors converge transiently to small residual sets characterized by prescribed performance functions and control parameters simultaneously and ultimately converge to zero, which is also proved by rigorously mathematical analysis using Lyapunov stability theorem. The closed-loop signals are kept globally ultimately uniformly bounded, and comparative simulation results are presented to demonstrate the effectiveness and advantages of the theoretical findings.

Event-triggered adaptive prescribed performance control of uncertain nonlinear systems with unknown control directions

The problem of event-triggered prescribed performance control for a class of uncertain nonlinear systems with unknown control directions and faults is investigated. Compared with the existing methods, a new set of error transformation functions is defined for the first time. Although no approximate structure is adopted, prescribed performance control (PPC) and event triggered control (ETC) are realized simultaneously for the nonlinear system considered in this paper for the first time. The proposed control scheme can guarantee that all closed-loop signals are bounded, and the tracking error, as well as all state errors, converges within the adjustable constraint functions. Finally, two simulation experiments verify the effectiveness of the proposed algorithm.

Event-triggered adaptive prescribed performance control for a class of pure-feedback stochastic nonlinear systems with input saturation constraints

Aiming at the tracking control problem of non-affine stochastic nonlinear systems with input saturation constraints, the event trigger control (ETC) based on Radial basic function neural networks (RBFNNs) and prescribed performance control (PPC) is considered. First, the mean value theorem is used to decouple the non-affine terms existing in the system. Second, the design process of PPC is reconstructed for a class of stochastic nonlinear systems, because the existence of stochastic disturbances has not been fully considered in previous literature on PPC, so that the system output is not to violate the set constraint bound by preset function. Finally, unlike the existing event triggering results, a special event triggering strategy is designed, which further takes into account the error between the preset function and the system output and the errors in all states of stochastic nonlinear systems, so it is expected that the amount of communications will be further reduced. Also, the proposed adaptive PPC scheme with event triggering mechanism can guarantee that all closed-loop signals are uniformly ultimately bounded (UUB) in probability within the appropriate compact sets. Finally, the effectiveness of the proposed method is verified by a practical example.

Observer-Based Adaptive NN Control for Uncertain Nonlinear Systems with Prescribed Performance and Fuzzy Dead-Zone Input

This paper addresses the issue of adaptive prescribed performance control for a category of uncertain nonlinear systems with fuzzy dead-zone input. Through employing the neural networks (NNs) and designing a state observer, the unknown functions and unmeasured system states are approximated, respectively. The problem of fuzzification caused from dead-zone input is handled via using the center-of-gravity theorem. Then, an integrated fuzzy controller is constructed by adopting integrated design approach. It is proved that the proposed integrated fuzzy controller can ensure that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a prescribed domain. Finally, some simulation results are shown to demonstrate feasibility of the presented method.

Robust adaptive fault‐tolerant tracking control for a class of high‐order nonlinear system with finite‐time prescribed performance

SummaryIn this article, an improved prescribed performance adaptive control strategy is developed to handle the output tracking control problem for a class of nonlinear high‐order systems with actuator faults. The actuator faults considered include the bias fault and gain fault models. A technique of adding a power integrator is utilized to deal with the controller design problem of high‐order system. With the help of backstepping technology and the classic adaptive control, an output tracking control scheme is proposed, which can guarantee that all signals of the closed‐loop system are bounded and the tracking error converges to a finite‐time predetermined region. Finally, the feasibility of the presented control method is tested through the simulation results.

Robust adaptive prescribed performance control for dynamic positioning of ships under unknown disturbances and input constraints

A robust adaptive prescribed performance control (RAPPC) law is proposed for dynamic positioning (DP) of ships subject to unknown time-varying disturbances with the control input magnitude and rate constraints. A simple error mapping function is first constructed to achieve the DP prescribed performance control design. Next, an adaptive disturbance observer is proposed to online estimate the unknown time-varying disturbances and an auxiliary dynamic system is introduced to addresses the effects of the input magnitude and rate constraints. Then, incorporating the above into the dynamic surface control method, the DP control law with prescribed performance is proposed. Theoretical analysis and simulation results prove that the proposed DP RAPPC law makes the ship's position and heading be maintained at the desired values with prescribed positioning performance.

Prescribed performance adaptive finite-time control for uncertain horizontal platform systems

This paper presents a new approach to the design of prescribed performance adaptive control for uncertain horizontal platform systems with the finite-time convergence. Following an appropriate performance function and error transformation, a new adaptive control law is proposed by using a novel integral non-singular terminal sliding mode surface. The proposed approach simultaneously guarantees that (i) the transient responses of the closed-loop system possess some advanced properties such as the existence of the prespecified lower bound of the convergence rate and of the pre-established upper bound of the maximum overshoot; and (ii) the finite-time convergence of the state trajectories/tracking errors to zero. The global stability and finite-time convergence are strictly analyzed. The proposed method is clarified and verified through two numerical simulation examples.