Prescribed Performance Control Scheme Research Articles

Robust adaptive prescribed performance control for nonlinear systems with arbitrary initial states

The initial state of nonlinear MIMO strict feedback systems is often unpredictable and random, and existing prescribed performance control (PPC) techniques can only guarantee system output constraints within a fixed initial value performance boundary. In this paper, an adaptive PPC method tailored for nonlinear systems was introduced, enabling the system stable tracking regardless of the arbitrary initial states. To guarantee that the tracking error consistently meets the prescribed performance boundary(PPB) envelope, we introduce a nonlinear mapping between the initial value of the prescribed performance functions(PPFs) and the system tracking errors, resulting in an asymmetric time-varying performance boundary. Building upon this foundation, an adaptive PPC scheme is proposed under the backstepping framework, integrated with a nonlinear disturbance observer (NDO). This method ensures that the tracking error remains within the desired PPB, regardless of external disturbances or system initial states. To prevent ‘complexity explosion’, a dynamic surface control (DSC) technology is employed to filter the virtual control signals of each subsystem. Furthermore, the ultimate uniform boundedness of the closed-loop signal has been demonstrated, and a practical flight vehicles roll control case was introduced to validate the efficacy of the proposed method.

Fixed-time anti-disturbance control for nonlinear turbofan engine with impulsive prescribed performance

To analyze the robust control problem of turbofan engine within a large flight envelope, a fixed-time prescribed performance control scheme is proposed for the nonlinear turbofan engine in presence of unknown disturbances and possibly discontinuous reference signals. Firstly, the equilibrium manifold expansion (EME) modeling method is adopted for the turbofan engine to construct an affine nonlinear model. Then, considering the possibly discontinuous reference signals, a novel fixed-time prescribed performance function (FxTPPF) with impulsive characteristic is presented to successfully deal with the singularity problem caused by its discontinuity situation. In what follows, a fixed-time nonlinear disturbance observer (FxTNDO) is developed to realize fast estimation of disturbances within fixed time. According to the transformed error system and disturbance estimations, a fixed-time anti-disturbance composite controller is further developed. By borrowing Lyapunov stability theory, the boundedness of all error signals in the impulsive closed-loop system is proved. Finally, simulation results indicate that this control scheme can ensure rotor speeds effectively to track the desired commands within a predefined time after the appearance of a discontinuity and the tracking errors are limited to the performance bound all along.

Nonlinear disturbance observer-based finite-time prescribed performance control for MSVs with input saturation

ABSTRACT A finite-time prescribed performance control scheme based on an improved nonlinear disturbance observer is proposed for tracking the trajectory of marine surface vessels (MSVs) under the disturbance of the marine environment. The objective of this paper is to design a nonlinear disturbance observer based on state estimation error feedback that accurately estimates and compensates for the unknown disturbance problem. An adaptive law is applied to estimate the upper bound of its error, removing the requirement of a priori knowledge of the unknown lumped disturbance upper bound. This paper also introduces a non-logarithmic performance function in order to efficiently solve the problem of considering both transient and steady state MSVs performance simultaneously. In addition, the adaptive dynamic system is introduced to overcome the adverse effects caused by nonlinear saturation factors for the input-constrained problem. With this control strategy, the system output error converges to a pre-defined region within a finite amount of time and meets the prescribed performance requirements. Finally, simulation and comparison verify the control scheme's effectiveness and superiority.

Non-Fragile Prescribed Performance Control of Robotic System without Function Approximation

In order to address the fragility issues associated with the current prescribed performance control (PPC) strategy and ensure both transient and steady-state performance of the tracking error, a non-fragility prescribed performance control scheme is proposed. A non-fragile prescribed performance control method for robotic systems with model uncertainties and unknown disturbances is developed. This method not only addresses the inherent vulnerability defects of the existing prescribed performance control but also effectively reduces the computational complexity of the controller. Firstly, addressing the fragility issues of existing PPC, a new non-fragile prescribed performance control strategy is proposed. To address the fragile issue with the current PPC, the shift function is employed to handle the tracking error. Based on the non-fragile PPC mentioned above, a new prescribed performance controller is designed without the requirement for approximation or estimation. This effectively reduces the complexity of controller design. At last, the feasibility of achieving non-fragile prescribed performance is verified through stability analysis, and the superiority of the designed controller is confirmed through simulation comparisons. The results show that the designed controller effectively resolves the control singularity issue arising from the inherent limitations of the PPC.

Adaptive prescribed performance based on recursive nonsingular terminal sliding mode control for quad-rotor systems under uncertainty and disturbance: Real-time validation

In this paper, at the aim of the fast trajectory-following control of the Unmanned Aerial Vehicle (UAV) systems subject to uncertainty and disturbance, the adaptive prescribed performance control based recursive nonsingular terminal sliding mode control is suggested. Afterward, for the fast trajectory-following control of the uncertain and perturbed quad-rotor system, a recursive nonsingular terminal sliding mode strategy is recommended. Since the better transient and steady-state response of the sliding mode surface is of the utmost importance in the design of the controller, the prescribed performance control scheme is proposed in which the transformed prescribed form of the previously proposed recursive nonsingular terminal sliding surface is obtained to prove that the recursive nonsingular terminal sliding surface can converge to a preset region. Whereas unknown bounded uncertainty and disturbance always exist in the UAV system's dynamical model which decreases its performance and efficiency, the adaptive mechanism is applied to approximate uncertain bounds of uncertainty and disturbance to advance the implementation of the UAV system. Later, quick reachability of the prescribed form switching surface is demonstrated using Lyapunov concept. Ultimately, simulation results using MATLAB/Simulink over a quad-rotor system and real-time simulation using the Speedgoat Real-Time Target Machine platform are conducted to validate the feasibility and performance of the proposed method.

A connectivity-preserving performance guarantee for cooperative control method with improved switching event-triggered mechanism

An adaptive tracking control scheme is designed for multiagent systems. To ensure a certain communication range between agents, a connectivity-preserving performance guarantee mechanism is proposed, which increases the consideration of the connection information between agents and the leader to further improve the cooperativity. Meanwhile, different from traditional constraint error methods, a boundary-based prescribed performance control scheme is constructed, which has the characteristic of getting the variable preset boundary. Furthermore, the improved switching event-triggered mechanism is developed, and the threshold parameters can be adjusted in real-time to adaptively change the update frequency of the controller. All signals are bounded in the closed-loop system. Finally, some simulation results affirm the validity of the control scheme.

Adaptive prescribed performance control for wave equations with dynamic boundary and multiple parametric uncertainties

<abstract><p>In modern engineering, the dynamics of many practical problems can be described by hyperbolic distributed parameter systems. This paper is devoted to the adaptive prescribed performance control for a class of typical uncertain hyperbolic distributed parameter systems, since uncertainties are inevitable in practice. The systems in question simultaneously have unknown in-domain spatially varying damping coefficient and unknown boundary constant damping coefficient. Moreover, dynamic boundary condition is considered in the present paper. These characteristics make the control problem in the paper essentially different from those in the related works. To solve the problem, using adaptive technique based projection operator, backstepping method developed for ODEs and Lyapunov stability theories, a powerful adaptive prescribed performance control scheme is proposed to successfully guarantee that all states of the resulting closed-loop system are bounded, furthermore, the original system state converges to an arbitrary prescribed small neighborhood of the origin. Compared with the existing results, the developed control schemes can not only effectively handle the serious uncertainties, but also overcome the technical difficulties in the infinite-dimensional backstepping control design method caused by the dynamic boundary condition and guarantee prescribed performance.</p></abstract>

Adaptive Fuzzy Prescribed Performance Output-Feedback Cooperative Control for Uncertain Nonlinear Multiagent Systems

The paper considers the prescribed performance output-feedback cooperative control of multi-agent systems with nonparametric uncertainties. Scale and performance functions are proposed to construct a barrier function, based on which the adaptive prescribed performance control scheme is devel- oped. Therein, the fuzzy observers are employed to estimate the unavailable states. The proposed scheme has the following characteristics: 1) the tracking errors are always limited to a specified boundary. 2) the tracking error converges to a specified accuracy within a given time, and the settling time and tracking accuracy are determined only by the user and no longer depend on the initial conditions. 3) the distributed fuzzy controller design uses only the output information from agent and its neighbor. The effectiveness and practicality of the proposed method are demonstrated by two simulation examples.

Finite-time adaptive neural prescribed tracking control of stochastic nonlinear systems with multiple power terms and unknown time-varying powers

This research addresses the problem of finite-time tracking error constrained control for a class of non-strict stochastic nonlinear systems with unknown time-varying powers and multiple power terms. Based on the conversion from constrained tracking error to an unconstrained signal with the same effect, by adopting the backstepping technique together with adaptive neural network control, a controller with upper and lower time-varying power bounds is designed to meet the prescribed performance control scheme in finite-time. Finally, two simulation examples are shown to verify the effectiveness of the commendatory control method.

Robust Trajectory Tracking Control for Constrained Small Fixed-Wing Aerial Vehicles with Adaptive Prescribed Performance

A novel approximation-free adaptive prescribed performance control scheme for the longitudinal motion tracking of input and state constrained small fixed-wing UAVs is designed in this work. The proposed controller employs the adaptive prescribed performance technique to impose output performance specifications in accordance with actuation limitations regarding the amplitude and the rate of the control signal. Furthermore, state constraints are introduced to ensure the proper operation of the closed-loop system. The adoption of PPC methodology results in a low complexity control algorithm with easy gain selection which facilitates its practical implementation. Finally, a comprehensive simulation study as well as comparative simulation paradigms on an Aerosonde model clarifies and verifies the superiority and the effectiveness of the proposed controller to control the longitudinal motion of UAVs in the presence of wind gusts.

Output regulation problem with prescribed performance for nonlinear lower-triangular system

ABSTRACT This paper addresses the output regulation problem with prescribed performance for nonlinear lower-triangular systems. To achieve the transient prescribed performance, the output transformation technique and barrier Lyapunov function technique are introduced to solve the output regulation problem. The prescribed performance control scheme based on normal backstepping is constructed not only to restrict the output error of the closed-loop system keeping in a prescribed performance bound, but also to achieve that the output tracks a designed trajectory asymptotically. The effectiveness of the proposed method is illustrated by two simulation examples.

Barrier function-based nonsingular prescribed performance terminal sliding mode tracker for under-actuated nonlinear systems: Experimental study

In this paper, an adaptive concave barrier function scheme coupled with the non-singular terminal sliding mode control technique is proposed for finite-time tracking control of the under-actuated nonlinear system in the existence of model uncertainty, external disturbance and input saturation. Firstly, the dynamical equation of under-actuated nonlinear n-order system is expressed under model uncertainty, external disturbance and input saturation. Secondly, for the improvement of stability performance of the system in the existence of input saturation, a compensation system is designed to overcome the constraint on the control input. Afterward, the tracking errors between actual states of the system and differentiable reference signals are defined and the sliding surface based on the defined tracking errors is presented. Then, for gaining the better transient and steady-state performance of the closed-loop system, the prescribed performance control scheme is adopted. Based on this method, the transformed prescribed form of the previous determined sliding surface is obtained to ensure that the sliding surface can reach to a predefined region. Afterward, for assurance of the finite-time reachability of transformed sliding surface, the nonsingular terminal sliding surface is recommended. In addition, for the compensation of the model uncertainty and external disturbance existed in the system, the adaptive-based concave barrier function technique is used to estimate the unknown bounds of uncertainty and exterior disturbance. Finally, for demonstration of the proposed control method, the simulations and experimental implementation are done on the air levitation system.

Fixed-Time and Fault-Tolerant Path-Following Control for Autonomous Vehicles With Unknown Parameters Subject to Prescribed Performance

With the consideration of actuator faults, including the unknown steering mechanism misalignments and motor traction losses, this article presents a fixed-time control protocol to follow reference paths and velocities for autonomous ground vehicles (AGVs) with preset performance constraints. To provide sufficient large boundaries for the initial states, the hyperbolic tangent function is employed to predefine the constraints with respect to the path-following and velocity control performance. Based on the homeomorphic mapping and barrier Lyapunov theorem, the fixed-time prescribed performance control (PPC) objective-integrated fault-tolerant scheme can be achieved for the controlled AGV. In comparison to three different fixed-time controllers without the fault-tolerant or PPC scheme, the hardware-in-the-loop (HIL) test results demonstrate that the proposed control protocol can always provide superior control performance for the AGV under various maneuvering conditions.

Multivariable Finite-Time Composite Neural Control via Prescribed Performance for Error Norm

This work investigates finite-time tracking control for a multi-input–multi-output plant with multisource uncertainties. A multivariable finite-time prescribed performance control scheme is proposed, where the norm of the tracking error vector is constrained with a prescribed bound. Due to the positiveness of the norm of the error vector, a novel error transformation is given to transform the “constrained” problem into an equivalent “unconstrained” problem. Meanwhile, the composite neural adaptive law is established to attenuate the effect of multisource uncertainties. The parametric perturbations are counteracted by neural adaptive terms. Time-varying uncertain control gains and external disturbances in the multivariable systems are compensated by adaptively estimating their bounds and applying the Lyapunov control design. To tackle the practical tracking problem, the aforementioned method is integrated into a dynamic-surface-based backstepping framework. Additionally, the practical quaternion-based attitude tracking problem is addressed, in which a quaternion-based form of error-norm constraint is constructed to express the generality and scalability of our proposed.

Dual extended state observer–based prescribed performance control of output-constrained hydraulic-driven barrel pitching servo system

This research focuses on the position-tracking control of the output-constrained hydraulic-driven barrel pitching servo system with partial unknown states, strong nonlinearities, and huge model uncertainties. Based on the established nonlinear dynamic model of the hydraulic-driven barrel pitching servo system, a dual extended state observer–based prescribed performance dynamic surface control approach is proposed. The dual extended state observer is developed to simultaneously estimate the angular velocity, mismatched lumped uncertainty in the velocity dynamic channel, and matched lumped uncertainty in the pressure dynamic channel. A novel barrier Lyapunov function–inspired error transformation function contributes to the integration of the prescribed performance control into the backstepping controller and circumvents the complex logarithmic calculation caused by the traditional error transformation function. The prescribed performance control scheme restrains the tracking error within the constraint boundaries in the entire moving process. Dual uncertainty compensation is added to the prescribed performance control scheme to further improve the control performance of the hydraulic-driven barrel pitching servo system. The dynamic surface control technique is applied in the last step of the controller design to prevent the ‘differential explosion’ in the traditional backstepping controller. The theoretical stability and convergence of the proposed controller are proved in the sense of Lyapunov, and the practical effectiveness of the dual extended state observer–based prescribed performance dynamic surface control is verified via extensive comparative experiments.

Singularity-Avoidance Prescribed Performance Control for Spacecraft Attitude Tracking

The attitude tracking control problem with preassigned performance requirements has earned tremendous interest in recent years, and the Prescribed Performance Control (PPC) scheme is often adopted to tackle this problem. Nevertheless, traditional PPC schemes may suffer singularity problems when the expected state constraint is violated. This may cause a decrease in the control effect or even the unstable of the system. Motivated by this issue, this paper proposes a Singularity-Avoidance Prescribed Performance Control scheme (SAPPC) to deal with these problems, of which the core is a shear mapping-based error transformation procedure that globally transforms the original error state without singularity. Based on the presented non-singular error transformation, this paper presents a perspective to guarantee the satisfaction of given transient performance requirements by leading the state trajectory converging along a preassigned smooth trajectory called Reference Performance Function (RPF). Based on the concept of the RPF, this paper naturally adopts an error-defined-type state constraint, providing a time-varying constraint boundary and alleviating the potential over-control problem at the steady state. Further, in order to validate the proposed SAPPC scheme, a simple backstepping controller is developed by employing the predefined-time stability technique and the dynamic surface control technique. Finally, theoretical analysis and numerical simulation results are presented to validate the proposed control scheme's effectiveness and robustness.

Robust Adaptive Prescribed Performance Control for Unknown Nonlinear Systems With Input Amplitude and Rate Constraints

A novel approximation-free prescribed performance control scheme for unknown nonlinear systems with amplitude and rate saturation on the control input signal is designed in this letter. The proposed control strategy employs nested smooth saturation functions and introduces a reconciling relaxation of the performance constraints based on the actuator limitations. The straightforward gain selection along with the low complexity of the control scheme, simplifies the practical implementation of our algorithm. The adoption of the adaptive prescribed performance control technique ensures the desired trade-off between input and output constraints for any input-to-state stable (ISS) system. Inevitably, for generic systems, the boundedness properties are guaranteed only locally; thus, we provide a sufficient boundedness condition for all closed-loop signals. Finally, an illustrative simulation study is conducted to demonstrate the efficacy of the proposed approach.

Appointed-Time Control for Flexible Hypersonic Vehicles with Conditional Disturbance Negation

This paper investigates the anti-disturbance control design for flexible air-breathing hypersonic vehicles (FAHVs) with appointed-time prescribed tracking performances. The challenging issues include multisource disturbances, cross-coupling effects of the vehicle dynamics, and asymmetric amplitude and rate saturations. To address these issues, we propose an appointed-time prescribed performance control scheme for FAHVs via conditional disturbance negation technique. In contrast to existing disturbance rejection approaches, the proposed control scheme not only estimates the disturbances first in a fixed time, but also evaluates the estimated disturbances and selectively conducts compensation actions according to the insight of the FAHV dynamic characteristics. To further enhance convergence rate, the composite appointed-time prescribed performance controllers are designed for FAHVs via time-varying barrier Lyapunov function and nonsmooth backstepping technique, which ensure satisfactory transient response and steady-state performances. In addition, the asymmetric amplitude and rate saturation problem of actuators are dealt with by introducing unified approximation dynamics. It is rigorously proved that the practical appointed-time convergence of the tracking errors and the fixed-time convergence of all signals in the resultant FAHV closed-loop system can be achieved under the proposed control scheme. Finally, extensive comparative simulations are provided to demonstrate the feasibility and superiority of the proposed approach.

Hypersonic tracking control under actuator saturations via readjusting prescribed performance functions

Prescribed performance control (PPC) has been shown to be an effective tool in pursuing prescribed transient and steady-state specifications. Unfortunately, the existing PPC is incapable of handling the peaking of errors caused by actuator saturations, which is due to the short of the ability of readjusting the prescribed performance functions. In this article, we propose a novel PPC scheme, namely the readjusting-performance-function-based approach, for hypersonic flight vehicles subject to actuator saturations. A new sort of performance functions containing readjusting terms are developed to impose prescribed constraints on the velocity tracking error and the altitude tracking error. More specially, the prescribed performance functions can be adaptively readjusted to guarantee that tracking errors are always within them. This eliminates the singular problem that is usually encountered by traditional PPC. To deal with the actuator saturation problem, a novel compensated system (CS) is exploited for the velocity dynamics. Then, the CS is further extended to the altitude subsystem by reforming it as a high-order formulation. Besides the aforementioned baseline controllers, optimal control protocols are also addressed based on adaptive dynamic programming. Finally, comparison simulation results are given to verify the advantages.

Nonlinear Extended State Observer Based Prescribed Performance Control for Quadrotor UAV with Attitude and Input Saturation Constraints

In this paper, a prescribed performance control scheme of the quadrotor unmanned aerial vehicle (UAV) under attitude and input saturation constraints is introduced. According to the underactuated feature, the quadrotor UAV system can be decomposed into an underactuated subsystem and a fully actuated subsystem. With the feedback linearization technique, a single nonlinear extended state observer (ESO) is proposed, and multiple observations are utilized to estimate both matched and unmatched disturbances, which not only can obtain a uniform convergence, but also reduces the complexity of the observer’s parameter adjustment. To improve system stability, an input saturation algorithm for each single rotor is introduced to modify the final control output. In addition, the limited attitude for the quadrotor UAV is also considered as a saturation constraint in the control scheme with a compensation auxiliary system. On this basis, dynamic surface control (DSC) with prescribed performance is adopted to guarantee the bounded convergence and steady-state error. All state errors of the closed-loop system are proven to be uniformly bounded using the Lyapunov theory, and the simulation results are given to demonstrate the stability, effectiveness, and superiority of the proposed control strategies at last.