Prescribed Performance Control Problem Research Articles

Velocity-free event-triggered control for a class of uncertain axis-motion systems with prescribed performance

This paper investigates the fixed-time prescribed performance control problem for a class of axis-motion servo systems subject to the external disturbances and parameter uncertainties. To eliminate the requirement for velocity measurements in the control process, an auxiliary observer is first designed to reconstruct the velocity signal of the controlled plant. Subsequently, an error transformation procedure incorporating a prescribed performance index is integrated into the control system architecture. To overcome the limitations of periodic control design, a robust event-triggered controller is developed, ensuring that the dynamic error of the closed-loop system exhibits fixed-time convergence. Through rigorous theoretical analysis and proofs, it is demonstrated that the proposed event-triggered strategy guarantees Zeno-behavior-free operation. Finally, simulation results are presented to validate the effectiveness of the proposed control algorithm.

A low-complexity fixed-time prescribed performance control for uncertain full-vehicle active suspensions with hydraulic actuators

This paper addresses the low-complexity fixed-time prescribed performance control problem for uncertain full-vehicle active suspension systems. Different from existing results that ignore the dynamics of the actuator, this paper considers a hydraulic actuator in the controller design. To address the nonlinearities of hydraulic active suspension systems, a new low-complexity fixed-time prescribed performance control method is proposed. In this method, the function approximators (e.g. neural networks (NNs) and fuzzy systems (FSs)) are not needed, which means that the heavy computational costs are avoided. Furthermore, by developing a fixed-time performance function, the proposed method can ensure that the suspension motions converge to the prescribed range within a finite time. Based on the Lyapunov theorem and Extreme Value Theorem, the stability of the closed-loop suspension system is strictly proved. Finally, the comparative simulation results show that the proposed method effectively improves the attitude stability and ride comfort of the suspension system.

Neuroadaptive‐based fixed‐time control for robotic manipulators with uniform prescribed performance under unknown disturbance

AbstractAchieving faster convergence, smaller transient overshoots, and higher steady‐state tracking accuracy is essential to improve the efficiency, robustness, and applicability of robotic manipulators. This article introduces an innovative adaptive fixed‐time uniform prescribed performance controller for the manipulator facing model uncertainties and unknown disturbances. Initially, by designing a modified prescribed performance function inspired by variable superposition, this study redefines the unified prescribed performance control problem into a simplified parameter selection problem. This approach allows for the incorporation of varied performance metrics within a singular control scheme, addressing both transient and steady‐state performances concurrently without shifting control frameworks. Then, to alleviate computational demands, an adaptive neural network employing a single‐parameter weight update technique compensates for uncertainties of the manipulator dynamic model. Additionally, a disturbance observer is designed to mitigate the impact of non‐parametric disturbances. Moreover, integrating fixed‐time theory with the Lyapunov stability analysis method guarantees the convergence of all error signals to a near‐zero compact neighborhood at a fixed time. Finally, the advantages and comprehensive performance of the proposed method are confirmed by numerical simulations and real‐world experiments.

Nonlinear prescribed performance sliding mode control of hypersonic vehicles

SummaryThis paper addresses the adaptive saturation prescribed performance control problem for air‐breathing hypersonic vehicles with parameter uncertainties and unknown external disturbances. First of all, different from the traditional performance function, a novel class of performance functions is presented without the initial state information, which does not require to reset parameters even if the initial velocity and altitude change. To ensure the successful design of the velocity controller and altitude controller, the constrained errors are transformed into the unconstrained errors by the projection technique. Secondly, the adaptive neural network and the sliding mode control techniques are combined to design the adaptive neural network sliding mode controllers, which guarantee that the velocity and altitude tracking errors can respectively approach the predetermined regions within the identical preset finite time. Finally, the effectiveness of the designed controllers is verified by an example with comparisons.

Optimized Adaptive Fuzzy Security Control of Nonlinear Systems With Prescribed Tracking Performance.

This article studies the optimized fuzzy prescribed performance control problem for nonlinear nonstrict-feedback systems under denial-of-service (DoS) attacks. A fuzzy estimator is delicately designed to model the immeasurable system states in the presence of DoS attacks. To achieve the preset tracking performance, a simper prescribed performance error transformation is constructed considering the characteristics of DoS attacks, which helps obtain a novel Hamilton-Jacobi-Bellman equation to derive the optimized prescribed performance controller. Furthermore, the fuzzy-logic system, combined with the reinforcement learning (RL) technique, is employed to approximate the unknown nonlinearity existing in the prescribed performance controller design process. An optimized adaptive fuzzy security control law is then proposed for the considered nonlinear nonstrict-feedback systems subject to DoS attacks. Through the Lyapunov stability analysis, the tracking error is proved to approach the predefined region by the preset finite time, even in the presence of DoS attacks. Meanwhile, the consumed control resources are minimized due to the RL-based optimized algorithm. Finally, an actual example with comparisons verifies the effectiveness of the proposed control algorithm.

Fault-tolerant prescribed performance control of nonlinear systems with process faults and actuator failures

This paper investigates the fault-tolerant prescribed performance control problem for a class of multiple-input single-output unknown nonlinear systems subject to process faults and actuator failures. In contrast to the related works, we consider a general class of nonlinear systems with both multiplicative nonlinearities and additive nonlinearities corrupted by the process faults; only the boundedness of the process faults and the continuity of the nonlinear functions are required, without the explicit or fixed structures of the fault functions. To conquer this problem, a less-demanding and low-complexity fault-tolerant prescribed performance control approach is proposed. The controller is independent of the specific information of faults or the system model and does not invoke fault diagnosis or neural/fuzzy approximation to acquire such knowledge. It achieves the reference tracking with the predefined rate and accuracy. A comparative simulation on a single-link robot is conducted to illustrate the effectiveness and superiority of the proposed approach.

Adaptive decentralized prescribed performance control for a class of large‐scale stochastic nonlinear systems subject to input saturation and full state constraints

SummaryThis paper focuses on an adaptive decentralized prescribed performance control problem for a class of large‐scale stochastic nonlinear systems with asymmetric input saturation and full state constraints. Firstly, the obstacle of input saturation is overcome by introducing the Gaussian error functions. Secondly, the transient performance of the system output is realized by introducing the asymmetric error transfer functions. Thirdly, the full state constraints are considered in the backstepping control process, and the boundary of state constraints is ensured by constructing barrier Lyapunov functions. Then, the multidimensional Taylor network is employed to approximate the unknown nonlinearity, and an adaptive decentralized controller is designed. Finally, it is shown that the proposed control strategy can ensure that the closed‐loop system is semi‐global ultimately uniformly bounded in probability, and the tracking error of the system can be kept within an adjustable neighborhood of the origin. Two simulation examples are provided to illustrate the feasibility of the proposed control strategy.

Adaptive neural network prescribed performance control for dual switching nonlinear time-delay system

This paper investigates the adaptive neural network prescribed performance control problem for a class of dual switching nonlinear systems with time-delay. By using the approximation of neural networks (NNs), an adaptive controller is designed to achieve tracking performance. Another research point of this paper is tracking performance constraints which can solve the performance degradation in practical systems. Therefore, an adaptive NNs output feedback tracking scheme is studied by combining the prescribed performance control (PPC) and backstepping method. With the designed controller and the switching rule, all signals of the closed-loop system are bounded, and the tracking performance satisfies the prescribed performance.

Feasibility Conditions-Free Prescribed Performance Decentralized Fault-Tolerant Neural Control of Constrained Large-Scale Systems

This article investigates the command filter-based decentralized prescribed performance adaptive fault-tolerant compensation control strategy for uncertain nonlinear large-scale systems subject to asymmetric time-varying full-state constraints. Via integrating the performance function with command filter-based backstepping technique, the prescribed performance control problem is addressed, under which the complexity of controller design is reduced. Under the prescribed performance control framework, the nonlinear transformed function is constructed so as to ensure that the asymmetric time-varying full-state constraints free from feasibility conditions imposed on virtual control signals are not violated. Besides, the effect of infinite number of time-varying actuator faults is compensated with the aid of projection adaption design. Furthermore, based on the piecewise Lyapunov function analysis, it is rigorously testified that entire involved signals are bounded, desired constraints are not breached and tracking errors within the predefined domains. Finally, the effective performances of the developed control algorithm are confirmed by some simulation results.

Finite-Time Fault-Tolerant Prescribed Performance Control of Connected Vehicles With Actuator Saturation

This paper investigates the prescribed performance control problem for a vehicular platoon (i.e., a group of vehicles that travels in close proximity to one another, nose-to-tail, at highway speeds) simultaneously considering actuator faults and saturation. In the first case, a Gaussian error function (GEF) is applied to replace the nonsmooth actuator saturation of each vehicle in a smooth way. Then, a finite-time prescribed performance function (FNPPF) is proposed, which guarantees the tracking error of the platoon system converges to a predetermined region in a defined time. Subsequently, by combing the fuzzy-logic system (FLS) and parameter learning algorithm, an adaptive control scheme is developed in the context of sliding mode control, which guarantees all signals in the closed-loop system are practically finite-time stable. Finally, numerical simulations are carried out for a six-vehicle platoon to show the effectiveness of the proposed algorithm.

Prescribed Performance Control for Multiagent Systems via Fuzzy Adaptive Event-Triggered Strategy

This article discusses the prescribed performance control problem for multiagent systems involving the state triggering and the controller output triggering simultaneously. To successfully apply the backstepping technique in the event-triggered control design, the virtual control signal is constructed by the original system state. Compared with the existing results on the prescribed performance, a new barrier Lyapunov function is developed with considering the characteristics of multiagent systems, and a fuzzy adaptive event-triggered control protocol is proposed by the backstepping procedure. It guarantees that the consensus tracking error converges to a predefined region of the origin in a preset finite time. At the same time, all other closed-loop signals remain bounded without the Zeno behavior. Finally, a simulation example confirms the availability of the developed control scheme with a comparison.

Adaptive neural prescribed performance control for switched pure-feedback non-linear systems with input quantization

Purpose This paper aims to investigate an adaptive prescribed performance control problem for switched pure-feedback non-linear systems with input quantization. Design/methodology/approach By using the semi-bounded continuous condition of non-affine functions, the controllability of the system can be guaranteed. Then, a constraint variable method is introduced to ensure that the tracking error satisfies the prescribed performance requirements. Meanwhile, to avoid the design difficulties caused by the input quantization, a non-linear decomposition method is adopted. Finally, the feasibility of the proposed control scheme is verified by a numerical simulation example. Findings Based on neural networks and prescribed performance control method, an adaptive neural control strategy for switched pure-feedback non-linear systems is proposed. Originality/value The complex deduction and non-differentiable problems of traditional prescribed performance control methods can be solved by using the proposed error transformation approach. Besides, to obtain more general results, the restrictive differentiability assumption on non-affine functions is removed.

Prescribed Performance Attitude Stabilization of a Rigid Body Under Physical Limitations

This article investigates the prescribed performance control problem associated with attitude stabilization of a rigid body, considering angular velocity constraint, actuator faults, and input saturation. The desired performance specifications in transient and steady-state phases including convergence speed, overshoot, and steady-state value for attitude variable are also provided. To this end, the prescribed performance control methodology is combined with backstepping-based barrier Lyapunov function so as to develop a controller with simple structure compared to the existing constrained controls. The main idea behind the control design is to remove partial differential and complex function terms to considerably decrease complexity of the proposed controller. Moreover, a hyperbolic tangent function and an auxiliary system are employed to develop the constrained virtual rotation velocity control and to consider input saturation. The simulation results carried out on a rigid spacecraft confirm efficiency and success of the proposed constrained attitude control method.

Event-Triggered Adaptive Asymptotic Tracking Control of Uncertain MIMO Nonlinear Systems With Actuator Faults.

In this article, an adaptive event-triggered fault-tolerant asymptotic tracking control problem guaranteeing prescribed performance is addressed for a class of block-triangular multi-input and multioutput uncertain nonlinear systems with unknown nonlinearities, unknown control directions, and actuator faults. Through a systematic co-design of the adaptive control law and the event-triggered mechanism, including fixed and relative threshold strategies, a control scheme with low structure and calculation complexity is designed to conserve system communication and computation resources. In this design, the output asymptotic tracking is achieved. The Nussbaum gain technique is incorporated to overcome unknown control directions with a new adaptive law, and a type of barrier Lyapunov function is adopted to handle the prescribed performance control problem, which contributes to a novel control law with strong robustness. The robust controller can address the uncertainties and couplings derived from the system structure, actuator faults, and event-triggered rules, without using approximating structures or compensators. Besides, the explosion of complexity is avoided. It is proved that all signals of the closed-loop system remain bounded, and system tracking errors asymptotically approach 0 with the prescribed performance, while the Zeno behavior is prevented. Finally, the effectiveness of the proposed control scheme is evaluated via an application example of the half-car active suspension system.

Velocity-Free Adaptation Compensation Control of MEMS with Prescribed Performance

This study investigates the prescribed performance control problem for microelectro-mechanical system (MEMS) gyroscope subject to system parameters’ uncertainty. A finite-time observer is firstly designed to estimate the unmeasurable velocity state of MEMS gyroscope. Subsequently, a coordinate transformation with the performance function is introduced into an error system which will be kept bounded to ensure expected dynamic and steady-state responses. Based on the proposed finite time-velocity reconstruction system, the adaptive backstepping design procedure is further designed to deal with the lumped uncertainty term. Furthermore, when considering actuator saturation, an improved control strategy is developed with a nonlinear input updating law, and meanwhile, it is proved that the system error converges to a preset compact set around zero in a preassigned time. Simulation results show the effectiveness and reliability of the proposed methods.

Three-dimensional prescribed performance sliding mode guidance law for intercepting maneuvering target

This article describes three-dimensional sliding mode guidance laws with prescribed performance. The proposed guidance laws can ensure that the line of sight (LOS) angle converges according to the prescribed performance, and the convergence rate, the steady-state error and the maximum overshoot can be preset in advance. By combining the LOS tracking error with the performance constraint function, a new error variable function is designed, and then the prescribed performance control problem is transformed into that of the boundedness of the error variable function. The key concept in this approach is to design a new sliding mode surface to ensure that the error variable function is bounded, so as to ensure that the system state converges according to the prescribed performance. Additionally, this article discusses the problem whereby the upper bound of the aggregate uncertainty, including the target information, is unavailable. An adaptive guidance law is presented for this scenario. Finally, simulations comparisons are conducted with other forms of guidance laws. Simulation results show that the guidance laws proposed in this article achieve effective performance.

Learning-based adaptive fault tolerant control for hypersonic flight vehicles with abrupt actuator faults and finite time prescribed tracking performance

This paper addresses the finite time prescribed performance control problem for hypersonic flight vehicle systems with abrupt actuator faults and time-varying uncertainties. The considered actuator faults contains abrupt gain faults and saltatorial bias faults, and the unknown discontinuous variations of the fault parameters are permitted. In virtue of the finite time performance functions and error transformation, the predefined tracking performance including the convergence time, the tracking error and the overshoot for the velocity and altitude can be ensured. By adaptively estimating the lower bonds of the gain faults and the upper bounds of the bias faults, the unwanted effects of the abruptly faulty actuators can be circumvented. Meanwhile, for the purpose of compensating the unknown nonlinearities, the learning-based control strategy has been employed. Finally, a number of simulation results on the hypersonic flight vehicles are conducted to demonstrate the validity of the proposed approach.

Adaptive Fuzzy Prescribed Performance Control of Nontriangular Structure Nonlinear Systems

In this article, a new n -step fuzzy adaptive output tracking prescribed performance control problem is investigated for a class of nontriangular structure nonlinear systems. In the control design process, the mean value theorem is used to separate the virtual state variables needed for the control design, and the implicit function theorem is exploited to assert the existence of the desired continuous control. The fuzzy logic systems are used to identify the unknown nonlinear functions and ideal controller, respectively. By constructing a novel iterative Lyapunov function, a new n -step adaptive backstepping control design algorithm is established. The prominent characteristics of the proposed adaptive fuzzy backstepping control design algorithm are as follows: one is that it can ensure the closed-loop control system is the semiglobally uniformly ultimately bounded and the tracking error can converge within the prescribed performance bounds. The other is that it solves the controller design problem for the nontriangular nonlinear systems that the previous adaptive backstepping design techniques cannot deal with. Two examples are provided to show the effectiveness of the presented control method.

Prescribed performance fixed-time recurrent neural network control for uncertain nonlinear systems

This paper investigates fixed-time prescribed performance control problem for uncertain strict-feedback nonlinear systems with unknown dead zone. First, a novel prescribed performance function (PPF) is proposed and a coordinate transformation is employed to transform the prescribed performance constrained system into an unconstrained one. Next, recurrent neural network is introduced to estimate the uncertain dynamics and fixed-time differentiator is utilized to obtain the derivative of virtual control. Then, a fixed-time dynamic surface control is developed to deal with dead zone and guarantee the convergence of the tracking error within a fixed time. Lyapunov stability analysis shows that the presented control scheme can achieve the fixed-time convergence of the error variables, while the other closed-loop system signals are bounded. Finally, numerical simulation validates the effectiveness of the presented control scheme.

Event-Triggered Adaptive Control for Prescribed Performance Tracking of Constrained Uncertain Nonlinear Systems

This paper studies the prescribed performance tracking control problem for a pure-feedback nonlinear system with full-state constraints. By incorporating the asymmetric barrier Lyapunov functions 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. The numerical simulations are provided to illustrate the performances of the designed adaptive controller and the event-triggered adaptive controller.