Prescribed Performance Control Research Articles

Zero‐sum game‐based H∞ optimal finite‐time prescribed performance control for nonlinear multiagent systems with actuator faults

AbstractThis article proposes an optimal leader‐follower consensus control protocol with finite‐time prescribed performance for nonlinear multiagent systems suffering from the actuator fault based on the zero‐sum game framework. First, to guarantee the specified performance of the system within a finite time frame, a novel error transformation function (ETF) is constructed. The ETF proposed in this paper can adjust the mapping range of error transformation to achieve better error convergence performance, thereby enhancing the flexibility of the controller design. Then, to compensate for the negative impact of actuator fault, an error‐related item is separated from the optimal performance index function to design an online fault estimator, which can obtain a better error estimation accuracy. Furthermore, to lessen the need for difficult‐to‐verify persistent excitation signal in adaptive dynamic programming algorithm, both historical and real‐time data are applied to adjust the updating law of neural network weight. Moreover, it demonstrates that the signals within the closed‐loop system are bounded and the expected finite‐time prescribed performance can be ensured in the presence of faults. Finally, a numerical example of multiple single‐link robots manipulator system is executed to validate the efficacy of the developed scheme.

Event-based appointed-time cooperative formation for linear multiagent systems with actuator saturation

This paper considers the time-varying formation (TVF) tracking issue of a class of multiagent systems (MASs) with input saturation. Meanwhile, the prescribed transient and steady-state performance of MASs is guaranteed. Compared to the existing prescribed performance control (PPC) approaches, the maximum convergence time of the designed algorithm is preassigned. To save network resources, an event-based protocol is introduced to achieve lower information communication frequency, where Zeno behavior is excluded. Furthermore, an improved control strategy is employed where an auxiliary system is designed to improve the performance under actuator saturation. According to Lyapunov stability theory, the expected practical TVF tracking control problem is solved for the MASs. Finally, the effectiveness of the designed schemes is demonstrated by the simulation examples.

Pneumatic servo position control optimization using adaptive-domain prescribed performance control with evolutionary mating algorithm

Pneumatic servo systems face challenges such as friction, compressibility, and nonlinear dynamics, necessitating advanced control techniques. Research suggests model-based, model-free, hybrid, and optimization-based methods have their strengths. Therefore, this study presents an optimal control strategy using Adaptive Domain Prescribed Performance Control (AD-PPC) cascaded with PID and optimized using the Evolutionary Mating Algorithm (EMA) for a pneumatic servo system (PSS). The goal is to achieve faster transient control and stable rod-piston positioning with minimal friction through the hysteresis phenomenon of the targeted proportional valve-controlled double-acting pneumatic cylinder (PPVDC) representing the PSS. The novel EMA optimizes the cascaded controller based on the tracking error as its objective function. Simulation studies verify the proposed AD-PPC-PID controller with the PPVDC model plant, iteratively optimized by the EMA. The analytical study compares this setup's control system and optimization model with the same control system model using alternative optimization methods. The testing employs step and multi-step signals for PPVDC's rod-piston position input. Results show that the EMA-tuned AD-PPC-PID outperforms AD-PPC-PID controller with other optimizers. For both input trajectory tests, EMA-tuned AD-PPC-PID shows faster response times, with average improvements of 30 % in settling times and 70 % in tracking performance metrics compared to other optimizers, making it robust for nonlinear system applications like PPVDC rod-piston positioning.

Prescribed Performance Fault-Tolerant Attitude Tracking Control for UAV with Actuator Faults

This paper proposes a prescribed performance fault-tolerant control based on a fixed-time extended state observer (FXTESO) for a carrier-based unmanned aerial vehicle (UAV). First, the attitude motion model of the UAV is introduced. Secondly, the proposed FXTESO is designed to estimate the total disturbances including coupling, actuator faults and external disturbances. By using the barrier Lyapunov function (BLF), it is proved that under prescribed performance control (PPC), the attitude tracking error is stable within the prescribed range. The simulation results for tracking the desired attitude angle show that the average overshoot and stabilization time of PPC-FXTESO is 0.00455rad and 6.2s. Comparatively, the average overshoots of BSC-ESO and BSC-FTESO are 0.035rad and 0.027rad, with stabilization times of 14.97s and 12.56s, respectively. Therefore, the control scheme proposed in this paper outperforms other control schemes.

Decentralized adaptive fault‐tolerant control for interconnected nonlinear time‐delay systems with uniform prescribed performance

AbstractIn this article, the prescribed performance tracking control problem is studied for interconnected nonlinear time‐delay systems with sensor and actuator faults. Based on the dynamic gain technique and the backstepping control method, a delay‐independent adaptive state feedback controller is designed. Besides, by embedding a smooth function into the controller, the unknown external disturbances, sensor and actuator faults are successfully compensated. Furthermore, we can deal with the asymmetric prescribed performance control with semi‐global or global requirements uniformly by selecting the initial value of the the scaling function. Based on Lyapunov theory, it is proved that the system output of each subsystem can closely track the desired signal and the boundedness of all signals in the closed‐loop systems can be ensured under the proposed control method. Finally, the effectiveness of the proposed control strategy is proved by two simulation examples.

Fixed-time observation and predefined performance regulation for oxygen excess ratio of vehicular fuel cells under input saturation

The efficiency, health and lifetime of vehicle-mounted fuel cells highly rely on the oxygen excess ratio (OER). Faced with urgent research limitations, this article tackles the estimation and regulation for immeasurable OER, while suppressing the influences of dramatic stack current, uncertain system information, actuator saturation and performance constraint. Restricted by high cost and measurement difficulty, two fixed-time adaptive observers are proposed to rebuild unavailable OER and lumped disturbance respectively, which eliminate the dependence of estimation time on initial states and alleviate the peaking issue. Further, a fixed-time prescribed performance controller is developed to elevate the tracking performance for the estimated OER, in which the overshoot, regulation time and convergence region can be quantitatively constrained, regardless of initial conditions. Specially, to exclude undesired control singularity, an improved performance function is established to automatically adjust the predefined constraint boundaries depending on the captured variations of stack current and anti-saturation auxiliary signal. The hardware-in-loop validation results under custom working conditions and a typical vehicle driving cycle exhibit that the estimation and regulation of OER reach stability within 0.2s and 1s respectively, besides, the maximum absolute errors in observing and controlling the OER are limited to around 0.6 and 0.8 respectively, with great adaptability to different scenarios.

Robust Fixed-Time Fault-Tolerant Control for USV with Prescribed Tracking Performance

The unmanned surface vessel (USV) is an emerging marine tool with its advantages of automation and intelligence in recent years; the good trajectory tracking performance is an important capability. This paper proposes a novel prescribed performance fixed-time fault-tolerant control scheme for an USV with model parameter uncertainties, unknown external disturbances, and actuator faults, based on an improved fixed-time disturbances observer. Firstly, the proposed observer can not only accurately and quickly estimate and compensate the lumped nonlinearity, including actuator faults, but also reduce the chattering phenomenon by introducing the hyperbolic tangent function. Then, under the framework of prescribed performance control, a prescribed performance fault-tolerant controller is designed based on a nonsingular fixed-time sliding mode surface, which guarantees the transient and steady-state performance of an USV under actuator faults and meets the prescribed tracking performance requirements. In addition, it is proved that the closed-loop control system has fixed-time stability according to Lyapunov’s theory. Finally, upon conducting numerical simulations and comparing the proposed control scheme with the SMC and the finite-time NFTSMC scheme, it is evident that the absolute error tracking performance index of the proposed control scheme is significantly lower, thus indicating its superior accuracy.

Identification and Control of Flexible Joint Robots Based on a Composite-Learning Optimal Bounded Ellipsoid Algorithm and Prescribe Performance Control Technique

This paper presents an indirect adaptive neural network (NN) control algorithm tailored for flexible joint robots (FJRs), aimed at achieving desired transient and steady-state performance. To simplify the controller design process, the original higher-order system is decomposed into two lower-order subsystems using the singular perturbation technique (SPT). NNs are then employed to reconstruct the aggregated uncertainties. An adaptive prescribed performance control (PPC) strategy and a continuous terminal sliding mode control strategy are introduced for the reduced slow subsystem and fast subsystem, respectively, to guarantee a specified convergence speed and steady-state accuracy for the closed-loop system. Additionally, a composite-learning optimal bounded ellipsoid algorithm (OBE)-based identification scheme is proposed to update the NN weights, where the tracking errors of the reduced slow and fast subsystems are integrated into the learning algorithm to enhance the identification and tracking performance. The stability of the closed-loop system is rigorously established using the Lyapunov approach. Simulations demonstrate the effectiveness of the proposed identification and control schemes.

Adaptive adjustable performance function based direct prescribed performance control for spacecraft flying around mission

The control for spacecraft flying around mission is investigated in this paper based on the prescribed performance control (PPC). Considering the challenges in the traditional PPC framework, we design an adaptive adjustable performance function, which can self-adjust the performance requirement according to the saturation of the control input. Besides, a combined switching controller is designed and the controller behaves as a PPC in the convergence stage, and gradually switches to a nonlinear controller after entering a steady state, which can avoid the over-control problem caused by high-gain PPC after entering the steady state. Finally, the numerical simulations illustrate the effectiveness of the proposed control method.

Discrete-time sliding mode prescribed performance controller via Kalman filter and disturbance observer for load following of a pressurized water reactor

In practical implementations, most nuclear reactors employ digital controllers to accomplish the load following operation. However, most of the pre-existing works only focus on continuous time controller design, which may yield degraded control performance when the control strategy is employed by a digital controller owing to the finite sampling frequency and the inevitable discrete-time approximations. To this end, this paper proposes a discrete-time sliding mode prescribed performance controller (DTSMPPC) via Kalman filter (KF) and disturbance observer (DO) for a pressurized water reactor (PWR), aiming to achieve an easier implementation on the practical nuclear reactor systems. Specifically, the continuous mathematical model of the PWR system with consideration of model errors and disturbances is first transformed to a discrete-time form by virtue of Euler’s discretization technique. Then, based on this transformed discrete-time model, the KF and DO, which provide the estimates of unmeasured system states (relative density of delayed neutron precursor, average fuel temperature, xenon concentration, and iodine concentration) and uncertainties, respectively, are constructed using the input/output measurement information acquired from the nuclear reactor system merely. By incorporating the observed information provided by the KF and DO into the control framework, the proposed DTSMPPC enables the load following error to fulfill the accurate and robust performance requirement even in the presence of unmeasured system states and uncertainties, while at the same time ensuring the transient and steady-state load following error within a prescribed zone described by performance functions. The system stability and the aforementioned theoretical findings are proved through rigorous analysis and simulations. Simulation results also reveal that the proposed DTSMPPC via the KF and DO yields a superior load following performance compared with some previous control strategies.

Observer-based adaptive tracking control of robotic manipulators with predefined time-guaranteed performance: Theory and experiment

This paper investigates the challenging problem of fixed time trajectory tracking for robotic manipulators under the presence of unavailable model perturbation, external disturbance and from different initial states. Firstly, a novel fixed-time extended state observer (FESO) is designed to estimate and compensate the lumped disturbance, which is analyzed and proved to be stable in the sense of fixed time bounded stability. Secondly, a new type of fixed-time prescribed performance control (FPPC) is constructed to guarantee the system convergences to stable state within a predefined time and enhance transient performance. Furthermore, a novel continuous fixed time nonsingular fast terminal sliding mode variable is established, which addresses singularity obstacle in terminal sliding mode. Together with FESO and FPPC, a new fixed-time adaptive nonsingular fast terminal sliding mode controller (FANFTSMC) is developed. Meanwhile, an adaptive terminal sliding mode reaching law adopted in FANFTSMC promotes the robustness and decreases the chattering phenomenon. Then, the Lyapunov approach is given to clarify the advantages of FANFTSMC in terms of predefined time stabilization and which is demonstrated on a 2-DOF robotic manipulators. Thirdly, theoretical analysis and experiments are presented to illustrate the formulated control strategy owns fine performance and stronger robustness.

Prescribed performance control of a link-type exoskeleton powered by pneumatic muscles with virtual elasticity

Prescribed performance control of a link-type exoskeleton powered by pneumatic muscles with virtual elasticity

Event‐based adaptive finite‐time control scheme with improved performance assurance for nonlinear Markov jumping systems

SummaryThis article investigates the adaptive finite‐time control design with performance assurance for nonlinear Markov jumping systems. First, the radial basis function neural networks are applied to tackle unknown nonlinear terms. Subsequently, within the framework of the command‐filtered backstepping control, the new error compensation signals are devised to remove the effect caused by filter error. Additionally, an adaptive finite‐time prescribed performance control law with an event‐triggered mechanism is developed to achieve a balance between tracking performance and bandwidth consumption, which ensures that the closed‐loop system is practically finite‐time stable in mean square and guarantees that the tracking error adjusts to the predetermined area. Finally, two simulation examples are provided to verify the validity and superiority of the devised scheme.

Finite-time prescribed performance control for approaching non-cooperative target’s feature surface

Finite-time prescribed performance control for approaching non-cooperative target’s feature surface

Event-Triggered Robust Prescribed Performance Control for Proton Exchange Membrane Fuel Cell Temperature Considering Sensor Faults

Event-Triggered Robust Prescribed Performance Control for Proton Exchange Membrane Fuel Cell Temperature Considering Sensor Faults

Neural Network Iterative Learning for SISO Non-Affine Control Systems

This work introduces an identification scheme capable of obtaining the unknown dynamics of a nonlinear plant process. The proposed method employs an iterative algorithm that prevents confinement to a sole trajectory by fitting a neural network over a series of trajectories that span the desired subset of the state space. At the core of our contributions lie the applicability of our method to open-loop unstable systems and a novel way of generating the system’s reference trajectories, which aim at sufficiently stimulating the underlying dynamics. Following this, the prescribed performance control (PPC) technique is utilized to ensure accurate tracking of the aforementioned trajectories. The effectiveness of our approach is showcased through successful identification of the dynamics of a two-degree of freedom (DOF) robotic manipulator in both a simulation study and a real-life experiment.

Segmented hybrid event‐triggered control for underactuated autonomous underwater vehicles with an asymmetrical prescribed performance constraint

AbstractIn this technical article, the trajectory‐tracking problem of event‐based adaptive prescribed performance control for underactuated autonomous underwater vehicles (AUVs) is considered. The primary innovation of this article is the proposal of a segmented event‐triggered mechanism (SETM) that incorporates preselected convergence time. This mechanism allows for the regulation of communication frequency in the control channel (controller‐to‐actuator) according to the dynamic characteristics of the AUV system at different stages. In addition to presenting new design scheme based on SETM, an enhanced vision known as segmented hybrid event‐triggered mechanism (SHETM) is introduced. Notably, the minimum and maximum triggering intervals (MITI and MATI) for these two ETMs can be calculated from the corresponding resettable dynamic variables presented in the trigger conditions. Subsequently, by utilizing the proposed asymmetrical prescribed performance control (APPC) strategy, the system's output tracking error behaviors in both transient and steady‐state stages can be qualitatively predetermined through design parameters within the boundary function. Moreover, the minimum learning parameter (MLP) based RBFNN adaptive control law is developed to counteract the effects of model uncertainties and ocean current perturbations. Finally, rigorous theoretical analysis and simulation results confirm the viability of the proposed scheme.

Dynamic Event-Triggered Prescribed Performance Robust Control for Aggressive Quadrotor Flight

Aggressive flight has become increasingly important for expanding the applications of quadrotors. The typical characteristic of large and rapid changes in commands poses stringent demands on the maneuverability of quadrotors. Ensuring flight stability alone is not enough; dynamic responses must also be selectively constrained, presenting quadcopter flight control with daunting challenges. The prescribed performance control (PPC) method is seen as having the potential to solve this problem by allowing for the constrained control of specified performance, leading to extensive research. However, its practical application still faces challenges, such as the system divergence caused by errors exceeding boundaries due to sudden command mutations. This paper presents a robust dynamic event-triggered PPC (DETPPC) method for an aggressive quadrotor flight. By assessing the direction and proximity of tracking errors approaching constraint boundaries, a dynamic event-triggered compensation mechanism for performance function boundaries is established to mitigate the divergence caused by error surpassing and to preserve preset control over the targeted metrics. Controllers were designed for both the translational and rotational subsystems of the quadrotor, and stability analysis was conducted based on Lyapunov functions. Simulation tests on agile trajectory tracking and abrupt attitude control were carried out, demonstrating the effectiveness of the proposed method.

Prescribed performance under input saturation for uncertain strict-feedback systems: A switching control approach

We consider the problem of achieving prescribed performance metrics on the output tracking error, for uncertain strict-feedback systems, while satisfying inelastic control input constraints in the form of magnitude saturation. Inspired by the prescribed performance control (PPC) methodology, we propose a switching control strategy comprised of two operational units: a traditional PPC and a Safety Controller. The former enforces the output error to evolve strictly inside a user-defined performance envelope that incorporates all the desired performance characteristics. However, in the presence of input saturation this envelope can be easily violated, leading to PPC instability. On the other hand, the Safety Controller enables the safe escaping, thus avoiding the appearance of this internal instability phenomenon. We prove that the closed-loop system solution is complete and non-zeno. Furthermore, we show that the tracking error evolves inside a modified performance envelope, guaranteeing a prescribed minimum convergence rate and a controlled maximum steady-state error. Simulation studies clarify and verify the theoretical findings.

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.