Prescribed Performance Function Research Articles

Modeling and control for PEMFC hydrogen management subsystem based on neural network compensation and prescribed tracking accuracy

The hydrogen management subsystem plays an important role in fuel cell automobiles as it impacts the output performance of the polymer electrolyte membrane fuel cell (PEMFC). This paper investigates the design and implementation of the neural network-based control for anode pressure and hydrogen excess ratio (HER). Firstly, the coupled nonlinear multiple-input-multiple-output (MIMO) system is transformed into canonical form one by using input–output linearization. Secondly, the neural network control scheme is proposed to regulate the anode pressure and HER without using the exact prior knowledge of the system. Moreover, a prescribed performance function (PPF) is proposed to guarantee the overshoot and steady-state tracking errors within the quantitative boundaries. To avoid the laborious parameter selection, the restriction that the initial error is within the performance function bound is relaxed by proposing a tuning function. Finally, the Lyapunov stability theory, numerical simulations and hardware-in-loop (HIL) experiments show the effectiveness of the proposed controller. Simulation and HIL experiment results show that the proposed control strategy is effective in realizing quantitative adjustment of tracking error while showing the best performance indexes including the root mean square error (RMSE) and minimum deviation of tracking error (DTE) compared with the neural network controller (NNC) and traditional prescribed performance controller (TPPC).

Output-Feedback Prescribed Performance Control for the Full-State Constrained Nonlinear Systems and Its Application to DC Motor System

In this study, an output-feedback prescribed performance technique with disturbance compensation is performed for full-state constrained nonlinear systems. A prominent characteristic of this technique is that not only the prescribed tracking performance is achieved when the partial states are measurable but the associated disturbances and full-state constraints are also considered, which makes the design of a high-performance controller extremely difficult. To this end, extended state observer (ESO) and nonlinear disturbance observer (NDO) are integrated to estimate unknown disturbances and unmeasurable states. Moreover, the barrier Lyapunov function (BLF) and prescribed performance function (PPF) are associated to keep the tracking errors within specified ranges and constrain all system states at all times. Then, an output-feedback prescribed performance control (PPC) algorithm with state estimation and disturbance compensation is developed. Furthermore, the stability of the closed-loop controller–observer system is certificated by utilizing the Lyapunov theory. Finally, the effectiveness of the algorithm is verified by its application to the dc motor system.

Fixed-Time Trajectory Tracking Control of Unmanned Surface Vessels with Prescribed Performance Constraints

This study proposes a fixed-time precision tracking control scheme for unmanned surface vessels with complex disturbances and unknown system dynamics. The control scheme is based on a nonsingular fast terminal sliding mode and includes an adaptive fixed-time integral sliding mode lumped disturbance observer to precisely observe and compensate for lumped unknowns. To ensure system performance under both transient and steady-state conditions, a prescribed performance function was utilized to enable the trajectory tracking error to converge to a predetermined range. The proposed control scheme, called prescribed performance fixed-time precision tracking (PPFTPT), was designed to achieve precision tracking of a predetermined trajectory within a fixed time. The stability of the closed-loop system was analyzed using the Lyapunov stability theory. Simulation results using the Cybership II model confirmed the feasibility and superiority of the proposed PPFTPT scheme.

Finite-time sliding mode trajectory tracking control of an autonomous surface vehicle with prescribed performance

This paper investigates the finite-time sliding mode trajectory tracking control problem for the autonomous surface vehicle (ASV). A prescribed performance function is introduced to improve the transient and steady-state tracking performance simultaneously. Two PID-type sliding surfaces are constructed such that the closed-loop system can reach the sliding surface with good performance, on which the developed sliding mode controllers can make the system error go to zero. In order to demonstrate the effectiveness of the proposed algorithms, an application example of the surface vehicle CyberShip II is borrowed from Skjetne et al., (2005), for which detailed comparisons are made between finite-time second-order sliding mode control (2-SMC) and finite-time first-order sliding mode control (1-SMC). A large number of simulations show that the proposed 2-SMC algorithm can achieve better control accuracy in comparison with 1-SMC algorithm and existing results.

Barrier function-based prescribed-performance adaptive attitude tracking control for spacecraft with uncertainties

This paper addresses the problem of robust adaptive attitude tracking control for spacecraft with mismatched and matched uncertainties. The idea of disturbance estimation and compensation is introduced into the control design. First, finite-time disturbance observers are developed for different channels of spacecraft based on barrier functions for achieving finite-time asymptotic estimates of unknown bounded uncertainties in the system. Second, a class of prescribed performance functions is considered in the design of the barrier function. The spacecraft attitude adaptive tracking control strategy with finite-time convergence capability and prescribed performance is proposed based on the designed finite-time disturbance observers and barrier function. Finally, the theoretical findings are verified by numerical simulations and compared with the simulation results of existing methods.

Robust fixed-time H∞ tracking control of UUVs with partial and full state constraints and prescribed performance under input saturation

In this paper, a fixed-time tracking control problem for an unmanned underwater vehicle (UUV) is investigated in the case of strong external sudden disturbances, model uncertainty, time-varying disturbances and specified performance constraints. First, a modified barrier Lyapunov function (QABLF) is proposed to increase applicability by introducing the standard quadratic Lyapunov function (QLF) and the logarithmic asymmetric barrier Lyapunov function (ABLF). The QALBF has two types and can be constructed to avoid violations of full and partial state constraints by parameter modification. Second, adaptive antisaturation appointed-time prescribed performance functions (APPFs) are introduced in the QABLF for the first time to relax the overshoot restriction and reduce the effect of input saturation on the performance constraint. Third, based on the backstepping method, a robust H∞ control strategy is developed to address strong, sudden disturbances. An auxiliary variable is designed to compensate for input saturation. Next, an improved adaptive radial basis function neural network (ARBFNN) is proposed to match the time-varying disturbances and model uncertainty. Finally, composite robust fixed-time control is achieved with high robustness and transient performance, which guarantees that the closed-loop system is fixed-time convergent. Moreover, the feasibility of the proposed controller is verified by Lyapunov analysis and numerical simulation.

Observer-based prescribed performance adaptive neural output feedback control for full-state-constrained nonlinear systems with input saturation

In this study, a prescribed performance adaptive neural output feedback controller is developed for full-state-constrained nonlinear systems that are subject to uncertainties and input saturation. To approximate system unknown nonlinear functions, the radial basis function neural network is employed. And, based on the approximated outputs of neural network, the state observer and nonlinear disturbance observer are structured to evaluate unmeasured states and unknown lumped disturbances, respectively. Barrier Lyapunov function involving prescribed performance function is constructed to constrain tracking error and all states within the specified ranges. Then, based on the constructed neural network and observers, an output feedback controller is proposed to constrain the tracking error and states via backstepping technique. Moreover, an auxiliary dynamic system is established to deal with input saturation possible caused by the more efforts to constrain tracking error and states under rough working conditions. Moreover, stability of the entire closed-loop system is strictly certified using Lyapunov theory, and the desirable prescribed tracking performance without violation of all states is assured under the combined influence of uncertainties and input saturation. Finally, the proposed control method is verified by two examples.

Event-Triggered Prescribed Performance Fuzzy Fault-Tolerant Control for Unknown Euler–Lagrange Systems With Any Bounded Initial Values

This paper investigates the tracking problem of event-triggered prescribed performance fuzzy fault-tolerant control (FTC) for unknown Euler-Lagrange systems with actuator faults and external disturbances. Firstly, the barrier Lyapunov functions (BLFs) and prescribed performance functions are synthesized to guarantee that the tracking errors satisfy the preset transient performance. Different from existing prescribed performance control methods, which require the initial values of the tracking errors to be within the prescribed performance functions, an error transformation method is introduced to ensure that the tracking errors with any bounded initial values can enter the preset boundaries within a preset time. Then, considering the unavailability of system parameters, the fuzzy logic systems (FLSs) are used to approximate unknown parameters of the system. What's more, to solve the problem of limited communication and computing resources in practical systems, an improved event-triggered control (ETC) scheme is proposed, which can reduce the communication and computation burden without satisfying the input-to-state stability (ISS) assumption. Meanwhile, the Zeno phenomenon can be avoided. Furthermore, the effects of actuator faults and the event-triggered mechanism are handled by Nussbaum gain technology. Finally, the superiority of the proposed control algorithm is verified by simulation results.

Study on stability of formation for gravity field exploration subjected to disturbance based on prescribed performance control.

Double satellite formation for gravity field exploration is a complex space virtual instrument system with high-precision, whose normal manner is threatened by the space debris environment. The normal manner of the formation based on control with prescribed performance is studied. Based on the random impact of space debris, nonlinear dynamical equations with 20 variables are established considering the relative attitude of the double satellite. The interferential characteristics and expected stability under certain disturbance conditions by the space debris in low Earth orbit are analyzed. To simplify the relative motion of the formation and the motion of the test mass (TM) relative to the cage, a prescribed performance function is introduced to constrain the relative attitude errors of transient and steady states. An adaptive attitude control design method based on a prescribed performance function is proposed. Finally, the analysis is carried out. The results show that the probability of normal manner of the formation is about 78.45% in the first year and about 45.59% in the first three years. The normal manner of the double satellite formation for gravity field exploration can be effectively simulated and analyzed based on the prescribed performance control methods.

Optimal prescribed performance tracking control of nonlinear motor driven systems via adaptive dynamic programming

AbstractAlthough optimal regulation problem has been well studied, resolving optimal tracking control via adaptive dynamic programming (ADP) has not been completely resolved, particularly for nonlinear uncertain systems. In this paper, an online adaptive learning method is developed to realize the optimal tracking control design for nonlinear motor driven systems (NMDSs), which adopts the concept of ADP, unknown system dynamic estimator (USDE), and prescribed performance function (PPF). To this end, the USDE in a simple form is first proposed to address the NMDSs with bounded disturbances. Then, based on the estimated unknown dynamics, we define an optimal cost function and derive the optimal tracking control. The derived optimal tracking control is divided into two parts, that is, steady‐state control and optimal feedback control. The steady‐state control can be obtained with the tracking commands directly. The optimal feedback control can be obtained via the concept of ADP based on the PPF; this contributes to improving the convergence of critic neural network (CNN) weights and tracking accuracy of NMDSs. Simulations are provided to display the feasibility of the designed control method.

Adaptive Asymptotic Tracking Control for Flexible-Joint Robots With Prescribed Performance: Design and Experiments

This study reports the adaptive asymptotic tracking control problem for flexible-joint (FJ) robot systems, the output tracking error can be kept within the prescribed range in the initial stage of system operation, as time approaches infinity, the asymptotic tracking result can be obtained. The prescribed performance function and the positive integrable time-varying function are introduced simultaneously in the control design of FJ robot systems for the first time. The control scheme is designed under the frame of the adaptive backstepping method and command filtered technique, which successfully avoids the problem of complexity explosion. The radial basis function neural networks are used to deal with unknown uncertainties and the adaptive laws are designed to approximate the norms of weight vectors and approximation errors. Finally, the feasibility of the proposed scheme is proved by the simulation and the experiment of the 2-link FJ robot on the Quanser platform.

An HQP-Based Obstacle Avoidance Control Scheme for Redundant Mobile Manipulators Under Multiple Constraints

It is a challenging problem for redundant wheeled mobile manipulators to satisfy multiple physical constraints and avoid obstacles while performing certain tasks, not to mention constraining tracking performance. In this paper, a control scheme based on hierarchical quadratic programming-prescribed performance control (HQP-PPC) is proposed. The first layer of HQP can achieve trajectory tracking, obstacle avoidance and physical constraints. The second layer of HQP is used to guide the direction of obstacle avoidance and produce a smoother planned path. The prescribed performance function (PPF) can ensure tracking performance so that the physical constraints and obstacle avoidance constraints are satisfied in actual motion. Moreover, the proposed controller can guarantee the tracking performance of the end effector due to the characteristics of PPF. Finally, the effectiveness and superiority of the proposed method are verified by simulations and experiments.

Nonlinear Uncertainty Estimator-Based Robust Control for PMSM Servo Mechanisms With Prescribed Performance

Active nonlinear uncertainties compensation is crucial for realizing high-precision servo control. However, the rejection of the unknown uncertainties is still a challenging problem. In view of these issues, this paper proposes a novel nonlinear uncertainty estimator based time-varying sliding mode control scheme for servo systems with prescribed performance. A nonlinear uncertainty estimator, which employs first-order low-pass filter operations with only one tuning parameter, is constructed to deal with unknown nonlinearities, while the NDE estimation error and uncertainties of the servo system are handled by the robust integral of the sign of the error (RISE) feedbacks. Meanwhile, a modified prescribed performance function (PPF) with a faster convergence rate is incorporated into the control design to restricted the tracking errors within the predefined asymptotic boundaries. By combining PPF and NDE, a time-varying sliding mode controller is developed to eliminate the reaching phase and improve the control performance. The validity and feasibility of the presented control scheme are verified with simulations and experiments based on a motor driving system.

Prescribed performance control for dynamic positioning vessels with a dynamic event-triggered mechanism

This paper addresses the problem of trajectory tracking control for dynamic positioning vessels in the presence of unknown sea loads. Firstly, an integral disturbance observer is introduced to estimate the unknown sea loads, which enhances the estimation accuracy by incorporating an integral term. Then, a novel second-order prescribed performance function combined with a tracking differentiator is proposed. Compared to traditional performance functions, this function can better enforce error constraints. As a starting point, a Non-full-state event-triggered control (NFSETC) scheme and a full-state event-triggered control (FSETC) scheme are designed to achieve trajectory tracking while addressing environmental uncertainty and limited communication resources. Furthermore, a novel full-state event-triggered mechanism, utilizing a dynamic threshold event-triggered strategy with a performance safety evaluation factor (PSEF), is employed for stable control input, low communication consumption, and improved tracking accuracy. It is also proven that both the event-triggered controller and the full-state event-triggered controller do not exhibit the Zeno phenomenon. Finally, numerical simulations are conducted to verify the theoretical findings and effectiveness of the proposed method.

Optimal Pneumatic Actuator Positioning and Dynamic Stability using Prescribed Performance Control with Particle Swarm Optimization: A Simulation Study

This paper introduces an optimal control strategy for pneumatic servo systems (PSS) positioning using Finite-time Prescribed Performance Control (FT-PPC) with Particle Swarm Optimization (PSO). Pneumatic servo systems are widely used in industrial automation, as well as medical and cybernetics systems that involve robotics applications. Precision in pneumatic control is crucial not only for the sake of efficiency but also safety. The primary goal of the proposed control strategy is to optimize the convergence rate and finite time of the prescribed performance function in error transformation of the FT-PPC, as well as the Proportional, Integral and Derivative (PID) controller as the inner-loop controller for this system. The study utilizes a dynamic model of a pneumatic proportional valve with a double-acting cylinder (PPVDC) as the targeted plant and performs simulations with a multi-step input trajectory. This offline tuning method is essential for such nonlinear systems to be safely optimized, avoiding major damage to the real-time fine-tuned works on the controller. The results demonstrate that the proposed control strategy surpasses the performance of FT-PPC with a PID controller alone, significantly improving the system's performance, including suppressing overshoot and oscillation in the responses. Further validation through the actual system of PPVDC using the fine-tuned values of FT-PPC and PID with PSO is a future task and more challenging to come, as hardware constraints may vary with different environments such as temperatures.

Fixed-Time RBFNN-Based Prescribed Performance Control for Robot Manipulators: Achieving Global Convergence and Control Performance Improvement

This paper proposes a fixed-time neural network-based prescribed performance control method (FNN-PPCM) for robot manipulators. A fixed-time sliding mode controller (SMC) is designed with its strengths and weaknesses in mind. However, to address the limitations of the controller, the paper suggests alternative approaches for achieving the desired control objective. To maintain stability during a robot’s operation, it is crucial to keep error states within a set range. To form the unconstrained systems corresponding to the robot’s constrained systems, we apply modified prescribed performance functions (PPFs) and transformed errors set. PPFs help regulate steady-state errors within a performance range that has symmetric boundaries around zero, thereby ensuring that the tracking error is zero when the transformed error is zero. Additionally, we use a singularity-free sliding surface designed using transformed errors to determine the fixed-time convergence interval and maximum allowable control errors during steady-state operation. To address lumped uncertainties, we employ a radial basis function neural network (RBFNN) that approximates their value directly. By selecting the transformed errors as the input for the RBFNN, we can minimize these errors while bounding the tracking errors. This results in a more accurate and faster estimation, which is superior to using tracking errors as the input for the RBFNN. The design procedure of our approach is based on fixed-time SMC combined with PPC. The method integrates an RBFNN for precise uncertainty estimation, unconstrained dynamics, and a fixed-time convergence sliding surface based on the transformed error. By using this design, we can achieve fixed-time prescribed performance, effectively address chattering, and only require a partial dynamics model of the robot. We conducted numerical simulations on a 3-DOF robot manipulator to confirm the effectiveness and superiority of the FNN-PPCM.

Neural network-based depth and horizontal control for autonomous underwater vehicles with prescribed performance

This paper presents a study of horizontal and depth controller design for autonomous underwater vehicles (AUVs) regarding model uncertainties, input constraints, and ocean currents. Firstly, the depth-plane and horizontal-plane models of AUV are established comprehensively with ocean currents. Besides, the AUV's characteristics and physical limitations are also described. Secondly, extended perturbation observers (EPOs) are innovatively constructed to estimate ocean currents, which guarantee the accuracy in the case of time-varying ocean currents. To achieve the position errors with prescribed performance guarantees, a finite-time prescribed performance function is proposed such that the convergence time, maximum overshoot, and steady error bounds can be preset directly. Neural network-based adaptive control is adopted to deal with model uncertainties and environmental disturbances. Auxiliary systems with a smooth switching function are introduced to alleviate the effect of input saturation. Furthermore, rigorous theoretical analyses are also carried out to demonstrate the robust stability of the proposed controllers. Finally, extensive numerical simulation studies confirm the strong and conclusive evidence for the proposed method's effectiveness, robustness, anti-jamming ability, and feasibility.

Predefined‐time guaranteed performance attitude takeover control for non‐cooperative spacecraft with uncertainties

AbstractThis article addresses the predefined‐time guaranteed performance attitude tracking problem for takeover the non‐cooperative target spacecraft with model uncertainties, adversarial control torque and gravity gradient torque. Firstly, a novel prescribed performance function (NPPF) is exploited, and then a new non‐singular predefined‐time terminal sliding mode (NPTSM) surface with the transformed tracking error is constructed. Secondly, a non‐singular predefined‐time prescribed performance control (NPTPC) is designed to achieve the guaranteed performance within predefined‐time. It is proved that the proposed control can ensure that the attitude tracking error satisfies the prescribed performance boundaries all the time and converges to a preset small region centered around the equilibrium point within predefined time and then tends to the equilibrium point asymptotically. The appealing feature of the proposed control is predefined‐time stability with quantified transient performance and steady‐state accuracy. Simulations verify the effectiveness and improved performance of the proposed approach.

Adaptive fault-tolerant control for spacecraft formation under external disturbances with guaranteed performance

This paper investigates an adaptive fault-tolerant control problem for spacecraft formation flying (SFF) with actuator faults, external disturbances, and unknown inertial uncertainties. First, fault factors are introduced to describe the SFF orbit model with consideration of actuator bias faults and loss of actuator effectiveness. Then, an adaptive fault-tolerant controller is proposed by incorporating prescribed performance function, improved terminal sliding mode control and the proposed adaptive law. Finally, rigorous theoretical analysis ensures the uniformly ultimately bounded stability of the system through Lyapunov theory and simulation verifies the proposed algorithm.

Multivariable secure guidance for interceptors against cyber-attacks in guidance commands

Secure guidance for missiles against cyber-attacks is an interesting topic of both theoretical and practical importance, but so far few results are available. In this paper, two multivariable secure guidance laws are proposed for precise strikes interceptors with cyber-attacks in guidance commands. Different engagement scenarios are studied in three-dimensional space. Against highly maneuvering targets, the proposed secure guidance law can guarantee some states related to the line-of-sight (LOS) angular rates to converge to zero within finite time, where the cyber-attacks are indirectly estimated and compensated with the aid of an attack observer. Moreover, against non-maneuvering targets with impact angle constraints, the proposed secure guidance law is designed based on the backstepping technique, where the cyber-attacks are directly estimated and compensated. Particularly, prescribed performance functions are introduced in the second guidance law to flexibly determine the convergence rates of the LOS angles. Numerical simulations are performed to illustrate the effectiveness of the proposed schemes.