Prescribed Performance Tracking Control Research Articles

Distributed Prescribed Performance Tracking Control for Multiagent Systems With Collision Avoidance and Initial Restriction Overcoming

Distributed Prescribed Performance Tracking Control for Multiagent Systems With Collision Avoidance and Initial Restriction Overcoming

Low-Complexity Tracking Control of Unknown Strict-Feedback Systems With Quantitative Performance Guarantees.

This article is concerned with the prescribed performance tracking control problem for the strict-feedback systems with unknown nonlinearities and unmatched disturbances. The challenge lies in the realization of a complete performance specification for trajectory tracking in the sense of quantitatively regulating the peak value, overshoot, settling time, and accuracy while ensuring that the initial condition holds naturally. To this end, an error transformation, equipped with a shifting function, is introduced and incorporated with a new-type barrier function. Then, a class of performance functions is exploited to quantify the settling times and steady-state bounds of the intermediate errors. Moreover, to improve the flexibility of formulating performance specifications for the tracking error, a pair of asymmetric performance boundaries are further designed. With their combination, a novel robust prescribed performance control (PPC) approach is proposed in this article. It not only achieves the quantitative performance guarantees but also preserves the unique simplicity of PPC, evading the needs for function approximation, parameter identification, disturbance estimation, derivative calculation, or command filtering. The above theoretical findings are confirmed via three simulation studies.

Prescribed Performance Formation Tracking Control for Underactuated AUVs under Time-Varying Communication Delays

Achieving formation tracking control of underactuated autonomous underwater vehicles (AUVs) under communication delays presents a significant challenge. To address this challenge, a distributed prescribed performance control protocol based on a real-time state information online predictor (RSIOP) is proposed in this paper. First, we innovatively designed an RSIOP to achieve active compensation for the delayed state information of neighboring AUVs. Next, considering formation performance and safety, a low-complexity and practical nonlinear mapping function was used to implement prescribed performance tracking control for the AUV formation. Additionally, the adverse effects of external disturbance uncertainties and input saturation are also considered. Finally, the simulation tests demonstrated that the proposed formation control protocol can successfully achieve the predetermined formation tracking tasks in the presence of time-varying communication delays and external disturbances, while also enabling real-time changes in formation configuration during the process. Throughout, the protocol maintains input saturation limits, and the actual control inputs remain smooth, with no significant oscillations. Furthermore, comparative simulation tests verified the necessity of the RSIOP developed in this study and quantitatively demonstrated that the proposed control method exhibits superior performance in terms of formation control accuracy, error convergence speed, and transient-state constraints.

Finite-time prescribed performance tracking control for nonlinear time-delay systems with state constraints and actuator hysteresis

In this paper, the problem of adaptive neural network prescribed performance tracking control for a class of non-strict feedback time-delay systems constrained by full-state is studied. Radial basis function (RBF) neural networks (NNs) are integrated into the backstepping medium to deal with the uncertain functions and the barrier Lyapunov function (BLF) technique ensures that the state of the system does not exceed its limits. Subsequently, integrated with the Lyapunov–Krasovskii functional, the proposed control scheme makes the tracking errors converge to the preset region while the state constraint is not violated. Finally, the effectiveness of the scheme is supported by two simulation experiments.

Adaptive event-triggered finite-time prescribed performance control of PMSM stochastic system considering time-varying delays

This paper investigates the finite-time prescribed performance tracking control problem of permanent magnet synchronous motor (PMSM) considering stochastic disturbances and time-varying delays under event-triggered mechanism. A quintuple polynomial finite-time prescribed performance function (FPPF) is introduced to ensure the transient and steady-state performance of the system output, and a nonlinear transformation function is employed to convert the constrained error into an unconstrained one. The Lyapunov-Krasovskii function is constructed to address time delays. And the system uncertainties are approximated by the radial basis function neural networks (RBFNN). For the “explosion of complexity” caused by backstepping method, a tracking differentiator (TD) is employed. By combining finite time control, command filtering backstepping control, and event-triggered mechanism, the effect of the filter errors is decreased, and the update frequency of the control signals are reduced. It is shown that the proposed controller can guarantee finite time convergence bounded of all signals in the closed-loop system, and the tracking error can converge in finite time. Finally, simulation results are presented to illustrate the effectiveness of the proposed controller.

Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

Adaptive prescribed performance tracking control for a class of nonlinear systems with actuator faults via a quantized event-triggered control scheme

Adaptive prescribed performance tracking control for a class of nonlinear systems with actuator faults via a quantized event-triggered control scheme

Neural network-based prescribed performance tracking control for a class of nonlinear systems with mismatched disturbances

This paper addresses the prescribed performance tracking control problem for a class of nonlinear systems subject to mismatched uncertainties. A novel disturbance observer-based control (DOBC) scheme is proposed through combining radial basis function neural network (RBFNN) and prescribed performance function (PPF). In contrast to traditional DOBC, the proposed approach employs RBFNN technology to approximate unknown nonlinear functions in the system, instead of treating them as part of lumped disturbances. A novel disturbance observer is developed to estimate disturbances characterised by a nonlinear exogenous system. To enhance control performance, a PPF that characterises both transient and steady-state behaviour is used for the transformation of tracking errors. It can be proved that all the states of the closed-loop system can be guaranteed to be uniformly ultimately bounded (UUB), and that the tracking error evolves within the prespecified boundaries. Theoretical results are validated and supported by two simulation examples.

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.

Adaptive prescribed performance tracking control for underactuated unmanned surface ships with input quantization

Adaptive prescribed performance tracking control for underactuated unmanned surface ships with input quantization

Adaptive prescribed performance tracking control for uncertain nonlinear systems with unknown backlash-like hysteresis

In this paper, an adaptive prescribed performance tracking control(PPTC) problem of uncertain nonlinear systems with unknown hysteresis input is investigated. For the purpose of implementing the PPTC, a performance function and an error conversion function are introduced. Moreover, a backlash-like hysteresis model is adopted to describe the hysteresis nonlinearity, which makes the controller design feasible. Additionally, by converting the backlash-like hysteresis model into a linear model with bounded error, the difficulties caused by hysteresis behavior on controller design are settled. Thus, integrating multi-dimensional Taylor network(MTN) approximation technique into adaptive backstepping method, an adaptive control scheme for uncertain nonlinear systems is proposed. Apart from ensuring that all signals of the closed-loop system keep bounded, the proposed control scheme not only makes the tracking error converge to an arbitrarily small neighborhood around the origin, but also guarantees the tracking error trajectory within the limits set by PPTC. Ultimately, two simulations are applied to verify the validity of the proposed control scheme.

Adaptive prescribed performance tracking control of high‐order uncertain nonlinear systems under full‐state time‐varying constraints

AbstractIn this article, the adaptive finite time prescribed performance tracking control problem of a class of high‐order uncertain nonlinear systems under full state time‐varying constraints is addressed. By using the logarithmic function based nonlinear mapping technique rather than the barrier Lyapunov function based method, the obstacle of the full‐state constraints is resolved, and the undesired “feasibility conditions” in controller design are eliminated. By improving the prescribed performance control method, the initial value problem is overcome, and the finite‐time convergence of the tracking error can be ensured. Then, with the aid of the adding a power integrator method, an adaptive finite time prescribed performance tracking controller is designed, not only the tracking error but also the full states can be guaranteed to converge to a predefined constraint region in the predetermined time. Simulation examples are given to show the validness of the proposed control strategy.

Prescribed performance tracking control of multi-link robotic manipulator with uncertainties

<p style='text-indent:20px;'>This paper addresses the trajectory tracking problem with prescribed performance for a multi-link robotic manipulator subject to unknown dynamics and external disturbances. A predefined performance function is adopted to describe tracking errors' desired transient and steady-state performance. Then, the output error dynamics with performance constraints are transformed into an equivalent unconstrained system, whose stabilization is sufficient to guarantee the prescribed performance of the original system. An extended state observer with a friction model is designed to approximate unknown dynamics together with the unmeasurable velocity state, which extends the applicability of the proposed controller to manipulators with only position signals available. The friction model is lumped into it to improve the precision and velocity of estimation. It is proved via Lyapunov analysis that the proposed controller can theoretically guarantee the satisfaction of prescribed performance in the presence of uncertainties. The simulation results verify the reliability and effectiveness of the proposed method.</p>

Prescribed Performance Tracking Control for Nonlinear Multiagent Systems With Distributed Observation Errors Compensation

Prescribed Performance Tracking Control for Nonlinear Multiagent Systems With Distributed Observation Errors Compensation

Precise Tracking Control for Articulating Crane: Prescribed Performance, Adaptation, and Fuzzy Optimality by Nash Game.

Articulating crane (AC) is used in various industrial activities. The articulated multisection arm exacerbates nonlinearities and uncertainties, making the precise tracking control challenging. This study proposes an adaptive prescribed performance tracking control (APPTC) for AC to robustly fulfill the task of precise tracking control, with adaptation to resist time-variant uncertainties, whose bounds are unknown but lie in prescribed fuzzy sets. Particularly, a state transformation is applied to simultaneously track the desired trajectory and satisfy the prescribed performance. Adopting the fuzzy set theory to describe uncertainties, APPTC does not invoke any IF-THEN fuzzy rules. There is no linearizations, or nonlinear cancelation for APPTC, thus making it approximation free. The performance of the controlled AC is twofold. First, deterministic performance in fulfilling the control task is ensured by the Lyapunov analysis using uniform boundedness and uniform ultimate boundedness. Second, fuzzy-based performance is further improved by an optimal design, which seeks the optima of control parameters by formulating a two-player Nash game. The existence of Nash equilibrium is theoretically proved, and its acquisition process is given. The simulation results are provided for validations. This is the first endeavor that explores the precise tracking control for fuzzy AC.

Event‐triggered adaptive tracking control for nonlinear systems with input saturation and unknown control directions

AbstractThis article is concerned with event‐triggered adaptive tracking control design of strict‐feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event‐triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed‐loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy.

Event-triggered dynamic prescribed performance control for oxygen stoichiometry and stack temperature in PEM fuel cell systems with actuators faults

Oxygen stoichiometry (OS) and stack temperature (ST) significantly affect the output performance and durability of proton exchange membrane fuel cells. This paper investigates the prescribed performance tracking control strategy of OS and ST under external disturbances, modeling errors, actuators faults and limited communication resources. The total disturbances are compensated by a variable-bandwidth extended state observer to simplify the control design and enhance the system robustness. To tolerate excessive disturbances and relax the strict requirement on the initial conditions, a new event-triggered adaptive sliding mode controller that integrates modified dynamic performance constraints and nonsingular error transformation is developed to ensure the user-designed transient and steady-state performance constraints, while saving the communication costs and avoiding the chattering and jump in control signals. The numerical validation results under combined working scenarios indicate that the proposed controller always ensures the preset error constraints and possesses superior performance in tracking the optimal OS value 2 and the optimal ST value 353.15K than other three representative controllers, with the integral absolute errors of 0.732 for OS tracking and 12.94 for ST tracking; besides, it achieves satisfactory robustness to uncertain model parameters and relatively large initial tracking errors.

Finite-time prescribed performance tracking control of seeker stabilized platform in the discrete-time domain

Current prescribed performance control (PPC) focuses on continuous-time systems, while this article proposes a novel discrete-time version of PPC for finite-time tracking of seeker stabilized platform in the discrete-time domain. Firstly, the newly developed performance functions are employed to impose finite-time prescribed performance on tracking errors. After that, a type of stabilization functions with respect to transformed errors are constructed for back-stepping controllers designing. On this basis, transformed errors are indirectly stabilized, and thus the pursued prescribed transient and steady-state behaviors are ensured for tracking errors via Lyapunov synthesis. Different from existing sliding-mode-control based discrete-time PPC, the addressed approach eliminates the sliding-mode structure and hence avoids high frequency chattering caused by such framework. Finally, compared simulations validate the superiority over existing methods.

Neuroadaptive Performance Guaranteed Control for Multiagent Systems With Power Integrators and Unknown Measurement Sensitivity.

This article investigates the adaptive performance guaranteed tracking control problem for multiagent systems (MASs) with power integrators and measurement sensitivity. Different from the structural characteristics of existing results, the dynamic of each agent is a power exponential function. A method called adding a power integrator technique is introduced to guarantee that the consensus is achieved of the MASs with power integrators. Different from existing prescribed performance tracking control results for MASs, a new performance guaranteed control approach is proposed in this article, which can guarantee that the relative position error between neighboring agents can converge into the prescribed boundary within preassigned finite time. By utilizing the Nussbaum gain technique and neural networks, a novel control scheme is proposed to solve the unknown measurement sensitivity on the sensor, which successfully relaxes the restrictive condition that the unknown measurement sensitivity must be within a specific range. Based on the Lyapunov functional method, it is proven that the relative position error between neighboring agents can converge into the prescribed boundary within preassigned finite time. Finally, a simulation example is proposed to verify the availability of the control strategy.

Adaptive finite-time prescribed performance tracking control for hydraulic servo systems with friction compensation

Hydraulic systems present numerous challenges in the development of high-performance tracking controllers due to their highly nonlinear characteristics and heavy modeling uncertainties. Addressing this issue, this paper presents a friction compensation-based finite-time tracking control strategy with prescribed performance constraints. The system model is first derived, taking into consideration the nonlinear behaviors and potential uncertainties encountered in practical scenarios. Then, an adaptive finite-time prescribed performance controller is synthesized based on the backstepping framework. A novel form of finite-time performance function is introduced to constrain the tracking error, which provides the closed-loop system with a less complex guarantee of finite-time convergence and can also deliver the required transient performance and steady-state accuracy. Additionally, given the impact of uncertainty terms and the difficulty in obtaining the virtual command derivative, we employ neural networks (NNs) to estimate unknown dynamics and introduce command filters to acquire the intermediate signals, simplifying the backstepping control design process. Theoretical analysis indicates that the proposed control strategy can achieve the desired tracking performance and ensure the stability of the entire closed-loop system. Comparative numerical simulations are presented to confirm the usefulness of the suggested approach.