Transient Performance Of Tracking Error Research Articles

Prescribed performance control for nonlinear parameter-varying systems with an application to turbofan engine

In this paper, we investigated the problem of the prescribed performance control for the turbofan engine described by nonlinear parameter-varying (NPV) systems formulation. NPV systems for describing the turbofan engine are set up. Compared with the existing dynamic linear models and nonlinear models, the turbofan engine NPV model can show its dynamics time-varying features and nonlinearity. Meanwhile, based on the turbofan engine NPV system, a prescribed performance tracking controller is designed by error mapping function, and a class of state-and-parameter-dependent (SAPD) control synthesis conditions are formulated. These SAPD conditions can be effectively solved by sum-of-squares technique, and steady-state and transient performance of tracking error can be ensured. Finally, simulation results on the turbofan engine have been given to verify the feasibility and effectiveness of the prescribed performance tracking control scheme.

Distributed synchronization control for multiple tailless flying‐wing UAVs with predefined tracking accuracy and input nonlinearities

SummaryThis article addresses the distributed adaptive synchronization tracking control problem for multiple flying‐wing UAVs with predefined accuracy and unknown input nonlinearities. Considering that the multiple flying‐wing unmanned aerial vehicles (UAVs) system is a large‐scale nonlinear and strongly coupled system, the control schemes in existing literature which only consider longitudinal, lateral or attitude control may not be applicable in practical engineering. Thus, a full‐state flying‐wing UAV model containing both translational and rotational motions is established, whose dynamics are six‐degree‐of‐freedom with twelve‐state‐variables. Furthermore, to handle the problem that the prior knowledge of the actuator nonlinearities of multi‐UAV system are difficult to obtain, a more general input nonlinear model is established and the adaptive boundary estimation technique is developed. Finally, a performance‐oriented controller is proposed by incorporating a series of smooth functions into adaptive neural control design and Lyapunov analysis. Theoretical analysis and simulation results show that the presented control scheme can guarantee the satisfactory transient tracking error performance, and the tracking error converges to a user‐defined interval ultimately.

On Integrating Uncertainty Estimator Into PI Control for a Class of Nonlinear Uncertain Systems

Proportional-integral (PI) control/loop has been widely used in numerous industrial processes. This article focuses on integrating uncertainty estimator into PI controller for better robustness and transient performance against uncertain nonlinear coupling dynamics and time-varying disturbances. First, the descriptions for the sizes of three kinds of uncertainties in a class of multi-input-multi-output nonlinear systems are discussed. Then, the tuning laws of the typical uncertainty estimator, i.e., extended state observer (ESO), are quantitatively presented to ensure the stability of closed-loop systems. More importantly, it is shown that the desired transient performance of tracking error can be ensured by tuning the bandwidth of ESO. In addition, it is proven that much stronger disturbance rejection at low frequency can be achieved by integrating the uncertainty estimator module. The simulation results for calibration-free robotic eye-hand coordination system show the effectiveness of the proposed method.

Adaptive Neural Output Feedback Compensation Control for Intermittent Actuator Faults Using Command-Filtered Backstepping.

Effectively compensating unknown intermittent actuator faults in uncertain decentralized nonlinear systems is a very difficult problem, and very few results have been obtained. In this article, to address this issue, an adaptive neural output feedback compensation control scheme based on command-filtered backstepping is developed. First, we design a bank of observers to estimate the system states and utilize neural networks with random hidden nodes to approximate the unknown functions of these observers. Second, a smooth projection algorithm is used to online update estimated parameters in the controllers such that the possible ceaseless increase in the estimated parameters caused by intermittent actuator faults can be eliminated. Due to the presence of intermittent jumps of unknown parameters, a modified Lyapunov function is developed to analyze the system stability. It is proved that the boundedness of all closed-loop system signals is ensured and the ultimate bound of the tracking error depends on design parameters, adjustable jumping amplitude of Lyapunov function, and minimum fault time interval. Third, by analyzing the system transient performance, the peaking phenomenon at the starting instant of the system operation can be removed, and a root mean square type of bound is established to illustrate that the transient tracking error performance is tunable by design parameters. Finally, simulations studies are done to illustrate the effectiveness of the theoretical results.

Extended dimension fuzzy adaptive control for nonlinear uncertain stochastic systems with actuator constraints

In this paper, an extended dimension fuzzy adaptive control for nonlinear uncertain stochastic systems with actuator constraints is investigated. The approximation error is introduced into the control scheme as a time-varying function by extended dimension fuzzy logic systems (FLSs). Besides, the sign function as a norm of the FLSs vector, in order to reduce the amount of calculation, will create a challenging chattering problem. Further, actuator failures usually are uncertain in time, pattern, and value and may also occur in practice. In order to handle the above issues, backstepping technology is applied to stabilize stochastic nonlinear system with stochastic disturbance and uncertain actuator failures. It is proved that the asymptotic convergence performance and predetermined transient tracking error performance are guaranteed to be within a pre-established sound whether the actuator fails or not. Finally, simulation results have demonstrated the proposed theoretical results.

Adaptive neural output feedback fault tolerant control for a class of uncertain nonlinear systems with intermittent actuator faults

In real applications, actuators of control systems frequently encounter unknown intermittent faults during operation while effectively handing such faults is still a challenge. In this paper, an adaptive neural output feedback fault tolerant control (FTC) scheme based on the command filtered backstepping is developed for a class of uncertain nonlinear systems to address this challenge. In this scheme, a stable nonlinear observer is designed to estimate the system states and neural networks with random hidden nodes are utilized in this observer to approximate unknown functions. A projection algorithm is adopted to estimate system unknown parameters such that the boundedness of parameter estimates is guaranteed. It is proved that the boundedness of all signals in the closed-loop system can be ensured by the proposed modified Lyapunov function. Also the ultimate bound of the tracking error depends on design parameters, adjustable jumping amplitude of Lyapunov function and minimum fault time interval. A truncated L2 bound is established by iterative calculation to illustrate that the transient tracking error performance is determined by design parameters in the controller and observer. Applications on two simulation examples validate the effectiveness of the proposed scheme.

Indirect Adaptive Fuzzy Control Design With Guaranteed Tracking Error Performance For Uncertain Canonical Nonlinear Systems

In this paper, we consider the fuzzy controller design problem for output tracking of uncertain strict-feedback nonlinear systems. For comparison, a basic fuzzy control scheme is first constructed based on an existing approach representative in the field. The scheme can effectively reduce the number of parameter estimates, which benefits from the operation of handling the square of the norm of fuzzy weight vector. However, as a tradeoff of such an operation, the asymptotic tracking performance cannot be ensured and the $L_2$ -norm transient performance of tracking error cannot be established. To eliminate these performance costs without losing the advantage of the basic fuzzy control scheme, we further propose a performance-oriented fuzzy control scheme. It guarantees that all closed-loop signals are bounded and the tracking error converges to a prescribed interval asymptotically. Moreover, the $L_2$ -norm transient performance of tracking error is also established, which explicitly indicates that the transient performance of tracking error can be improved through changing controller design parameters with the performance-oriented fuzzy control scheme. Simulation examples are given to verify the obtained results.

Adaptive Neural Control of a Class of Stochastic Nonlinear Uncertain Systems With Guaranteed Transient Performance.

In this paper, an adaptive neural network control for stochastic nonlinear systems with uncertain disturbances is proposed. The neural network is considered to approximate an uncertain function in a nonlinear system. And computational burden in operation is reduced by handling the norm of the neural-network vector. However, it will arise chattering issue, which is a challenge to avoid it from the symbolic operation. Further, traditional schemes often view error of estimate as bounded constant, but it is a time-varying function exactly, which may lead control schemes cannot conform to practical situation and guarantee stability of systems. Thus, backstepping technology and the neural network technology combined to stabilize stochastic nonlinear systems together to handle the aforementioned issues. It is proved that the proposed control scheme can guarantee the satisfactory asymptotic convergence performance and predetermined transient tracking error performance. From simulation results, the proposed control scheme is verified that can guarantee the satisfactory effectiveness.

Hierarchical Decomposition Based Consensus Tracking for Uncertain Interconnected Systems via Distributed Adaptive Output Feedback Control

In this note, distributed adaptive controllers are developed for output consensus tracking of multiple linear systems with unknown parameters, uncertain subsystem interconnections and external disturbances. The subsystems are allowed to have non-identical dynamics and the same yet arbitrary order. It is assumed that only part of subsystems can have direct access to the time-varying trajectory information and the subsystem states are unmeasurable for local feedback control. In our design, the directed graph representing the information transmission status among subsystems is preprocessed by splitting it into a hierarchical structure. Then local adaptive controllers of subsystems in different layers can be computed in a sequential order and the difficulty on deriving mutually dependent local controls in previous consensus works are successfully overcome. In each subsystem, additional estimates are introduced to account for the unknown parameters and states in its neighbors' dynamics. Besides, only the information of local outputs and inputs need be collected from the neighboring subsystems. Certain robust terms are added in distributed adaptive laws to mitigate the effects of uncertain subsystem interactions and disturbances. It is proved that with our scheme, all closed-loop signals can be ensured bounded when the strengths of uncertain subsystem interconnections are sufficiently weak. The tracking errors for the entire group of subsystems will converge to a compact set and the transient tracking error performance can be adjusted by appropriately choosing design parameters.

Decentralized Backstepping Adaptive Output Tracking of Interconnected Nonlinear Systems

In this paper, we propose a new totally decentralized adaptive output tracking scheme for a class of nonlinear interconnected systems by using a backstepping approach. In the design, a smooth function is introduced to compensate for the effects of interactions from other subsystems. It is shown that the designed local adaptive controllers can ensure all the signals in the closed loop system are bounded. A root mean square type of bound is obtained for the tracking error as a function of design parameters. This implies that the transient tracking error performance can be adjusted by choosing suitable design parameters.