Robust adaptive control for prescribed performance tracking of constrained uncertain nonlinear systems

This paper proposes a robust adaptive control strategy for a class of state-constrained uncertain nonlinear systems with prescribed transient and steady-state behavior. The prescribed tracking performance can be characterized by constraints on an output tracking error. Both state and output constraints are achieved by bounding integral barrier Lyapunov functions in the backstepping procedure. A robust adaptive term is designed to compress auxiliary system uncertainties without the knowledge of their bounds. The satisfaction of control constraints and tracking error convergence are verified by theoretical analysis and are illustrated by simulation results.     

A new prescribed performance control approach for uncertain nonlinear dynamic systems via back-stepping

Though traditional prescribed performance control (PPC) schemes can guarantee tracking errors with desired transient performance, they cannot ensure the convergence of tracking errors with small overshoot. In this study, we propose a novel PPC methodology for a class of uncertain nonlinear dynamic systems based on back-stepping, guaranteeing output tracking with small (even zero) overshoot. Firstly, new performance functions are constructed to constrain tracking errors. Then, to facilitate control designs, the “constrained” systems are transformed into equivalent “unconstrained” ones by designing a series of transformed errors. Furthermore, robust back-stepping controllers, requiring no priori knowledge of uncertainties’ upper bounds, are developed utilizing transformed errors instead of initial tracking errors. Semi-globally uniformly bounded stability of the closed-loop control system is guaranteed via Lyapunov synthesis. Finally, simulation and experiment results are presented to verify the design.     

Event-triggered adaptive tracking control of uncertain nonlinear systems with prescribed performance and actuator failures

This article studies adaptive prescribed performance tracking control problem for a class of strict-feedback nonlinear systems with parametric uncertainties and actuator failures. Firstly, in order to compensate the multiple uncertainties and eliminate the influence of actuator failure, a new adaptive tracking controller based on first-order filter technology will be proposed, which simplifies the algorithm design process. Then, by introducing an asymmetric state transition function, the transient and steady performances of the output tracking error are both constrained such that the predetermined performance control goal is achieved. Moreover, to reduce the communication burden from the controller to the actuator, the event-triggered mechanism is designed, and there will be no Zeno phenomenon. Based on Lyapunov stability theory, it is strictly proved that output signal can track the reference signal and all the signals of the closed-loop system are bounded. Finally, a simulation example is performed and the results demonstrate effectiveness of the proposed strategy.     

Prescribed-time containment control with prescribed performance for uncertain nonlinear multi-agent systems

The existing studies on prescribed-time control cannot directly deal with nonlinear functions which don’t satisfy Lipschitz growth conditions. No results are available for prescribed-time containment control of pure-feedback UNMASs with prescribed performance. Therefore, completely unknown nonlinear function, prescribed-time tracking of system states and prescribed performance of containment errors are simultaneously considered in this paper. Fuzzy logic systems are utilized to approximate completely unknown nonlinear function. Prescribed-performance function is introduced and further incorporated into a novel speed function. Combining the proposed speed function and barrier Lyapunov function, this article presents a novel adaptive fuzzy prescribed-time containment control method which can guarantee, under prescribed performance, all followers converge to a convex formed by dynamic leaders in a prescribed time. Moreover, all tracking errors converge to predefined regions in a prescribed time. The effectiveness of the proposed prescribed-time containment control method are confirmed by strict proof and simulation.     

Finite-time performance guaranteed event-triggered adaptive control for nonlinear systems with unknown control direction

This paper studies the issue of finite-time performance guaranteed event-triggered (ET) adaptive neural tracking control for strict-feedback nonlinear systems with unknown control direction. A novel finite-time performance function is first constructed to describe the prescribed tracking performance, and then a new lemma is given to show the differentiability and boundedness of the performance function, which is important for the verification of the closed-loop system stability. Furthermore, with the help of the error transformation technique, the origin constrained tracking error is transformed into an equivalent unconstrained one. By utilizing the first-order sliding mode differentiator, the issue of “explosion of complexity” caused by the backstepping design is adequately addressed. Subsequently, an ingenious adaptive updated law is given to co-design the controller and the ET mechanism by the combination of the Nussbaum-type function, thus effectively handling the influences of the measurement error resulted from the ET mechanism and the challenge of the controller design caused by the unknown control direction. The presented event-triggered control scheme can not only guarantee the prescribed tracking performance, but also alleviate the communication burden simultaneously. Finally, numerical and practical examples are provided to demonstrate the validity of the proposed control strategy.     

Fixed-time adaptive fuzzy control scheme with prescribed tracking accuracy for uncertain nonlinear hysteretic systems

When the Preisach operator, a commonly used hysteresis model, is coupled with uncertain unparametrizable nonlinear dynamics of systems, its tracking control problem in particular with the demands for prescribed tracking accuracy and finite convergence time is challenging, and has not yet been solved in the existing literature. In this study, we focus on the problem, and develop a fixed-time adaptive fuzzy control scheme as a solution to it, based upon a novel decomposition of the Preisach model, the design of a robust control framework, and the integration of a direct adaptive fuzzy control approach. With our scheme, it can be rigorously proved that the tracking error goes to a predefined interval around zero in a bounded convergence time, and all signals in the closed-loop system are bounded. Besides theoretical analysis, the obtained results are also confirmed by experimental tests based on a real-life piezoactuated positioner.     

Fuzzy event-triggered control for nonlinear networked control systems

This paper is focus on an event-triggered control design problem for nonlinear networked control systems with missing data and transmission delay in the interval type-2 (IT2) fuzzy form. An event-triggered controller is presented under a sampled-state-error mechanism. By dividing the event-triggered interval into some subsets, stability analysis is carried out based on Lyapunov-Krasovskii functional (LKF), and the stability of the closed-loop system is ensured. The proposed design is applied to the continuous stirred tank reactor system (CSTR) and the manipulator system. The control strategy is effective, and the merit of the event-triggered mechanism is indicated.     

Distributed robust event-triggered adaptive control for a class of uncertain nonlinear multi-agent systems with actuator saturation

This paper studies the event-triggered consensus control problem for high-order uncertain nonlinear multi-agent systems with actuator saturation. By using a smooth Lipschitz function to approximate the saturation nonlinearity, an augment system and the Nussbaum function are adopted to deal with the residual terms of saturation nonlinearity based on adaptive backstepping method. Since excessive energy and communication resources will be consumed during the procedure to handle actuator saturation, two event-triggered mechanisms are proposed to save the communication resources and reduce the controllers’ update frequency. Whenever the triggered conditions are satisfied, the control signals transmitted to the actuators are updated and broadcasted to the neighboring area. A ’disturbance-like’ term is integrated so that the event-triggered control problem with actuator saturation can be transformed into a robust problem while the unknown disturbances are tackled by adaptive update laws. Moreover, the requirement for global communication topology known by all the agents is relaxed by introducing new estimators. All the signals in the closed-loop system are uniformly bounded and the consensus tracking errors are exponentially converged to a bounded set. Meanwhile, the Zeno behavior is excluded. Simulation results are employed to validate the advantages of our proposed methods.     

Hyperbolic tangent function-based fixed-time event-triggered control for quadrotor aircraft with prescribed performance

In this paper, the prescribed performance trajectory tracking problem of quadrotor aircraft with six degrees of freedom is addressed. Firstly, for the sake of facilitating the construction of controller, the aircraft is decomposed into position loop and attitude loop through time scale decomposition method. A fixed-time sliding mode controller is proposed to guarantee the convergence time of the aircraft system regardless of initial states. After that, to enhance security of control system, the hyperbolic tangent performance function is designed as performance index function to maintain the error within a prescribed range. Then, the event-triggered strategy is adopted to attitude subsystem which can significantly save communication resources, and the stability of control system is analyzed by Lyapunov method. In addition, the Zeno phenomenon is avoided which can be proved by ensuring the two consecutive trigger events have a positive lower limit. Finally, the validity of the constructed controller is confirmed by simulation results.     

Fuzzy adaptive output-feedback tracking control for nonlinear strict-feedback systems in prescribed finite time

The current paper addresses the fuzzy adaptive tracking control via output feedback for single-input single-output (SISO) nonlinear systems in strict-feedback form. Under the situation of system states being unavailable, the system output is used to set up the state observer to estimate the real system states. Furthermore, the estimation states are employed to design controller. During the control design process, fuzzy logic systems (FLSs) are used to model the unknown nonlinearities. A novel observer-based finite-time tracking control scheme is proposed via fuzzy adaptive backstepping and barrier Lyapunov function approach. The suggested fuzzy adaptive output feedback controller can force the output tracking error to meet the pre-specified accuracy in a fixed time. Meanwhile, all the closed-loop variables are bounded. Compared to some existing finite-time output feedback control schemes, the developed control strategy guarantees that the settling time and the error accuracy are independent of the uncertainties and can be specified by the designer. At last, the effectiveness and feasibility of the proposed control scheme are demonstrated by two simulation examples.     

Double-channel event-triggered adaptive tracking control of nonstrict-feedback nonlinear systems

This paper develops a novel way to control nonstrict-feedback nonlinear systems by using only one approximator, namely a neural network (NN) or a fuzzy logic system (FLS), in the first step of backstepping, such that the computational simplicity is ensured. The bounded property of basis functions solves the “algebraic loop” problem. The double-channel event-triggered control (ETC) is completed both in sensor-to-controller (SC) and controller-to-actuator (CA) channels, where the separate triggering conditions are fabricated. To solve the “jumps of virtual control laws (JVCL)” problem bedeviling the backstepping combined with ETC, this paper opens an avenue while guaranteeing the closed-loop stability with the aid of undetermined virtual control laws.     

Adaptive prescribed performance control for nonlinear robotic systems

This paper investigates the problem of asymptotic tracking control of nonlinear robotic systems with prescribed performance. The control strategy is developed based on a modified prescribed performance function (PPF) to guarantee the transient behavior, while the requirements on the accurate initial tracking error in the classical PPF can be remedied. The fuzzy logic system (FLS) is used to approximate the unknown dynamics. In the existing PPF based adaptive control schemes with FLSs, the tracking error does not achieve asymptotic convergence. To address this issue, a robust integral of the sign of the error (RISE) term is incorporated into the control design to reject the FLS approximation errors and external disturbances, such that the asymptotic convergence is achieved. Finally, numerical simulation and experimental results validate the effectiveness of the proposed control scheme.     

Adaptive fault-tolerant control with prescribed performance for switched nonlinear pure-feedback systems

In this paper, the problem of adaptive fuzzy fault-tolerant control is investigated for a class of switched uncertain pure-feedback nonlinear systems under arbitrary switching. The considered actuator failures are modeled as both lock-in-place and loss of effectiveness. By utilizing mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Under the framework of backstepping design technique and common Lyapunov function (CLF), an adaptive fuzzy fault-tolerant control (FTC) method with predefined performance bounds is developed. It is proved that under the proposed controller, all the signals of the close-loop systems are bounded and the state tracking error for each step remains within the prescribed performance bound (PPB) regardless of actuator faults and the system switchings. In addition, the tracking errors and magnitudes of control inputs can be reduced by adjusting the PPB parameters of errors in the first and last steps. The simulation results are provided to show the effectiveness of the proposed control scheme.     

Improved decentralized prescribed performance control for non-affine large-scale systems with uncertain actuator nonlinearity

This work considers a decentralized control problem for non-affine large-scale systems with non-affine functions possibly being discontinuous. A semi-bounded condition for non-affine functions is presented to guarantee the controllability, and the non-affine system is transformed to an equivalent pseudo-affine one based on the mild condition. Different from conventional control schemes on specific actuator nonlinearity, the controller proposed in this paper can deal with a series of actuator nonlinearities such as backlash and deadzone nonlinearity. A time-varying stable manifold involving the tracking error and its high-order derivatives is utilized to handle the high-order dynamics of each subsystem. Besides an improved prescribed performance controller independent of the initial condition is constructed to ensure the finite-time convergence of the error manifold to a predefined region. The boundedness and convergence of the closed-loop system are proved by Lyapunov theory and the counter-evidence method. Two examples are performed to verify the theoretical findings.     

Command filter-based finite-time adaptive fuzzy control for nonlinear systems with uncertain disturbance

In this paper, a command filter-based adaptive fuzzy controller is constructed for a class of nonlinear systems with uncertain disturbance. By using the error compensation signals and fuzzy logic system, a command filter-based control strategy is presented to make that the tracking error converge to an any small neighborhood of zero and all closed-loop signals are bounded. In the design procedure, fuzzy logic system is employed to estimate unknown package nonlinear functions, which avoids excessive and burdensome computations. The control scheme not only resolves the explosion of complexity problem but also eliminates the filtering error in finite-time. An example has evaluated the validity of the control method.     

An improved design strategy for approximation-based adaptive event-triggered tracking of a class of uncertain nonlinear systems

This paper presents an improved adaptive design strategy for neural-network-based event-triggered tracking of uncertain strict-feedback nonlinear systems. An adaptive tracking scheme based on state variables transmitted from the sensor-to-controller channel is designed via only single neural network function approximator, regardless of unknown nonlinearities unmatched in the control input. Contrary to the existing multiple-function-approximators-based event-triggered backstepping control results with multiple triggering conditions dependent on all error surfaces, the proposed scheme only requires one triggering condition using a tracking error and thus can overcome the problem of the existing results that all virtual controllers with multiple function approximators should be computed in the sensor part. This leads to achieve the structural simplicity of the proposed event-triggered tracker in the presence of unmatched and unknown nonlinearities. Using the impulsive system approach and the error transformation technique, it is shown that all the signals of the closed-loop system are bounded and the tracking error is bounded within pre-designable time-varying bounds in the Lyapunov sense.     

On direct adaptive control design for nonlinear discrete-time uncertain systems

In this paper, we develop a direct adaptive control framework for adaptive stabilization of the MIMO nonlinear uncertain systems, which can be represented as discrete-time normal form with input-to-state zero dynamics. The framework is Lyapunov-based and guarantees partial stability of the closed-loop systems, such that the adaptation of the feedback gains can stabilize the closed-loop system without the knowledge of the system parameters. In addition, our results show that the adaptive feedback laws can be characterized by Kronecker calculus. Two numerical examples are given to demonstrate the efficacy of the proposed framework.     

Reduced-order K-filters-based event-triggered adaptive command filtered tracking control for stochastic constrained nonlinear systems

To ensure better performance and simultaneously save resources, an event-triggered adaptive command filtered dynamic surface control (ACFDSC) method for uncertain stochastic nonstrict-feedback nonlinear systems with dynamic output constraints and prescribed performance is designed in this article. Firstly, with the help of reduced-order K-filters, linearly parameterized neural networks and specific coordinate transformation technique, the unmeasurable states, nonlinearities, two types of unmodeled dynamics and output constraints are dealt with respectively. Then, an event-triggered ACFDSC strategy is proposed to ensure that the tracking error reaches a specific bound within a finite time. By introducing the compensated signal into the complete Lyapunov function, and with the assistance of the compact set defined in the stability analysis, all signals are strictly demonstrated to be semi-globally uniformly ultimately bounded. The simulation results verify the effectiveness of the proposed method.     

New distributed adaptive protocols for uncertain nonlinear leader-follower multi-agent systems via a repetitive learning control approach

In this paper, the distributed consensus problem of leader-follower multi-agent systems with unknown time-varying coupling gains and parameter uncertainties are investigated, and the fully distributed protocols with the adaptive updating laws of periodic time-varying parameters are designed by using a repetitive learning control approach. By virtue of algebraic graph theory, Barbalat’s lemma and an appropriate Lyapunov-Krasovskii functional, it is shown that each follower agent can asymptotically track the leader even though the dynamic of the leader is unknown to any of them, i.e., the global asymptotic consensus can be achieved. At last, a simulation example is given to illustrate the feasibility and efficiency of the proposed protocols.