Observer-based Adaptive Controller Design for Nonlinear Saturation Systems With Output Constraints

Adaptive fuzzy dynamic surface control of nonlinear systems with input saturation and time-varying output constraints

This paper considers the adaptive neuro-fuzzy control scheme to solve the output tracking problem for a class of strict-feedback nonlinear systems. Both asymmetric output constraints and input saturation are considered. An asymmetric barrier Lyapunov function with time-varying prescribed performance is presented to tackle the output-tracking error constraints. A high-gain observer is employed to relax the requirement of the Lipschitz continuity about the nonlinear dynamics. To avoid the "explosion of complexity", the dynamic surface control (DSC) technique is employed to filter the virtual control signal of each subsystem. To deal with the actuator saturation, an additional auxiliary dynamical system is designed. It is theoretically investigated that the parameter estimation and output tracking error are semi-global uniformly ultimately bounded. Two simulation examples are conducted to verify the presented adaptive fuzzy controller design.

This paper presents an adaptive neural tracking control approach for uncertain stochastic nonlinear time‐delay systems with input and output constraints. Firstly, the dynamic surface control (DSC) technique is incorporated into adaptive neural control framework to overcome the problem of ‘explosion of complexity’ in the control design. By employing a continuous differentiable asymmetric saturation model, the input constraint problem is solved. Secondly, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time‐delay terms, RBF neural network is utilized to identify the unknown systems functions, and barrier Lyapunov functions (BLFs) are designed to avoid the violation of the output constraint. Finally, based on adaptive backstepping technique, an adaptive neural control method is proposed, and it decreases the number of learning parameters. Using Lyapunov stability theory, it is proved that the designed controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two simulation examples are provided to further illustrate the effectiveness of the proposed approach.

The control performance of quadrotor unmanned aerial vehicles (UAVs) in complex environments can be affected by external disturbances and other factors. In this paper, an adaptive neural network backstepping controller based on the barrier Lyapunov function (BLF) is designed for a quadrotor UAV with internal uncertainties, input–output constraints and external disturbances. Radial basis function neural networks are used to approximate the uncertainties in the dynamic model of the UAV, while the minimum parameter learning method is combined to accelerate the adjustment speed of neural network weights. A robust term is designed to balance the total system disturbance and improve the anti-interference performance. The BLF is used to handle the output constraint so that the constrained parameters cannot break the predefined constraints. An auxiliary system is introduced to solve input saturation and avoid the dependence of tracking error on the input amplitude in the method of approximating input saturation using the smoothing function. The stability of the control system is demonstrated by the Lyapunov method. The simulation results show that the proposed method has high tracking accuracy compared with the backstepping dynamic surface control method, and the input and output are in the predefined range.

In this work, considering the influence of input saturation and time-varying output constraints, an adaptive neural networks force/position control method is proposed for a class of uncertain robotic manipulators in contact with the external environment. Radial basis function neural networks are introduced to approximate the system uncertainty and only one parameter needs to be updated online. The output constraints are satisfied by converting the constrained system to an unconstrained one. Moreover, an auxiliary dynamic system is applied in the transformed unconstrained system to handle the input saturation nonlinearity and the Moore–Penrose pseudo-inverse term is introduced for controller design. All signals in the closed-loop system are proved to be bounded by using the Lyapunov method. To show the good performance of the given scheme, comparative simulation is conducted on a two-joint manipulator, which is controlled by the proposed adaptive neural networks force/position tracking controller and a conventional force/position controller without considering input saturation and output constraints. Simulation results show that the adaptive neural network force/position controller has better control performance than the traditional method.

This article addresses the adaptive tracking control problem of tethered aircraft systems subject to airflow disturbances, output constraints and actuator nonlinearities of saturation, dead-zone, and fault. By combining the nonlinear reconstruction model of the actuator, composed of the ideal and actual reconstruction forms, with the auxiliary system containing a saturation function, the controller design difficulty incurred by actuator nonlinearities is solved. Meanwhile, to guarantee the normal operation of the system under input saturation and output constraints with excessively large initial output values, the constraint function and the auxiliary system building the bridge between input saturation and output constraints are simultaneously introduced to modify the output constraint boundary. Furthermore, considering airflow disturbances, uncertainties and actuator faults in systems, extended state observers are designed to estimate the lumped disturbance. Then, an adaptive tracking controller is proposed to guarantee the outputs meet the modified constraints, and all signals in the closed-loop system are bounded. Finally, the simulation results demonstrate the effectiveness of the proposed controller.

This article investigates the problem of unified output constraints for a class of uncertain interconnected nonlinear systems, where the measurement of system states is affected by unknown drifts in the powers of the measurement functions. Compared to previous works on output constraints, the main challenge addressed in this article is the unavailability of the true system states during the controller design process and the nondifferentiability of the sensor's output functions. To achieve the control objectives, the following control scheme is proposed in this study. First, a novel barrier Lyapunov function is introduced, which is specifically designed to handle systems with unknown measurement drifts. This function can be uniformly applied to satisfy both scenarios of systems with or without output constraints. Second, the adding a power integrator (AAPI) technique and dynamic surface control (DSC) techniques are enhanced to effectively handle the unknown measurement drifts and avoid singularity problems in the controller design. The decentralized controller proposed in this article can realize that the outputs are strictly constrained within predefined boundaries and guarantees convergence of all system states to an arbitrarily small neighborhood. Finally, we provide two simulation examples to validate the effectiveness of our proposed control strategy.

In this paper, robust adaptive control problem is discussed for a class of output feedback nonlinear switched systems with unmodeled dynamics and time-varying constraints. Based on the common Lyapunov function (CLF), an adaptive output feedback dynamic surface control (DSC) scheme is developed. Radial basis function neural networks are utilized to approximate unknown continuous functions, and K-filters and a dynamic signal are designed to estimate the unmeasured states and deal with the dynamic uncertainty. An asymmetric barrier Lyapunov function (ABLF) is introduced to handle output constraint. It is proved that the designed controller can guarantee the semi- global uniform ultimate boundedness (SGUUB) for all the signals in the closed-loop system under arbitrary switchings. The simulation results are provided to demonstrate the effectiveness of the proposed method.

This paper presents a neural adaptive controller for a class of nonlinear system in the presence of input saturation and arbitrary unknown information by integrating the design framework of neural networks (NNs) with the dynamic surface control (DSC) and backstepping technique. NNs are directly used to deal with unknown nonlinear terms. By introducing a well-defined smooth function and a Nussbaum function, a novel robust adaptive control scheme is developed to guarantee the states of system to be semi-globally uniformly ultimately bounded (SGUUB). Owing to the introduction of DSC, the problem of ‘explosion of complexity’ inherent in the backstepping design is effectively eliminated. Simulation results demonstrate the effectiveness and simplicity of the proposed method.

Disturbance observer-based adaptive neural control for underactuated surface vehicle with constraint of input saturation

This paper studies the problem of finite-time fuzzy adaptive dynamic surface control (DSC) design for a class of single-input and single-output (SISO) high-order nonlinear systems with output constraint. Fuzzy logic systems (FLSs) are utilized to identify the unknown smooth functions. By adopting Barrier Lyapunov function (BLF), the problem of output constrain is handled. Combining adding a power integrator and adaptive backstepping recursion design technique, a novel fuzzy adaptive finite-time DSC algorithm is proposed. Based on finite-time Lyapunov stable theory, the developed control algorithm means that all the signals of the closed-loop system are semi-global practical finite-time stable (SGPFS) and the tracking error converges to a small neighborhood of origin in finite time. In addition, the output does not violate the given constrain bound. Finally, both numerical and practical simulation examples are given to illustrate the effectiveness of the proposed control algorithm.

Adaptive control for hypersonic vehicle with input saturation and state constraints

This paper addresses the problem of adaptive output feedback control for a class of non-triangular time-varying delay system with input constraints and full-state constraints. A variable separation approach is adopted to overcome the design difficulty from the non-triangular structure. A novel Lyapunov function is introduced to compensate the time-delay terms. Unknown functions are approximated by the radial basis function neural networks. Only one parameter needs to be adjusted online, and a dynamic surface control technique is employed to reduce the computation burden. Combining the barrier Lyapunov function with a backstepping technique in the controller design procedure, the proposed controller guarantees that all the signals in the closed-loop system are uniformly ultimately bounded and the full-state constraints are met. The simulation results demonstrate the effectiveness of the proposed approach.

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

This paper focuses on the problem of the event-triggered adaptive containment control for a class of nonlinear multiagent systems (MASs) with prescribed performance and immeasurable states. First, the radial basis function neural networks (RBFNNs) are adopted to approximate the uncertain smooth nonlinear function, and the neural network-based state observer is designed to estimate the unmeasurable state. Besides, to reduce the control resource consumption and get a better balance between the system performance and network constraints, the switching threshold-based event-triggered control strategy is introduced. Based on this, the novel distributed containment controller is designed by utilizing the adaptive backstepping technique and the dynamic surface control (DSC) technique to guarantee that the output of each follower converges to the convex hull formed by multileader. Moreover, the containment errors can be converged to the prescribed boundary and all signals in closed-loop system are semi-global uniformly ultimately bounded (SGUUB) as well. Finally, the simulation examples are carried out to illustrate the efficiency of the proposed controller.