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An improved prescribed performance control using a backstepping technique and adaptive fuzzy is proposed for a strict feedback nonlinear dynamic system. A new virtual variable was defined to generate the virtual control that forces the tracking errors to fall within prescribed boundaries, and an adaptive fuzzy system was used to obtain required approximation performances. A strict feedback controller and adaptive laws for estimating the unknown non-linear function were designed to avoid a singularity problem and calculation of the explosive number of terms generated by the error transformations of conventional error constraint method and the recursive steps of traditional backstepping control. Lyapunov stability analysis confirmed the boundedness and convergence of the closed-loop system. The prescribed error constraint performance of the proposed control scheme was validated by applying it to control the position of a second-order non-linear system and a robot manipulator.

This article studies the dynamic neural learning issue for strict-feedback nonlinear systems with full state constraints by utilizing the nonlinear transformed function (NTF) method. To handle the issue of state constraints control, a NTF is introduced to convert the original constrained states into the equivalent unconstrained ones. For the transformed system states, a stable adaptive neural control strategy is put forward in combination with the dynamic surface technology. Subsequently, a new lemma, instead of the traditional system decomposition method, is developed to simplify the recurrent verification process of neural network (NN) inputs. Such a new lemma promotes the validation of exponential convergence for NN weight estimates in a steady-state time, and the convergent weights are stored as the learned knowledge. Moreover, a novel corollary is given to verify that the unknown system dynamics under two cases with and without state constraints are almost the same during the steady-state control process, thereby indicating the learned dynamical knowledge from the case with state constraints is also suitable for the case without state constraints. For the two cases, by reusing the learned knowledge, a neural learning controller is established for the better control performance and less online calculations. Simulation studies testify the efficacy of the developed method.

This article focuses on the prescribed-time tracking control problem for non-strict feedback nonlinear systems (NFNS) with unknown system uncertainties and external disturbances. In contrast to the previous work on finite-time and fixed-time stabilization control for a class of NFNS, the prescribed-time zero-error tracking control is realized. Firstly, the fuzzy logic system is used to handle unknown nonlinear functions. Secondly, the “complexity explosion” problem is solved in the control structure through a designed command filter and a new prescribed-time error compensation algorithm, which realizes the preset time compensation of the filter error signal to zero, and effectively eliminates the impact of the filter error signal on the system performance. Furthermore, a dynamic event-triggered mechanism (DETM) is proposed based on the co-design approach to effectively reduce the waste of communication resources and optimize network resource utilization. Meanwhile, based on the Lyapunov stability theory, it is proved that the system tracking errors will converge to zero within a prescribed time, which can be determined by the user in advance arbitrarily while avoiding the Zeno phenomenon. It is important to note that the preset time can be adjusted within the physical limits of the system, independent of the system initial conditions. Finally, the effectiveness of the proposed control method algorithm is verified by numerical simulation results and experimental studies.

A self-modified flexible prescribed performance control is proposed for a class of strict feedback nonlinear systems with input saturation, unmeasured states, and actuator faults. The proposed method introduces key functions to achieve flexible finite-time prescribed performance with global and semi-global properties by adjusting the initial value of a time-varying scaling function. In addition, this study proposes a novel finite-time auxiliary system to modify performance boundaries in the presence of input saturation, allowing for the attainment of self-modified flexible finite-time prescribed performance. To approximate unmeasured states, an RBF neural network state observer is introduced. Additionally, dynamic surface control is used to address the complexity associated with backstepping. The closed-loop system’s stability is demonstrated to be semi-globally practically finite-time stable. Comparative simulations are conducted to validate the proposed control scheme’s effectiveness.

This paper considers the problems of finite-time prescribed performance tracking control for a class of strict-feedback nonlinear systems with input dead-zone and saturation simultaneously. The unknown nonlinear functions are approximated by fuzzy logic systems and the unmeasurable states are estimated by designing a fuzzy state observer. In addition, a non-affine smooth function is used to approximate the non-smooth input dead-zone and saturated nonlinearity, and it is varied to the affine form via the mean value theorem. An adaptive fuzzy output feedback controller is developed by backstepping control method and Nussbaum gain method. It guarantees that the tracking error falls within a pre-set boundary at finite time and all the signals of the closed-loop system are bounded. The simulation results illustrate the feasibility of the design scheme.

This paper addresses the inverse optimal security control problems for a class of stochastic non-strict feedback nonlinear cyber-physical systems under sensor and actuator attacks. The concerned system model includes both stochastic disturbances and more general nonlinearity. First, to make the control design feasible, a linear state transformation is applied to the attacked system. Furthermore, in the process of backstepping design, based on the Nussbaum gain function formula, fuzzy logic system approximation method, and inverse optimal control theory, combing the available output signal, an output feedback inverse optimal controller is proposed. Specifically, the designed controller not only ensures that the system is secure under network attacks but also optimal in terms of the cost function. Finally, two physical examples are given to verify the effectiveness of the proposed control scheme in various network attacks.

This study investigates the adaptive fuzzy fault-tolerant control (FTC) problem for a class of uncertain non-linear strict-feedback systems with unmeasured states. The considered non-linear systems contain unknown continuous functions and do not satisfy the matching condition. The actuator failures under study are types of both abrupt faults and lock-in-place and loss of effectiveness. The fuzzy logic systems are employed to approximate the unknown continuous functions, and a fuzzy state observer is developed and the unmeasured states are obtained. Under the framework of the backstepping design technique and incorporated by the dynamic surface control approach and predefined performance bounds, an adaptive fuzzy FTC method has been presented. From the Lyapunov stability analysis, it is shown that all the signals of the resulting closed-loop system are bounded and the tracking error surfaces remain within the prescribed performance bounds in the presence of unknown non-linear actuator faults. The simulation results and comparisons with the previous methods indicate the effectiveness of the proposed adaptive fuzzy FTC.

The predefined-time fuzzy adaptive output feedback control problem is considered for non-strict feedback stochastic nonlinear systems with state constraints. Since the controlled plant contains unknown nonlinear dynamics and unmeasured states, the unknown nonlinear dynamics are handled by using fuzzy approximation technique, and a fuzzy state observer is established to estimate unmeasured states. Then, under the frameworks of a predefined-time stability theory and backstepping control design technique, a new fuzzy adaptive output feedback control method is proposed. It is proved that the controlled system is semi-global practically predefined-time stable in probability by constructing suitable barrier Lyapunov functions. Finally, the spring–mass–damper system is given to confirm the effectiveness of the presented control method.

An event-triggered (ET) neural-networks (NNs) adaptive output-feedback control approach is proposed for a class of input-saturated strict-feedback nonlinear systems with external disturbance. Compared with overall existing event-triggered control strategies, which are free from control input nonlinearities and suffer from the explosion of complexity, the proposed event-triggered-based NNs controller is able to handle system input saturation along with completely avoiding the complexity explosion problem. First, by introducing alternative state variables, and by implementing a low-pass filter, the difficulty arising from the cascading of the input-saturated strict-feedback system has been avoided. Thus, the system is converted to the normal canonical system, for which the controller synthesis is much simpler without resort to traditional back-stepping approach. Then, an observer is adopted to estimate the unknown states of the newly derived canonical system based on strictly positive real theory. In the design procedure, the unknown nonlinear functions are approximated by NNs to design a baseline controller, for which an additional robust term is embedded to deal with the input saturation nonlinearity, unknown disturbances and approximation errors using only two adaptive parameters. The proposed ET adaptive NNs control scheme is shown to guarantee the convergence of the output of the system to a small neighborhood of the origin along with the boundedness of all signals in the closed loop. Finally, simulation examples are presented to show the effectiveness of the proposed controller.

This paper proposes a novel scheme to investigate the adaptive optimal tracking control problem of a class of strict-feedback nonlinear system via adaptive dynamic programming (ADP). First of all, by employing backstepping technique, a tracking error system is established. Then, the solution to adaptive optimal tracking control problem of strict-feedback nonlinear system is shown to be obtainable by solving the optimal regulation problem of established tracking error system. The solution of optimal regulation problem can be found by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. In order to solve the HJB equation, a neural network (NN)-based online ADP algorithm is provided. To relax traditional Persistence of Excitation (PE) conditions, the historical and instantaneous state data are used to deign the NN weights tuning law simultaneously. In the provided ADP algorithm, the optimal control input is calculated in a forward-in-time manner without requiring any value or policy iterations. Based on the Lyapunov theory, we demonstrate that uniform ultimate boundedness (UUB) of all the signals in the closed-loop system are guaranteed. Application to the adaptive optimal tracking control of a nonholonomic mobile robot system demonstrates the efficacy of the provided ADP scheme. The designed ADP scheme achieves good tracking performance under different reference signals.