Nonstrict-feedback Form Research Articles

Adaptive finite-time neural control of nonstrict-feedback nonlinear systems with input dead-zone and output hysteresis

This paper explores the adaptive finite-time neural control issue for nonlinear systems with input dead zone and output hysteresis in nonstrict-feedback form. The unknown functions are estimated by employing the radial basis function neural networks (RBFNN) approach. A systematic adaptive finite-time control method is introduced using the backstepping technique and neural network approximation properties. The stability of the system is also examined by using semi-global practical finite-time stability theory. The established control approach guarantees the boundedness of all signals within the closed-loop system, enabling the system output to accurately follow the desired signal within a finite time framework while maintaining a small and bounded tracking error. Finally, simulation results are shown to demonstrate the efficacy of the suggested strategy.

Decentralized fuzzy DSC for uncertain large-scale interconnected switched systems in non-strict feedback form with input saturation

This paper demonstrates a fuzzy decentralized dynamic surface control (DSC) scheme for switched large-scale interconnected nonlinear systems under arbitrary switching, which contains non-strict feedback form and unknown input saturation uncertainties. An auxiliary design system is established to handled input saturation. Uncertainties of non-strict feedback form are learned by fuzzy logic systems (FLSs) approximators, DSC method is designed to conquer “explosion of complexity” inherented by repeated differential of virtute controller in backstepping approach. Ii is shown that based on common Lyapunov function (CLF) design and analysis scheme, all the closed-loop systems signals are uniformly ultimately bounded (UUB), simulation results are provided to demonstrate the effectiveness of this proposed strategy.

Practical fixed-time neural control for MIMO non-strict feedback nonlinear systems: an adaptive neural network approach

ABSTRACT This paper studies the non-singular practical fixed-time neural adaptive control issues for multi-input and multi-output (MIMO) nonlinear systems with non-strict feedback form. Neural networks (NN) are used to estimate the unknown nonlinearities and deal with the problem of an algebraic loop. Under the framework of the backstepping control design, a practical fixed-time adaptive NN control method is developed by using the adding power integration technology. According to the Lyapunov function theory, it is proved that the closed-loop system is practical fixed-time stable, and the system can track the desired reference signal within a fixed time. Finally, the proposed practical fixed-time control method is applied to a multi-motor control platform, which proves the effectiveness of the control method.

Adaptive Neural Finite-Time Control of Non-Strict Feedback Nonlinear Systems With Non-Symmetrical Dead-Zone.

The control design method for a class of non-strict feedback nonlinear systems is studied in this brief considering uncertain nonlinearities and unknown non-symmetrical input dead-zone. Combining with the finite-time command filtered backstepping (FCFB) technique, a novel finite-time adaptive control approach is proposed in which a neural network-based methodology is adopted to cope with the uncertain nonlinearities in the non-strict feedback form. The input dead-zone model is transformed into a simple linear system with unknown gain and bounded disturbance which is estimated by an adaptive factor. Using the finite-time Lyapunov theory, the system convergence is proved. And the effectiveness of the proposed control scheme is verified through comparative numerical simulations.

Adaptive actor‐critic neural optimal control for constrained nonstrict feedback nonlinear systems via command filter

AbstractThe actor‐critic neural optimal control is investigated for the state‐constrained nonlinear systems in the nonstrict feedback form with unmodeled dynamics in this paper. The filtering errors in the traditional dynamic surface control (DSC) are countervailed by the introduced compensation signals. Two design phases together determine the input: the feedforward input design and the near optimal input design. In the feedforward input design, a mapping rule is established to keep all the states in the finite range, and a first‐order adjunctive signal is designed to treat the unmodeled dynamics. In the near optimal input design, the cost function relying on the reconstructed error system is minimized by the near optimal input via adaptive dynamic programming (ADP). In the whole design processing, the unknown nonlinear uncertain parts are fitted by the radial basis function neural networks (RBFNNs). The stability analysis illustrates all the signals are bounded in the controlled system. Two simulation examples are employed to verify the theoretical findings.

Adaptive neural dynamic surface control with fixed-time prescribed performance for uncertain nonstrict-feedback stochastic switched systems

An adaptive neural dynamic surface control (DSC) problem with fixed-time prescribed performance (FTPP) is investigated for a class of nonstrict-feedback stochastic switched systems. Differently from the existing works for FTPP problem, the stochastic switched systems with nonstrict-feedback form and completely unknown systems are considered in this paper, and the unknown functions are approximated by some radial basis function (RBF) neural networks (NNs). The desired adaptive neural controller is designed by using common Lyapunov function method and defining fixed-time prescribed performance function (PPF). And based on the adaptive DSC scheme with the nonlinear filter, the “explosion of complexity” problem is avoided. Besides, the constructed fixed-time PPF just need to meet the requirement of second derivative exists. According to the Lyapunov stability theory, the FTPP of output tracking error is achieved, and all signals of closed-loop system remain bounded in probability. Finally, simulation results are presented to verify the availability of the designed control strategy.

Adaptive Neural Control of Nonlinear Nonstrict Feedback Systems With Full-State Constraints: A Novel Nonlinear Mapping Method.

In this work, a neural-networks (NNs)-based adaptive asymptotic tracking control scheme is presented for a class of uncertain nonstrict feedback nonlinear systems with time-varying full-state constraints. First, we construct a novel exponentially decaying nonlinear mapping to map the constrained system states to new system states without constraints. Instead of the traditional barrier Lyapunov function methods, the feasible conditions which require the virtual control signals satisfying the constraint requirements are removed. By employing the Nussbaum design method to eliminate the effect of unknown control gains, the general assumption about the signs of the unknown control gains is relaxed. Then, the nonstrict feedback form of the system can be pulled back to the strict feedback form through the basic properties of radial basis function NNs. Simultaneously, the intermediate control signals and the desired controller are constructed by the backstepping process and the Nussbaum design method. The designed controller can ensure that all signals in the whole closed-loop system are bounded without the violation of the constraints and hold the asymptotic tracking performance. In the end, a practical example about a brush dc motor driving a one-link robot manipulator is given to illustrate the effectiveness of the proposed design scheme.

Distributed event-triggered output-feedback synchronized tracking with connectivity-preserving performance guarantee for nonstrict-feedback nonlinear multiagent systems

In this paper, we present a connectivity-preserving performance function approach for the distributed output-feedback synchronized tracking of uncertain heterogeneous nonlinear multiagent systems in a nonstrict-feedback form. Compared with existing output-feedback cooperative control results using neural networks, this paper contributes to developing a universal output-feedback synchronized control methodology that uses a connectivity-preserving performance function to ensure both initial network connectivity and preselected synchronization performance with a designable convergence time. To this end, a neural-network-based adaptive observer for each follower is designed to ensure the boundedness of estimation errors of unmeasurable states. Then, local event-triggered synchronized trackers using only relative output information and the connectivity-preserving performance function are constructed to guarantee the closed-loop stability in a low-complexity sense, where no adaptive neural networks and command filters are not required in the local trackers. Finally, a purely academic example and a practical platoon-control problem of multiple uncertain vehicular systems are considered to clarify and verify the proposed connectivity-preserving performance function approach in the simulation.

Adaptive neural quantized control for fractional-order full-state constrained non-strict feedback systems subject to input fault and nonlinearity

In this work, an adaptive neural network (NN)-based quantized fault-tolerant controller (FTC) has been designed for incommensurate fractional-order (FO) nonlinear systems (NSs) in the non-strict feedback form subject to independent asymmetric time-varying full-state constraints, input quantization, unknown dynamics, infinite number of actuator faults and unknown input nonlinearities. It is assumed that the controller communicates with the actuator via a network with limited bandwidth. To avoid network congestion, the control signal is first quantized by an asymmetric hysteresis quantizer (HQ), then transmitted to the actuator via the network. By incorporating the backstepping algorithm, barrier Lyapunov functions (BLFs) and fractional direct Lyapunov stability (FDLS) theorem, a novel method has been proposed to design a control scheme for FO state constrained NSs and establish the closed-loop stability. In this method, the Lyapunov function of each step of the backstepping algorithm is chosen based on the BLF and parameter estimation error of the considered step and their boundedness is shown from the last step to the first one. Under the proposed control approach, the full-state constraints are met, the tracking error can be made small by selecting proper design parameters and all closed-loop signals remain bounded. Finally, three simulation examples have been provided to demonstrate the designed controller effectiveness.

Adaptive Fuzzy Asymptotic Tracking for Nonlinear Nonstrict-feedback Systems With Input Quantization

This article investigates an adaptive fuzzy tracking control problem for the nonlinear nonstrict-feedback systems with quantized input. The control signal has a new transformation since a time varying auxiliary signal and a hyperbolic tangent function are introduced to the controller. Moreover, a novel adaptive fuzzy control scheme is proposed such that input quantization can be solved by applying hysteresis quantizer in the case of unknown quantization parameters. For traditional adaptive quantization control schemes with nonstrict-feedback form, current studies have shown that the tracking error can only converge to a small neighborhood of the origin. Based on the proposed control method, all the signals in the closed-loop system are bounded, and the tracking error can converge to zero asymptotically. Finally, the effectiveness of the presented method is shown via the numerical simulation results.

Distributed adaptive bipartite consensus tracking of high-order nonstrict-feedback nonlinear multi-agent systems

This paper is concerned with the problem of adaptive bipartite tracking problem for multi-agent systems (MASs) over signed directed graphs with unknown nonlinear functions. Each following agent is modelled by a higher-order nonlinear system in nonstrict-feedback form. The virtual and the actual control items of the considered system are the power functions with positive odd integers rather than linear items. A distributed neural-based adaptive backstepping scheme is proposed, where the unknown nonlinear dynamics are approximated by Neural networks. Under the proposed protocol, the bipartite output tracking errors converge to a small neighbourhood of the origin and all the signals of the closed-loop system remain semiglobally uniformly ultimately bounded. Since the considered high-order non-strict feedback nonlinear MASs in our paper include some existing nonlinear MASs as the special case, our result can be extended to control more general nonlinear MASs. Finally, the simulation results illustrate the validity of the proposed schemes by a numerical example and a practical example about a group of forced damped pendulums.

Command-Filter-Based Fixed-Time Bipartite Containment Control for a Class of Stochastic Multiagent Systems

This article studies the command-filter-based fixed-time bipartite containment control problem for a class of nonlinear stochastic multiagent systems (MASs). The considered stochastic MASs in nonstrict feedback form is subject to unknown nonlinear functions and stochastic disturbances, which can be solved by exploiting the universal approximation property of radial basis function neural networks. In addition, the event-triggered mechanism is used to improve the utilization of communication resources while avoiding Zeno behavior. The control protocol based on the command-filtered backstepping technique is proposed to ensure that the followers can converge to the convex hull formed by the leaders. Moreover, the closed-loop stability of stochastic MASs is proved to be semiglobal practical fixed-time stability. Finally, a numerical example simulation and an actual system simulation about a group of five single-link manipulator systems are presented to verify the effectiveness of the proposed method.

A Novel Distributed Bipartite Consensus Control of Nonlinear Multiagent Systems via Prioritized Strategy Approach

In this brief, the adaptive bipartite consensus tracking problem is considered for nonlinear MASs over signed directed graphs with unknown nonlinear functions in high-order and nonstrict-feedback form. By proposing a prioritized strategy, a more relaxation condition that a signed digraph only containing a spanning tree is used in this brief, and all the agents in the system can be achieved a bipartition. Besides, it is worth pointing out that the higher-order form and the nonstrict-feedback structure are a part of the each follower model, which makes the controller design process more complicated. A distributed neural-based adaptive backstepping technology is applied, where the unknown nonlinear functions are approximated by Neural networks (NNs). Under the proposed protocol, all the agents achieve the bipartite consensus with bounded errors. The feasibility of the newly designed method are verified by MATLAB simulation analysis.

Finite-time adaptive neural command filtered control for non-strict feedback uncertain multi-agent systems including prescribed performance and input nonlinearities

In this paper, the issue of finite-time consensus tracking control (CTC) is discussed for uncertain nonlinear multi-agent systems (MASs) with prescribed performance and input saturation. By constructing a finite-time performance function (FTPF), the tracking errors converge to a predefined attenuation range within finite-time. By using tanh(·) function and mathematical transformation, the effect of input saturation is solved. The unmodeled dynamics and dynamic disturbances of the system are solved by means of measurable dynamic signals. Through the Young’s inequality and the properties of Gaussian function, the coupling problem between multi-agents and the system controller design problem in non-strict feedback form are successfully dealt with. Furthermore, a finite-time adaptive neural controller is designed based on command filter, which not only guarantees the finite-time stability of the system, but also makes the tracking errors reach a predefined bound in a finite-time. Stability analysis proves that the proposed method is feasible, and simulation verifies its effectiveness.

Fixed-Time Fuzzy Adaptive Tracking Control for Output-Constrained Uncertain Nonlinear Systems in Nonstrict-Feedback Form

Fixed-Time Fuzzy Adaptive Tracking Control for Output-Constrained Uncertain Nonlinear Systems in Nonstrict-Feedback Form

Command filtered fixed‐time control for a class of multi‐agent systems with sensor faults

AbstractIn this article, the command filtered fixed‐time fault‐tolerant control (FTC) problem is investigated for multi‐agent systems (MASs). The considered MASs with nonstrict feedback form are affected by unknown nonlinear functions and sensor faults, which are solved by using the properties of neural networks (NNs). In the design process, in order to avoid the “singularity” and “explosion of complexity” problems, an adaptive command filtered fixed‐time NN fault‐tolerant controller is devised. Based on the Lyapunov stability theory, all output signals of leader and followers in the closed‐loop system are synchronized within fixed time. Finally, the effectiveness of the proposed control scheme is verified by simulation experiments.

Adaptive intelligent-estimation-based tracking controller design strategy for switched nonlinear systems with unmodeled dynamics and an output constraint

This paper focuses on the intelligent-estimation-based tracking controller design problem for a class of switched non-lower triangular nonlinear systems with unmodeled dynamics and an output constraint. It should be pointed out that the design process of controller is quite difficult due to the existence of unmodeled dynamics and switched events in the system, hence some sophisticated and delicate mathematical theories and design techniques need to be adopted. In our proposed design procedure, the structural feature of Gaussian functions is utilized to conquer the obstruction of nonstrict-feedback form. Furthermore, the difficulties resulted from the unmodeled dynamics are solved by the established dynamic signal Based on the above technical algorithm, the results can be obtained as follows: (a) All signals in the switched closed-loop system are bounded. (b) The output of the system fluctuates in a small neighborhood near the reference signal without the violation of the output constraint. Finally, the simulation results are provided to verify the potency of the developed approach.

Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control

In this paper, a generalized nontriangular normal form is presented to facilitate designing a recursive integral backstepping control for the class of underactuated nonholonomic systems, i.e., wheeled mobile robots (WMRs) that perform posture stabilization and trajectory tracking in environments without obstacles. Based on the differential geometry theory, we develop a multiple input multiple output (MINO) generalization of normal form using the input-output feedback linearization technique. Then, the change of variables (diffeomorphism) transform the state-space model of WMR, incorporating both kinematic and dynamic models into nontriangular normal form. As a result, the system dynamics can be represented as internal and external dynamics. The nonlinear internal dynamics of WMR pose serious challenges to design a suitable controller due to its internal dynamics being not minimum phase and non-strict feedback form structure. The proposed backstepping controller is designed in two steps. First, a standard integral backstepping controller is designed to stabilize the robot’s orientation angle. Then, a recursive integral backstepping control technique is applied to achieve asymptotic convergence of position error to zero. Hence, both asymptotic posture stabilization and trajectory tracking are achieved in semi-global regions, except the nonzero initial condition of the orientation angle. The asymptotic stability of the entire closed-loop system is shown using the Lyapunov criteria.

Adaptive control design for uncertain switched nonstrict-feedback nonlinear systems to achieve asymptotic tracking performance

In this paper, the adaptive asymptotic tracking control issue is addressed for uncertain switched nonlinear systems with nonstrict-feedback form under the dynamic surface control (DSC) framework. In contrast to most traditional control schemes that can only achieve bounded error tracking performances, the proposed control method in this paper can make the switched systems with unknown nonlinear functions achieve an asymptotic tracking performance. It is completed by introducing nonlinear filters with a compensation term to remove the boundary layer error stemming from using linear filters in the DSC process. Meanwhile, the approximation error caused by the use of radial basis function (RBF) neural networks (NNs) is compensated by an online updated parameter. Furthermore, the nonstrict-feedback form is handled by adopting the inherent properties of RBF NNs. Then, in terms of the backstepping technique and the common Lyapunov function (CLF) approach, the desired control law with only two adaptive laws is set up. Finally, the validity of the developed strategy is verified via simulation results.

Adaptive fuzzy constraint control for switched nonlinear systems in nonstrict feedback form

SummaryIn this paper, the adaptive fuzzy controller design problem is investigated for a class of switched nonlinear systems in nonstrict feedback form, in which the unknown functions are considered and are approximated. Moreover, the system states are constrained in corresponding compact. By using Barrier Lypunov function method and backstepping technique, the adaptive fuzzy controller is designed such that all the signals in the closed‐loop system are bounded, the system output can track the desired signal to small compact, and all the system states satisfy the constraint conditions. Finally, the simulation results show the effectiveness of the proposed method.