Adaptive Neural Dynamic Surface Control With Prespecified Tracking Accuracy of Uncertain Stochastic Nonstrict-Feedback Systems

Multicontact Safety-Critical Planning and Adaptive Neural Control of a Soft Exosuit Over Different Terrains

Many previous works on wearable soft exosuits have primarily focused on assisting human motion, while overlooking safety concerns during movement. This article introduces a novel single-motor, altering bi-directional transfer soft exosuit based on impedance optimization and adaptive neural control, which provides assistance to the lower limbs using Bowden cables. This innovative soft exosuit integrates control barrier functions into the impedance optimization, allowing multiple safety constraints to be considered simultaneously, enabling the system to adaptively learn the impedance of the human ankle joint by analyzing the measured interaction forces at the ankle joint, so that the updated reference trajectories comply with safety requirements. To effectively track the updated reference trajectories, we have introduced an adaptive neural controller based on the integral barrier Lyapunov function. This controller is designed to perform the control task under strict safety constraints. The stability of this control approach is meticulously demonstrated through extensive Lyapunov analysis. In contrast to traditional soft exosuits designed purely for assistance, the key advantage of this technology is its ability to adapt to different terrains while ensuring the safety of human movement during assistance. Through experimental testing, we obtain average tracking errors of 0.0062, 0.0062, and 0.0063 rad for flat, grass, and gravel surfaces, respectively, demonstrating the effectiveness of the proposed strategy.

Adaptive neural fault-tolerant tracking control for state-constrained systems subject to multiple power drift faults

The adaptive neural fault-tolerant control (FTC) for state-constrained systems containing novel sensor and actuator faults is investigated in this article. This work considers not only common actuator bias and gain faults, but also a novel type of fault caused by the power drift of system, namely the power drift faults. In addition, sensor faults in the form of unknown power drifts are also considered in this work. To compensate the impact of multiple power drift faults, a novel controller is established by introducing new auxiliary signals. The radial basis function neural networks (RBFNNs) are employed to resolve some uncertain functions and reduce the computational complexity. By combining the backstepping approach and barrier Lyapunov functions, a new adaptive FTC algorithm is developed. Based the presented controller, all signals in this system remain semi-globally bounded and the control error is guided to a small range near zero. Simultaneously, system constraints are not violated. At last, a simulation experiment is performed to confirm the validity and feasibility of the developed algorithm.

Event-triggered adaptive compensation control for stochastic nonlinear systems with multiple failures: An improved switching threshold strategy

This paper considers the event-triggered adaptive fault-tolerant control (FTC) problem for a class of stochastic nonlinear systems suffering from finite number of actuator failures and abrupt system external failure. Unlike existing event-triggered mechanisms (ETMs), this paper proposes an improved switching threshold mechanism (STM) that effectively addresses the potential system security hazards caused by large signal impulses when both the magnitude size of the controller and its rate of change are too large, while also saving energy consumption. Especially, when the occurrence of both actuator failure and system external failure may lead to over-change rate of the controller, by using the multi-dimensional Taylor network (MTN) approximation technique, the adaptive fault-tolerant control scheme designed based on the improved STM not only has lower resource consumption, but also indirectly improves the control performance of the system by ensuring the system security operation. Not only does it ensure that all signals of the closed-loop system are bounded in probability and the tracking error converges through the proposed control scheme. The feasibility and superiority of the developed scheme is well shown by dynamic model simulations.

Dual Flexible Prescribed Performance Control of Input Saturated High-Order Nonlinear Systems

This article first presents a dual flexible prescribed performance control (DFPPC) approach of input saturated high-order nonlinear systems (IS-HONSs). Compared to the existing PPC approaches of IS-HONSs, under which the performance constraint boundaries (PCBs) are usually fixed and bounded, resulting in a restriction of the initial error in the algorithm implementation; in addition, the coupling relationship between performance constraints and input saturation is usually ignored, resulting in the methods are very fragile when input saturation occurs. By designing the novel tensile model-based PCBs that depend on output and input constraints, the proposed DFPPC method provides sufficient resilience for both the initial conditions and the input saturation, so that the proposed DFPPC method can not only be suitable for multiple types of initial errors by adjusting the parameters, including , , and , where , and denote the initial PCBs; but also can achieve a good balance between input saturation and performance constraints, i.e., when the control input reaches or exceeds the saturation threshold, the PCBs can adaptively extend to avoid the singularity, and when the control input returns to the saturation threshold range, the PCBs are then adaptively restored to the original PCBs. The results show that the proposed DFPPC algorithm guarantees semi-global boundedness for all closed-loop signals, while ensuring that the system output accurately tracks the desired signal, and it consistently maintains the tracking error within the PCBs. The developed algorithm is illustrated by means of simulation instances.

Stochastic Neural Network Control for Stochastic Nonlinear Systems With Quadratic Local Asymmetric Prescribed Performance

This article presents an adaptive neural network control scheme with prescribed performance for stochastic nonlinear systems. Unlike existing adaptive stochastic control schemes that primarily utilize deterministic neural networks for approximations in complex stochastic environments, we employ stochastic neural networks to approximate the stochastic nonlinear terms, effectively resolving the "memory overflow" issue. Moreover, we propose a novel prescribed performance design method, which distinguishes itself from the previous prescribed performance control schemes by integrating a quadratic characteristic capable of suppressing transient input vibrations, along with a local asymmetric characteristic that optimize both transient output overshoot and steady-state error bias. Furthermore, the proposed control scheme is implemented within a fixed-time framework to ensure that all closed-loop systems are fixed-time bounded in probability, with the tracking error consistently within the predefined performance bounds. Simulation results validate the effectiveness of the proposed control scheme.

Tracking control problem of nonlinear strict-feedback systems with input nonlinearity: An adaptive neural network dynamic surface control method

In this work, the tracking control problem for a class of nonlinear strict-feedback systems with input nonlinearity is addressed. In response to the influence of input nonlinearity, an auxiliary control system is constructed to compensate for it. To process unknown nonlinear dynamics, radial basis function neural networks (RBFNNs) are introduced to approximate them, and some adaptive updating control laws are designed to estimate unknown parameters. Furthermore, during the dynamic surface control (DSC) design process, first-order low-pass filters are introduced to solve the complexity explosion problems caused by repeated differentiation. After that, an NN-based adaptive dynamic surface tracking controller is proposed to achieve the tracking control. By applying the proposed controller, it can be guaranteed that not only the output of the system can track the desired trajectory, but also that the tracking error can converge to a small neighborhood of zero, while all signals of the closed-loop system are bounded. Finally, the effectiveness of the proposed controller is verified through two examples.

Predefined Accuracy Adaptive Tracking Control for Nonlinear Multiagent Systems With Unmodeled Dynamics

This article focuses on an adaptive dynamic surface tracking control issue of nonlinear multiagent systems (MASs) with unmodeled dynamics and input quantization under predefined accuracy. Radial basis function neural networks (RBFNNs) are employed to estimate unknown nonlinear items. A dynamic signal is established to handle the trouble introduced by the unmodeled dynamics. Moreover, the predefined precision control is realized with the aid of two key functions. Unlike the existing works on nonlinear MASs with unmodeled dynamics, to avoid the issue of "explosion of complexity," the dynamic surface control (DSC) method is applied with the nonlinear filter. By using the designed controller, the consensus errors can gather to a precision assigned a priori. Finally, the simulation results are given to demonstrate the effectiveness of the proposed strategy.

Prescribed Performance Fault-Tolerant Control of Strict-Feedback Systems via Error Shifting

This article investigates the prescribed performance control (PPC) problem for a class of nonlinear strict-feedback systems with sensor/actuator faults. A shifting function is introduced to modify the output tracking error generated by the practically measured system state, based on which an improved PPC method is proposed to achieve the convergence of output tracking error to the prescribed region, and this convergence is shown to be independent of the initial tracking condition and insusceptible to sensor/actuator faults. The faults-induced uncertainties together with the nonlinear dynamics are compensated by involving a radial basis function neural network (RBFNN) to make the controller robust adaptive fault-tolerant without prior knowledge of fault coefficients. Via Lyapunov stability analysis, it is proven that all signals in the closed-loop system are semiglobally uniformly ultimately bounded. The effectiveness and superiority of the method are demonstrated by two simulation examples.

Dynamic Gain Reduced-Order Observer-Based Global Adaptive Neural-Network Tracking Control for Nonlinear Time-Delay Systems

In this article, a globally adaptive neural-network tracking control strategy based on the dynamic gain observer is proposed for a class of uncertain output-feedback systems with unknown time-varying delays. A reduced-order observer with novel dynamic gain is proposed. An n th-order continuously differentiable switching function is constructed to achieve the continuous switching control of the system, thus further ensuring that all the closed-loop signals are globally uniformly ultimately bounded (GUUB). It is proved that by adjusting the designed parameters, the tracking error converges to a region which can be adjusted to be small enough. The effectiveness of the control scheme is demonstrated by two simulation examples.

Finite-time adaptive dynamic surface synchronization control for dual-motor servo systems with backlash and time-varying uncertainties

The dual-motor driving servo system is continuously developed to satisfy strict safety and reliability requirements. However, several factors may degrade the system's performance, such as transmission backlash, parameter drift, and motor dynamic characteristic differences. To overcome these factors, this study proposes a finite-time tracking and synchronization control method for dual-motor servo systems that suffer from backlash and time-varying uncertainties. Our solution utilizes an adaptive dynamic surface and cross-coupling control scheme to deal with tracking and synchronization control issues and compensate for the unknown time-varying uncertainties. Through synchronizing the speed and acceleration states, the proposed controller guarantees high control performance and eliminates the force fighting caused by the motor's dynamic characteristic differences. In addition, finite-time control ensures the tracking error converges to an arbitrarily small neighborhood of zero in finite time. Moreover, the singularity problem in the derivative of the virtual control signal is avoided by introducing a new compensation term. Several simulations prove the proposed controller's stability and effectiveness.

Singularity-Free Fixed-Time Adaptive Control with Dynamic Surface for Strict-Feedback Nonlinear Systems with Input Hysteresis

An adaptive fixed-time dynamic surface tracking control scheme is developed in this paper for a class of strict-feedback nonlinear systems, where the control input is subject to hysteresis dynamics. To deal with the input hysteresis, a compensation filter is introduced, reducing the difficulty of design and analysis. Based on the universal approximation theory, the radial basis function neural networks are employed to approximate the unknown functions in the nonlinear dynamics. On this basis, fixed-time adaptive laws are constructed to approximate the unknown parameters. The dynamic surface technique is utilized to handle the complexity explosion problem, where fixed-time performance is ensured. Moreover, the designed controller can avoid singularities and achieve fixed-time convergence of error signals. Simulation results verify the efficacy of the method developed, where a comparison between the scheme developed with existing results is provided.

Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method

This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. Then, an adaptive neural tracking control law is proposed in the last step. By using the dynamic surface control method, the “explosion of complexity” problem of conventional backstepping is avoided. Based on the application of the Nussbaum gain function control technique, the unknown control gain problem is well solved. With the help of the radial basis function neural network, the unknown nonlinear dynamics are approximated. Furthermore, through Lyapunov stability analysis, it is proved that the proposed control law can guarantee that all signals in the closed-loop system are bounded and the tracking error can converge to an arbitrarily small domain of zero by adjusting the design parameters. Finally, two examples are provided to illustrate the effectiveness of the proposed control law.

Tracking Control of Physical Systems with Application to a System with a DC Motor: A Bond Graph Approach

In this paper, the bond graph modeling for the control of tracking systems has been applied. The closed loop system is built by the bond graph model of the system to be controlled, an additional bond graph according to the tracking input signal, and feedback gains in the physical domain. Hence, a procedure to obtain the closed loop tracking system is proposed. The proposal of modeling and tracking control systems in this paper determines symmetries in the bond graph approach with respect to the traditional algebraic approach. The great advantage of this graphical approach is that the mathematical determination of the system model is not necessary. Moreover, the coefficients of the characteristic polynomial using unidirectional causal loops of the closed loop system modeled in bond graphs are obtained. A case of study of a DC motor connected to an electrical supply network and a mechanical load is considered. Tracking control for the step, ramp, and acceleration type input signals in a bond graph approach are applied. In order to show the effectiveness of the proposed procedure, the simulation results are shown.

Adaptive Asymptotic Regulation for Uncertain Nonlinear Stochastic Systems with Time-Varying Delays

In this paper, for a class of uncertain stochastic nonlinear systems with input time-varying delays, an adaptive neural dynamic surface control (DSC) method is proposed. To approximate the unknown continuous functions online, the neural network approximation technique was applied, and based on the DSC scheme, the desired controller was constructed. A compensation system is presented to compensate for the effect of the input delay. The Lyapunov–Krasovskii functionals (LKFs) were employed to compensate for the effect of the state delay. Compared with the existing works, based on using the DSC scheme with the nonlinear filter and stochastic Barbalat’s lemma, the asymptotic regulation performance of this closed-loop system can be guaranteed under the developed controller. To certify the availability for the designed control method, some simulation results are presented.

Dynamic Event-Triggered Adaptive Tracking Control for a Class of Unknown Stochastic Nonlinear Strict-Feedback Systems

In this paper, the dynamic event-triggered tracking control issue is studied for a class of unknown stochastic nonlinear systems with strict-feedback form. At first, neural networks (NNs) are used to approximate the unknown nonlinear functions. Then, a dynamic event-triggered controller (DETC) is designed through the adaptive backstepping method. Especially, the triggered threshold is dynamically adjusted. Compared with its corresponding static event-triggered mechanism (SETM), the dynamic event-triggered mechanism (DETM) can generate a larger execution interval and further save resources. Moreover, it is verified by two simulation examples that show that the closed-loop stochastic system signals are ultimately fourth moment semi-globally uniformly bounded (SGUUB).

A novel adaptive control design method for stochastic nonlinear systems using neural network

This paper presents a novel method for designing an adaptive control system using radial basis function neural network. The method is capable of dealing with nonlinear stochastic systems in strict-feedback form with any unknown dynamics. The proposed neural network allows the method not only to approximate any unknown dynamic of stochastic nonlinear systems, but also to compensate actuator nonlinearity. By employing dynamic surface control method, a common problem that intrinsically exists in the back-stepping design, called “explosion of complexity”, is resolved. The proposed method is applied to the control systems comprising various types of the actuator nonlinearities such as Prandtl–Ishlinskii (PI) hysteresis, and dead-zone nonlinearity. The performance of the proposed method is compared to two different baseline methods: a direct form of backstepping method, and an adaptation of the proposed method, named APIC-DSC, in which the neural network is not contributed in compensating the actuator nonlinearity. It is observed that the proposed method improves the failure-free tracking performance in terms of the Integrated Mean Square Error (IMSE) by 25%/11% as compared to the backstepping/APIC-DSC method. This depression in IMSE is further improved by 76%/38% and 32%/49%, when it comes with the actuator nonlinearity of PI hysteresis and dead-zone, respectively. The proposed method also demands shorter adaptation period compared with the baseline methods.