Adaptive Dynamic Surface Control Research Articles

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 fuzzy fixed-time dynamic surface control for stochastic nonstrict nonlinear systems with unknown dead-zones

This paper focuses on an adaptive fuzzy fixed-time control problem for stochastic nonstrict nonlinear systems with unknown dead-zones by using dynamic surface control (DSC) technology. Fuzzy logic systems (FLSs) and DSC technology are used to approximate nonlinear functions and reduce the computational complexity, respectively. At the same time, the influence of the dead-zone disturbance is offset by transforming the dead-zone model into the nonlinear model that can be approximated by the FLSs. Then, based on the fixed-time stability theory, an adaptive fuzzy fixed-time tracking control strategy is proposed, which can ensure semi-global practical fixed-time stability of the system and the tracking error converging to a small neighborhood near the origin. Finally, two simulation examples are given to prove the effectiveness of the proposed control strategy.

Response to corrigendum for ‘Adaptive dynamic surface control of a two‐axis gimbal system’

Response to corrigendum for ‘Adaptive dynamic surface control of a two‐axis gimbal system’

Corrigendum: ‘Adaptive dynamic surface control of a two‐axis gimbal system’

AbstractAn adaptive Dynamic Surface Controller (DSC) is designed for a two‐axis gimbal system with actuator dynamics in the presence of parametric uncertainties in [1]. A Lyapunov stability analysis is used to guarantee the convergence of the tracking error to the origin and boundedness of all closed‐loop signals. The main objective of this corrigendum is to point out several errors that occurred throughout the paper, resulting in the inaccuracy of the used dynamic model and ineffectiveness of the proposed controller. It should be noted that taking into account the corrections stated in this corrigendum, the main result of the original paper is still valid.

Command filter based adaptive finite‐time dynamic surface control for nonlinear systems with unknown input delay under discontinuous input

AbstractIn this article, the adaptive finite‐time quantized and event‐triggered dynamic surface control (DSC) schemes are proposed for a class of strict‐feedback nonlinear system with time varying input delay. In order to ensure the completeness of the DSC method, an improved dynamic surface control method based on command filtering is adopted. The designed filtering error compensation signal can not only effectively compensate the filtering error, but also deal with the discontinuous input possessing unknown input delay. The problem of finite‐time control design and stability analysis with the difficulties brought by discontinuous input with unknown time‐varying input delay is solved through the design of the new compensation signal and the corresponding Lyapunov functional. Theoretical analysis shows that all signals in the closed‐loop system are bounded in finite time. The simulation examples also verify the effectiveness of the adaptive finite time DSC schemes proposed in this article.

Fractional‐order dynamics and adaptive dynamic surface control of flexible‐joint robots

AbstractThis paper establishes a novel fractional‐order model for n‐links flexible‐joint (FJ) robots and proposes an adaptive dynamic surface control (DSC) scheme to address the tracking control problem. The fractional‐order FJ model is built by fractional‐order viscoelastic dynamics model to have a more concise form. An adaptive DSC strategy is proposed to address the tracking control problem based on backstepping method. By selecting the appropriate orders for fractional filters, the controller could solve the “explosion of complexity” problem. The unknown nonlinearities of FJ robot systems are approximated by Radial basis function (RBF) neural networks (NNs). Based on the Lyapunov stability theory, the bounds of all signals in the closed‐loop system are achieved. The simulation results confirm the effectiveness of the presented control scheme.

Dynamic Event-Triggered Communication-Based Adaptive Consensus Tracking of Uncertain Nonlinear Multiagent Systems in Pure-Feedback Form

This study is aimed at investigating a dynamic event-triggered communication-based adaptive distributed consensus control problem for a class of uncertain pure-feedback nonlinear multiagent systems with limited communication resources. The nonaffine nonlinear functions of multiagent systems are assumed to be unknown and heterogeneous, and intermittent inter-agent communication is considered to occur within a directed network. A novel adaptive distributed dynamic surface control strategy using neural networks is developed to manage non-differentiable virtual control laws associated with the intermittent communication between agents with uncertain nonaffine nonlinear parts. The key contribution of this research is the derivation of dynamic event-triggering conditions using distributed tracking errors to efficiently adjust inter-event times, while ensuring the consensus tracking performance and robustness against unexpected external disturbances. Compared with the existing static event-triggered communication approach, the proposed controller can alleviate the communication burden among agents. Using technical lemmas, it is shown that all signals of the considered system are semiglobally uniformly ultimately bounded, and Zeno behavior is strictly excluded. Comparative simulation results illustrate the effectiveness of the proposed dynamic event-triggered control approach.

Neural Predictor-Based Dynamic Surface Predictive Control for Power Converters

In this letter, a neural predictor-based dynamic surface predictive control framework, endowed with the merits of adaptive dynamic surface control and finite control-set model predictive control, is proposed where the estimation of neural predictor is incorporated to identify the system dynamics and lumped unknown uncertainties. The key features of the proposal are that, first, the issue of “explosion of complexity” inherent in the classical back-stepping control is avoided, second, the model uncertainties and disturbances are explicitly dealt with, and, third, the tedious determination procedure of weighting factors is removed. These features lead to a much simpler adaptive predictive control solution, which is convenient to implement in applications. Furthermore, a Lyapunov function is constructed, and the stability analysis is given. It demonstrates that all signals in the closed-loop system are uniformly ultimately bounded. Finally, this proposal is experimentally assessed, where the performance evaluation of steady-state and transient-state confirms the availability of the proposed solution for modular multilevel converter.

Finite-Time Adaptive NN Backstepping Dynamic Surface Control for Input-Delay Fractional-Order Nonlinear Systems

This article focuses on a finite-time adaptive dynamic surface control (DSC) approach for a kind of nonstrict fractional-order nonlinear systems (FONSs) with input delay. An auxiliary compensation function is presented by using the integral function of the input signal to handle input delay problem. To overcome the problem of inherent computational complexity, a fractional-order filter is applied to approach the virtual controller and its fractional-order derivative in each step of the backstepping procedure. By using backstepping technology and neural network (NN), the finite-time adaptive DSC approach is developed, and finite-time stability criteria based on fractional-order Lyapunov method are introduced to prove the finite-time convergence of the tracking error into a small region around the origin. The effectiveness of the presented control scheme is demonstrated by two 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.

Synchronous Position Control of Gantry Table Using Adaptive Fraction-Order Dynamic Surface Control With Dendritic Neuron Model

This article introduces a three-degree-of-freedom (3DOF) model-based adaptive fractional-order dynamic surface control (AFODSC) system for a synchronous position control of a gantry table. First, the 3DOF model of the gantry table is investigated considering the rotational dynamics caused by inter-axis mechanical coupling and synchronous error. Then, a new fractional-order dynamic surface control (FODSC) approach is introduced using a fractional-order low-pass filter to provide an extra degree of freedom for the existing dynamic surface control (DSC) method. Because it is arduous to know the system uncertainty, the AFODSC is further elaborated by incorporating an adaptive mechanism and an uncertainty observation into the FODSC. In the proposed AFODSC, a modified dendritic neuron model observer (DNMO) is proposed to identify uncertainties, whereas an exponential compensator is designed to compensate for the observation error. Multiple adaptation laws are derived to adapt the parameters of DNMO on the basis of the Lyapunov stability theorem. Experimental results confirm that the proposed AFODSC system demonstrates favorable position tracking and synchronization accuracies for the gantry table compared with the conventional DSC system.

Observer-Based Event-Triggered Adaptive Fuzzy Control for Fractional-Order Time-Varying Delayed MIMO Systems Against Actuator Faults

This article presents the observer-based event-triggered adaptive hybrid fuzzy dynamic surface control strategy for a category of uncertain nonstrict-feedback fractional-order nonlinear multi-input multi-output systems, including unknown time-varying delays and actuator faults. First, an adaptive hybrid fuzzy state observer and a serial-parallel estimation system are constructed to estimate the unmeasured system states and incorporate them into the control design scheme, respectively, where some appropriate fuzzy logic systems are introduced to approximate the unknown nonlinear functions. According to the dynamic surface control technique, the designed adaptive fuzzy control approach can surmount the deficiency of “complexity explosion.” Then, an observer-based adaptive event-triggered control algorithm is developed by constructing the Lyapunov–Krasovskii functionals and estimating the compounded disturbances. Furthermore, it is proved that under the drive of the reference signals, all the signals in the closed-loop system are semiglobally uniformly ultimately bounded and Zeno behavior can be successfully excluded. Finally, an example with numerical simulations is utilized to exhibit the applicability of the obtained observer-based event-triggered adaptive fuzzy control approach.

Adaptive Dynamic Surface Control of Strict-Feedback Fractional-Order Nonlinear Systems with Input Quantization and External Disturbances

In this work, an adaptive dynamic surface control law for a type of strict-feedback fractional-order nonlinear system is proposed. The considered system contained input quantization and unknown external disturbances. The virtual control law is presented by utilizing a dynamic surface control approach at each step, where the nonlinear compensating term with the estimation of unknown bounded parameters is introduced to overcome the influence of unknown external disturbances and surface errors. Meanwhile, the adaptive laws of relevant parameters are also designed. In addition, an improved fractional-order nonlinear filter is developed to deal with the explosion of complexity raised by the recursive process. In the last step, an adaptive dynamic surface control law is proposed to ensure the convergence of tracking error, in which the Nussbaum gain function is applied to solve the problem of the unknown control gain generated by input quantization. Then, the fractional Lyapunov stability theory is applied to verify the stability of the proposed control law. Finally, simulation examples are given to illustrate the effectiveness of the proposed control law.

Neural adaptive finite-time dynamic surface control for the PMSM system with time delays and asymmetric time-varying output constraint

This paper presents a neural adaptive finite-time dynamic surface control for the permanent magnet synchronous motor system with time delays and asymmetric time-varying output constraint. The core challenge is how to address the time delays and asymmetric output constraint when designing a finite-time control scheme. Given this, a proper Lyapunov–Krasovskii functional is introduced to address time delays, and a nonlinear transformation function is considered to convert the output-constrained problem into an unconstrained one. Then, a neural adaptive finite-time dynamic surface control approach is devised in the finite-time backstepping framework, which applies neural networks to estimate the unknown nonlinear functions and introduces first-order filters to solve the “explosion of complexity” problems. Furthermore, it is demonstrated that all the signals of the resulting system are finite-time stable and the tracking error converges to a neighborhood of origin in finite time without violating the output constraint. Finally, the simulation results show that the integration of squared error results, the integral of time and absolute error results as well as the integration of absolute value error results of the proposed scheme is smaller than the tested scheme by 0.3458 , 22.2977 , and 2.2513 , respectively, when the time delays are considered. It further elucidates the availability and superiority of the developed method.

L’ Hopital’S rule-Based adaptive dynamic surface control for a class of strict-Feedback systems with unknown parameters

In this paper, a L’ Hopital’s rule-based adaptive dynamic surface control (L-ADSC) scheme is developed for a class of strict-feedback systems with unknown parameters using backstepping technique. The L-ADSC-derived backstepping technique is deployed to remove differentiation of complex virtual controller, thereby efficiently avoiding ”exlosion of complexity”. The L’ Hopital’s Rule is resorted to tackle singularity problem within controller synthesis. As a consequence, the proposed L-ADSC scheme guarantees that all signals of the closed-loop control system are semi-globally uniformly ultimately bounded. Simulation results show remarkable effectiveness.

Adaptive composite learning dynamic surface control for chaotic fractional-order permanent magnet synchronous motors

This paper aims to address the tracking problem of uncertain fractional-order permanent magnet synchronous motors with parametric uncertainties. To guarantee the system stability and offset the effect of parametric uncertainties, an adaptive backstepping composite learning neural control scheme based on interval excitation is presented. Moreover, dynamic surface technique is exploited to overcome the technical limitation of “explosion of complexity” caused by standard backstepping framework. In virtue of stability analysis and illustrative simulation, it is confirmed that the proposed control scheme not only attenuates the tracking error as small as possible, but also achieves satisfactory parametric convergence with high estimation precision.

Distributed Optimization for Fractional-Order Multi-Agent Systems Based on Adaptive Backstepping Dynamic Surface Control Technology

In this article, the distributed optimization problem is studied for a class of fractional-order nonlinear uncertain multi-agent systems (MASs) with unmeasured states. Each agent is represented through a system with unknown nonlinearities, unmeasurable states and a local objective function described by a quadratic polynomial function. A penalty function is constructed by a sum of local objective functions and integrating consensus conditions of the MASs. Radial basis function Neural-networks (RBFNNs) and Neural networks (NN) state observer are applied to approximate the unknown nonlinear dynamics and estimate unmeasured states, respectively. By combining the NN state observer and the penalty function, and the stability theory of the Lyapunov function, the distributed observer-based adaptive optimized backstepping dynamic surface control protocol is proposed to ensure the outputs of all agents asymptotically reach consensus to the optimal solution of the global objective function. Simulations demonstrate the effectiveness of the proposed control scheme.

Adaptive Dynamic Surface Control for Attitude Tracking of Spacecraft under Measurement Biases

Adaptive Dynamic Surface Control for Attitude Tracking of Spacecraft under Measurement Biases

Disturbance-observer-based adaptive dynamic surface control for nonlinear systems with input dead-zone and delay using neural networks

Disturbance-observer-based adaptive dynamic surface control for nonlinear systems with input dead-zone and delay using neural networks

Command filter based adaptive DSC of uncertain stochastic nonlinear systems with input delay and state constraints

In this paper, a command filter based dynamic surface control (DSC) is developed for stochastic nonlinear systems with input delay, stochastic unmodeled dynamics and full state constraints. An error compensation system is designed to constrain the filtering error caused by the first-order filter in the traditional dynamic surface design. On this basis, the stability proof of DSC for stochastic nonlinear systems based on command filter is proposed. The definition of state constraints in probability is presented, and the problem of stochastic full state constraints is solved by constructing a group of coordinate transformations with nonlinear mappings. The Pade approximation is adopted to deal with input delay. The stochastic unmodeled dynamics is considered, which is processed by utilizing the property of stochastic input-to-state stability (SISS) and changing supply function. All the signals of the system are proved to be semi-globally uniformly ultimately bounded (SGUUB) in probability, and the full state constraints are not violated. The two simulation examples also verify the effectiveness of the proposed adaptive DSC scheme.