Adaptive Dynamic Surface Control Research Articles

Adaptive dynamic surface control of stochastic nonstrict‐feedback constrained nonlinear systems with input and state unmodeled dynamics

SummaryIn this paper, the issue of adaptive neural control is discussed for a class of stochastic nonstrict‐feedback constrained nonlinear systems with input and state unmodeled dynamics. A dynamic signal produced by the first‐order auxiliary system is employed to deal with the dynamical uncertain terms. Radial basis function neural networks are used to reconstruct unknown nonlinear continuous functions. With the help of the mean value theorem and Young's inequality, only one learning parameter is adjusted online at recursive each step. Using the hyperbolic tangent function as nonlinear mapping, the output constrained stochastic nonstrict‐feedback system in the presence of unmodeled dynamics is transformed into a novel unconstrained stochastic nonstrict‐feedback system. Based on dynamic surface control technology and the property of Gaussian function, adaptive neural control is developed for the transformed stochastic nonstrict‐feedback system. The output abides by stochastic constraints in probability. By the Lyapunov method, all signals of the closed‐loop control system are proved to be semi‐global uniform ultimate bounded (SGUUB) in probability. The obtained theoretical findings are verified by two numerical examples.

Adaptive Fuzzy Dynamic Surface Control for Nonlinear Systems with Time-Varying Input Delay and Sampled Data

This paper studies fuzzy adaptive dynamic surface control strategy for nonlinear system with sampled data and time-varying input delay. By utilizing the approximated property of fuzzy logic systems (FLSs), a fuzzy estimator (FE) model is designed to identify the states of the original system, which is mainly used to provide information of estimation states to replace the sampled data of the nonlinear controlled system. In the proposed strategy, with the help of sampled-data activity, an integral term is designed to compensate the problem of time-varying input delay. Moreover, by invoking the dynamic surface control (DSC) technique, the problem of ‘explosion of complexity’ has been overcame. And the developed control strategy demonstrates that all signals of the controlled system are semi-globally uniformly ultimately bounded (SGUUB). Ultimately, two numerical simulation examples are given to prove the feasibility of the developed control method and theory.

Resilient adaptive control of switched nonlinear cyber-physical systems under uncertain deception attacks

This paper addresses the problem of resilient adaptive dynamic surface control against uncertain sensor and actuator deception attacks for a class of switched nonlinear cyber-physical systems. The concerned system dynamics suffer from both unknown switching mechanisms and more general nonlinearities. Furthermore, it is our aim to deal with deception attacks as adversaries can corrupt sensor and control data, resulting the conventional error surfaces inaccessible for feedback control design. To this end, we construct sensor attack compensators to mitigate the effects caused by the sensor attacks. In addition, neural networks are utilized to approximate the nonlinear terms and compensate the state-dependent actuator attacks. Then, we construct a common Lyapunov function and propose a dynamic surface-based resilient adaptive strategy, under which the equilibrium point of the resulted closed-loop system is semi-globally uniformly ultimately bounded under arbitrary switchings. Finally, we provide a continuously stirred tank reactor system under uncertain deception attacks to validate the effectiveness of the proposed control method.

Finite-Time Adaptive Fuzzy DSC for Uncertain Switched Systems

The finite-time adaptive fuzzy tracking control problem for a class of strict-feedback uncertain switched systems is investigated in this paper. Based on fuzzy approximation and adaptive dynamic surface control (DSC) technique, a finite-time adaptive state feedback fuzzy controller is developed via the common Lyapunov functions. Different from the existing works on uncertain switched systems, the DSC control scheme is developed based on a nonlinear filter to solve the “explosion of complexity” problem, and the structure of the proposed fuzzy controller is simple. Under the designed controller, all the signals of the closed-loop system remain semi-globally bounded, and within a finite-time interval, the system tracking error converges to an arbitrarily small region. That is, the semi-globally practical finite-time stability of the controlled system is guaranteed. To show the availability of the presented control scheme, a simulation example is given in this paper.

Adaptive control for non-affine nonlinear systems with input saturation and output dead zone

This paper disposes of the problem of adaptive dynamic surface control for non-affine nonlinear systems. The full state constraints, output dead zone and input saturation are fully considered in the controlled system. Invariant sets are used for a continuous and semi-bounded condition of non-affine functions. The “complexity explosion” issue caused by backstepping procedure is avoided via the dynamic surface control method. A Nussbaum function is used to handle the unknown control coefficient derived from the output dead zone, and barrier Lyapunov functions are employed to handle full state constraints. To counteract the effects of disturbance and uncertainty, the robust compensator is constructed. In addition, it is proved that all signals in the system are bounded and all states satisfy their constraints. Finally, the simulation results show the effectiveness of the proposed method.

Adaptive Fuzzy Finite-time Dynamic Surface Control for High-order Nonlinear System with Output Constraints

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.

An adaptive dynamic surface control of output constrained stochastic nonlinear systems with unknown control directions

SummaryThis article is concerned about an adaptive dynamic surface control (DSC) of output constrained stochastic nonlinear systems with unknown control directions and unmodeled dynamics. Nonlinear mapping‐based backstepping control design is presented for stochastic nonlinear systems with output constraint. The explosion of complexity exists in tradition backstepping method is avoided by using the DSC technique. The radial basis function neural networks are employed to deal with unknown nonlinear functions. Nussbaum gain technique is employed to handle the unknown control directions. And a dynamic signal is employed to dominate the unmodeled dynamics. The adaptive controller is designed can ensure that the tracking error converges on a small region of the origin. And all signals of the closed‐loop systems are semiglobal uniformly ultimately bounded. Finally, the results of the simulation cases are provided to show the effectivity of the designed controller scheme.

Switched-observer-based adaptive DSC design of nonstrict-feedback switched stochastic nonlinear time-delay systems

For switched stochastic nonlinear systems with time delay, an adaptive output-feedback tracking control problem is studied by using the dynamic surface control (DSC) method associated with a switched state observer. The time-varying delay terms are handled by constructing an appropriate stochastic Lyapunov–Krasovskii functional. The unknown nonlinearities in the considered systems are adaptively approximated by the function approximation approach—neural networks (NNs). It is shown that, under the average dwell time (ADT) method, the semiglobal uniformly ultimately boundedness (SGUUB) is guaranteed for all closed-loop signals by the developed switched controllers of different subsystems even in the presence of time delay, meanwhile, the tracking error is confined to a small residual set. A practical system example and a numerical example are provided to demonstrate the efficacy of the proposed scheme.

Distributed Rotating Encirclement Control of Strict-Feedback Multi-Agent Systems using Bearing Measurements

This paper focuses on the distributed multi-target rotating encirclement formation problem of strict-feedback multi-agent systems using bearing measurements. To this end, an estimator is presented to localize agents’ neighbor targets. Then, based on the trajectory planning method, a reference trajectory is constructed by three estimators, which are utilized to obtain the targets’ geometric center, the reference rotating radius and angular. Finally, an adaptive neural dynamic surface control scheme is proposed to drive all agents to move along their reference trajectories, which satisfy the multi-target rotating encirclement formation conditions. A numerical simulation is provided to verify the correctness and effectiveness of our proposed control scheme.

Improved Adaptive Fuzzy Output-Feedback Dynamic Surface Control of Nonlinear Systems With Unknown Dead-Zone Output

This article presents an adaptive fuzzy output-feedback dynamic surface control (DSC) for the nonlinear systems with dead-zone output nonlinearity. First, a novel smooth approximation of the output dead zone is given to conveniently fuse with the backstepping technique. After that a nonlinear fuzzy state observer is constructed to estimate the unmeasurable states, by employing the fuzzy logic systems for identifying the unknown compounded nonlinear functions, which releases the limitation in the existing references that the state observer needs to be linear in the presence of dead-zone output nonlinearity. Then, to reduce the effect of unknown dead-zone coefficients, an adaptive compensation mechanism is introduced by using the characteristic of hyperbolic tangent function, which can replace the widely used Nussbaum-type function-based control strategy. Furthermore, a novel DSC method based on the nonlinear filters is proposed, which not only avoids the issue of explosion of complexity inherent in the backstepping procedure, but also improves the system control performance. Under the certain assumptions, the stability of the closed-loop system is proved by use of Lyapunov function stability theory. Finally, the applicability of the proposed control method is rigorously verified by a single-link robot arm simulation example.

Cooperative Adaptive Dynamic Surface Control for a Class of High-Order Stochastic Nonlinear Multiagent Systems.

This article investigates the consensus tracking problem for high-order stochastic pure-feedback nonlinear multiagent systems (MASs) with dead zones. It should be pointed out that each follower's virtual and actual control items are the power-exponential functions with positive odd numbers instead of linear items. Because of the structural characteristics of the followers' dynamics, a technique called adding a power integrator is used, which effectively overcomes the difficulties of states and dead zone with power-exponential functions. Furthermore, radial basis function neural networks are employed to estimate unknown nonlinear functions and solve the problem of algebraic loop caused by the pure-feedback structure of MASs. Meanwhile, the problems of "explosion of complexity" caused by repeated differentiations of the virtual controller are solved by using the tracking differentiators. Based on the Lyapunov stability theorem, it is proved that all signals of the closed-loop systems are semiglobally uniformly ultimately bounded in probability, and the tracking errors can converge to a small neighborhood of the origin. Finally, simulation results are presented to verify the effectiveness of the proposed approach.

Tracking control of a class of nonlinear systems with output delay based on adaptive fuzzy dynamic surface control

ABSTRACTThis paper concerns with the tracking control problem of a class of unknown nonlinear time-delay systems in the presence of output delay and inaccessible states. To deal with the difficulties arising from unmeasurable states, a fuzzy logic observer based on delayed outputs is firstly employed. Then, based on the delayed output, observed states and filtered virtual control signals, proper change of coordinates is defined for the purpose of designing dynamic surface control. By introducing appropriate Lyapunov-Krasovskii functionals in the design procedures, a controller and adaptation laws are obtained for the control strategy of nonlinear systems subject to output delay. Moreover, by selecting design parameters and matrices based on the acquired stability criteria, it is proved that the proposed adaptive fuzzy dynamic surface output feedback control approach is able to guarantee the uniformly ultimately boundedness of all the signals in the closed loop unknown nonlinear output-delay systems. Finally, the theoretic achievements are applied to three well-known benchmark systems to illustrate the effectiveness and efficiency of the proposed approach.

Global tracking control of quadrotor based on adaptive dynamic surface control

This paper presents a global nonlinear tracking control system for a quadrotor unmanned aerial vehicle (UAV) in the presence of underactuation, external disturbances and model uncertainties. Quadrotor systems lack enough independent control inputs to control their entire configuration space directly due to underactuation. The proposed solution is to adopt a cascade feedback technique that splits the system dynamics into attitude and position dynamics. The proposed controller is developed directly on the special Euclidean group with a region of attraction covering the entire configuration space where its stability is proven using Lyapunov functions. The controller guarantees the asymptotical convergence of tracking error in the presence of model uncertainties and external disturbances. In particular, the control method combines three techniques: a second-order sliding mode control (SMC), a dynamic surface control, and a non-parametric adaptation mechanism. The SMC is used to stabilize the position dynamics (internal dynamics) by generating a proper attitude command for the attitude controller. The DMC control guarantees the attitude dynamics stability globally and tracking performance while avoiding the mathematical complexities associated with the highly nonlinear dynamics. The adaptation mechanism includes a radial basis function neural network to observe uncertainties without the need for prior training. The uncertainties considered include unmodeled dynamics, external disturbances and parameter uncertainties including the mass and inertial matrices as well as motor coefficients. The desirable features of the proposed control system are illustrated by both numerical simulation and experiments on a UAV testbed.

Prescribed performance adaptive DSC for a class of time-delayed switched nonlinear systems in nonstrict-feedback form: Application to a two-stage chemical reactor

This study deals with the tracking problem for a class of nonstrict-feedback switched nonlinear systems (SNSs) with unknown time-delay and unknown functions under arbitrary switching. To achieve this goal, an adaptive neural network-based dynamic surface control (DSC) based on backstepping approach is proposed. A neural network (NN) approximator based on radial basis functions (RBFs) is utilized to approximate unknown functions. Considering properties of Gaussian basis function in RBFNNs, an adaptive neural network DSC for nonstrict-feedback structure has been developed. A Lyapunov-krasovskii functional is applied to compensate the effect of unknown delay terms. Furthermore, a prescribed performance bound (PPB) control strategy is utilized to retain the tracking error within a predefined bound. Finally, a practical example is provided to prove the effectiveness of the proposed method.

Neuroadaptive finite-time output feedback control for PMSM stochastic nonlinear systems with iron losses via dynamic surface technique

In this paper, an observer-based adaptive neural network finite-time dynamic surface control method is proposed for the position tracking control of PMSM stochastic nonlinear systems with iron losses. First, the finite-time technology is used to realize the fast and effective tracking of the desired signal and make the system have better robust performance. Then, the adaptive neural network (NN) technology and state observer are applied to approximating the uncertain nonlinear functions and estimating the immeasurable states, respectively. And, the dynamic surface control (DSC) technology is used to resolve the “explosion of complexity” problem. In addition, the influence of iron losses and stochastic disturbances in the system is considered, and a quartic stochastic Lyapunov function is established to analyze the stability of the system. Finally, the simulation results show the effectiveness of the proposed method.

Neural networks-based adaptive dynamic surface control for vehicle active suspension systems with time-varying displacement constraints

This paper addresses controlling of displacements of vehicle active suspension systems with an active seat suspension and a human-body model. A neural networks-based dynamic surface control strategy is constructed for the active suspension systems. Specifically, asymmetric time-varying barrier Lyapunov functions are applied to ensure that the displacements of vehicle active suspensions do not violate their time-varying constraint bounds. Neural networks are used to approximate unknown functions in the active suspension systems and their basis function properties are employed to deal with functions with non-strict form. Dynamic surface control technique is used to reduce the complexity of the controller. Advantages of the control strategy are substantiated by two simulation examples.

Adaptive fuzzy backstepping control for a two continuous stirred tank reactors process based on dynamic surface control approach

This work demonstrates an adaptive fuzzy backstepping control for a two cascaded continuous stirred tank reactors (CSTRs) system based on the dynamic surface control (DSC). The proposed controller is able to ensure the internal stabilization of the closed-loop system and render outputs track their reference signals asymptotically, although the CSTRs system is highly nonlinear and strong coupling. The effective and robust performance of the proposed controller in this research is certificated by the simulation analysis. Compared with previous researches, the on-line computation of controller is effectively reduced, which means that the proposed controller is easy to implement in engineering. The adaptive fuzzy dynamic surface control appears the potential for CSTRs process in mill operation.

Error-Driven Nonlinear Feedback Design for Fuzzy Adaptive Dynamic Surface Control of Nonlinear Systems With Prescribed Tracking Performance

This paper addresses an error-driven nonlinear feedback design technique to improve the dynamic performance of fuzzy adaptive dynamic surface control (DSC) for a class of uncertain multiple-input-multiple-output nonlinear systems with prescribed tracking performance. The highlight of the error-driven nonlinear feedback technique is that the feedback gain self-regulates versus different levels of output and virtual tracking errors, this reflects the classical control design criterions commendably: relatively high feedback gains can be implemented to guarantee disturbances and uncertainties attenuation and so on to improve the control performance when small tracking errors are measured, and relatively small feedback gains can be implemented to circumvent the problems of actuator and states saturations when large tracking errors are measured. The complexity problem of the traditional backstepping design is circumvented owe to the peculiarity of DSC method. Caused by the compound error functions of nonlinear feedback dynamics, a nonquadratic Lyapunov function is used to deduce the conditions of closed-loop stability. Fuzzy logic systems and error transformation-based method are used in the online learning of completely unknown dynamics and the prescribed performance tracking, respectively. Comparative results are presented to demonstrate the effectiveness and preponderance of the proposed control scheme with comparison to existing ones.

Adaptive dynamic surface control using neural networks for hypersonic flight vehicle with input nonlinearities

SummaryThis study proposes an effective adaptive dynamic surface control (DSC) method based on the radial basis function neural networks and the auxiliary system for hypersonic flight vehicle (HFV) systems in the presence of system uncertainties, external disturbances, and state variable and control input constraints. Firstly, to enhance the robustness of the system, the neural network is combined with the robust term to deal with the uncertainties and external disturbances of the system. Secondly, to prevent the deterioration of the dynamic performance of the system due to the over‐adaptation of the neural networks and the robust terms caused by the state and control input constraints, the auxiliary system is added at each step in the DSC design to adjust the dynamic process of the reference signal and virtual control. Furthermore, the variable structure control is used to solve the problem of dead zone in the control input. Using the Lyapunov analysis method, all signals of the closed‐loop system are semi‐globally uniformly ultimate bounded. The simulation results illustrate the effectiveness of the proposed control scheme for the HFVs.

Robust adaptive dynamic surface back-stepping tracking control of high-order strict-feedback nonlinear systems via disturbance observer approach

In this study, we propose an adaptive tracking dynamic surface back-stepping control based on Nussbaum disturbance observer for uncertain high-order strict-feedback MIMO nonlinear systems with external disturbances, unknown parameters and modelling uncertainties. It is assumed that the control action is affected by input saturation; so to compensate the resulted undesirable effects, the tanh(.) function is used as an approximation to the saturation function. To tackle the unknown external disturbances and uncertainties, a Nussbaum disturbance observer is proposed. Moreover, an appropriate adaptive law is presented to deal with the unknown parameters. Then, the dynamic surface control method is used to overcome the inherent problem ‘explosion of complexity’ that appeared in the conventional back-stepping method. The Lyapunov stability analysis proves that the closed-loop system is semi-globally uniformly bounded. At last, reasonable effectiveness and applicability of the adaptive tracking dynamic surface control are illustrated by simulation results.