Adaptive Neural Control Design Research Articles

Adaptive Neural Network Control Scheme of Switched Systems with Input Saturation

This paper investigates a scheme of adaptive neural network control for a stochastic switched system with input saturation. The unknown smooth nonlinear functions are approximated directly by neural networks. A modified approach is proposed to deal with unknown functions with nonstrict feedback form in the design process. Furthermore, by combining the auxiliary design signal and the adaptive backstepping design, a valid adaptive neural tracking controller design algorithm is presented such that all the signals of the switched closed-loop system are in probability semiglobally, uniformly, and ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in probability. In the end, the effectiveness of the proposed method is verified by a simulation example.

Removing Feasibility Conditions on Adaptive Neural Tracking Control of Nonlinear Time-Delay Systems With Time-Varying Powers, Input, and Full-State Constraints.

This article investigates the tracking control for input and full-state-constrained nonlinear time-delay systems with unknown time-varying powers, whose nonlinearities do not impose any growth assumption. By utilizing the auxiliary control signal and nonlinear state-dependent transformation (NSDT) to counteract the effect of input saturation and cope with full-state constraints, respectively, and then introducing lower and higher powers and Lyapunov-Krasovskii (L-K) functionals in control design together with the adaptive neural-networks (NNs) method, an adaptive neural tracking control design is provided without feasibility conditions. It is proved that NNs approximation is valid, all the closed-loop signals are semiglobally bounded, and input and full-state constraints are not violated.

Adaptive neural consensus tracking control for a class of 2-order multi-agent systems with nonlinear dynamics

This paper investigates the problem of finite-time consensus tracking control for a class of 2-order nonlinear multi-agent systems (MASs). In order to present a consensus control protocol by adaptive neural control approach, a novel fast finite-time stability criterion is first set up, which provides a theoretical basis for applying approximation-based adaptive control approaches to solve the finite-time control issues. Furthermore, an adaptive neural fast finite-time consensus tracking controller is constructed based on the developed finite-time stability criterion. The suggested adaptive neural backstepping control design scheme successfully avoids the problem of singularity of controllers. Under the action of the presented protocol, the output of each follower tracks the reference signal and other signals of the closed-loop system remain bounded in finite time. The efficacy of the proposed control scheme is confirmed by simulation study.

Adaptive Neural Output-Feedback Controller Design of Switched Nonlower Triangular Nonlinear Systems With Time Delays.

In this article, we study the issue of adaptive neural output-feedback controller design for a class of uncertain switched time-delay nonlinear systems with nonlower triangular structure. The prominent contribution of this article is that the delay-dependent stability criterion of nonswitched nonlinear systems is successfully extended to that of switched nonlower triangular nonlinear systems. The design algorithm is listed as follows. First, a switched state observer is designed such that the error dynamic system can be generated. Second, neural networks, adaptive backstepping technique, and variable separation method are, respectively, applied to construct a common controller for all subsystems, in which the Lyapunov-Krasovskii functionals are deliberately constructed such that the average dwell-time scheme can be employed to guarantee the stability and performance of the closed-loop system, despite the existence of time delays. Third, the stability analysis process confirms in detail that all the variables of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, simulation study is given to show the validity of the proposed control approach.

Adaptive approximation-based design mechanism for non-strict-feedback nonlinear MIMO systems with application to continuous stirred tank reactor

This article is concerned with the problem of adaptive neural controller design for multi-input/multi-output nonlinear systems with input-saturations and disturbances. In the proposed design mechanism, we will take advantage of hyperbolic tangent functions to smooth the sharp corners of the input saturations and use Young’s inequality to handle the nonlinear terms derived from the deducing process, and meanwhile apply the intelligent algorithm to estimate the unknown nonlinearity via neural networks. Furthermore, the backstepping technique is used to complete the design of the controller and Lyapunov stability theory is employed to show that the whole closed-loop system is semi-global uniformly ultimately bounded and the tracking error is bounded subject to the small neighborhood of the origin. Finally, as a practical application of the researched design scheme, adaptive neural controller for a continuous stirred tank reactor is constructed.

Adaptive neural design frame for uncertain stochastic nonlinear non-lower triangular pure-feedback systems with input constraint

This paper dedicates to dealing with the adaptive neural design problem for uncertain stochastic nonlinear systems with non-lower triangular pure-feedback form and input constraint. On the basis of the mean-value theorem, the pure-feedback structure is first transformed into the desired affine structure, and then the well-known backstepping technology is applied to construct the actual input signal of the controller. Although the considered system has a fairly complex structure, a new adaptive neural tracking controller design frame is established via the flexible application of radial basis function (RBF) neural networks’ (NNs’) structural characteristics. The proposed design frame guarantees the control objective of this paper can be achieved. Finally, a simulation example is given to further illustrate the availability of the proposed control scheme.

Adaptive Neural Boundary Control Design for Nonlinear Flexible Distributed Parameter Systems

This paper proposes an adaptive neural boundary feedback control design for a nonlinear flexible distributed parameter system described by a nonuniform wave equation containing an unknown nonlinear function in the boundary conditions. In the proposed design method, a radial-basis-function neural network (NN) with an adaptive weight update law is used to approximate the unknown nonlinear term. By using this adaptive NN, an adaptive boundary feedback controller is constructed to ensure that the resulting closed-loop system is practically exponentially stable. The closed-loop stability of the system is analyzed by the Lyapunov direct method and technique of integration by parts, and the update law of an NN weight vector is determined simultaneously. The closed-loop well-posedness analysis is also provided by applying the C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -semigroup approach. Moreover, the proposed design method is extended for a nonlinear flexible distributed parameter system modeled by a nonuniform Euler-Bernoulli beam equation containing an unknown nonlinear function in the boundary conditions. Finally, extensive numerical simulation results are given to demonstrate the performance of the proposed adaptive neural boundary control design method.

Adaptive Neural Backstepping Control Design for A Class of Nonsmooth Nonlinear Systems

This paper investigates the problems of backstepping control for a class of nonsmooth nonlinear systems. With the help of set-valued functions (or maps) and set-valued derivatives, a new Lyapunov criterion is developed for nonsmooth systems. The concept of semi-globally uniformly ultimately bounded (SGUUB) stability that is widely used for smooth nonlinear systems in lower triangular form is, for the first time, applied to the nonsmooth case, and such a concept provides a theory foundation for the subsequent backstepping control design. Then, two types of continuous controllers are designed based on the backstepping technique and adaptive neural network (NN) algorithm. In the light of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions, the system under investigation is first transformed into an equivalent model. Then, the first type of controller can be efficiently designed by using the traditional backstepping technique. On the other hand, when the unknown uncertainty is taken into account in the equivalent systems, another type of controller is designed based on adaptive NN control strategy. It is proved that in both cases, all the closed-loop signals are SGUUB by using our proposed controllers. Finally, a numerical example with two types of controllers is supplied to show the availability of the provided control schemes.

Time-varying Barrier Lyapunov Function Based Adaptive Neural Controller Design for Nonlinear Pure-feedback Systems with Unknown Hysteresis

This paper deals with the adaptive neural network (NN) control problem for a class of pure-feedback systems with time-varying constrained states and unknown backlash-like hysteresis. First of all, the considered plant is transferred into a strict feedback system on account of the implicit function theorem and mean value theorem. Then, the time-varying Barrier Lyapunov functions (BLFs) are integrated into the backstepping techniques so that all the states do not transgress the corresponding constraint boundary. This approach avoids the procedure of finding inverse, and therefore greatly improves the robustness of controller. At the same time, the radial basis function (RBF) NNs are employed to identify the unknown internal dynamics, which is a key operation in each step. Based on the Lyapunov stability analysis scheme, all the closed-loop signals are proved to be uniformly ultimately bounded (UUB), and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are developed to further verify the proposed control strategy.

Adaptive NN Backstepping Control Design for a 3-DOF Helicopter: Theory and Experiments

This paper presents an adaptive neural network backstepping control design for an experimental helicopter with three rotational degrees of freedom. The helicopter system is described by a state-space model with unmodeled dynamics and external disturbances. By resorting to radial basis function neural networks with online gradient descent training, such unmodeled dynamics and external disturbances can be compensated in real time. With the help of Lyapunov stability criteria, it is proved that the desired trajectories can be boundedly tracked by the corresponding attitude angles of the helicopter under the proposed adaptive neural network backstepping controller. Compared with robust adaptive integral backstepping technique, our approach has smaller root mean squared error. Finally, four sets of contrastive experiment results are, respectively, given to show the effectiveness and advantages of the proposed control scheme.

Adaptive Neural Network Learning Controller Design for a Class of Nonlinear Systems With Time-Varying State Constraints

This paper studies an adaptive neural network (NN) tracking control method for a class of uncertain nonlinear strict-feedback systems with time-varying full-state constraints. As we all know, the states are inevitably constrained in the actual systems because of the safety and performance factors. The main contributions of this paper are that: 1) in order to ensure that the states do not violate the asymmetric time-varying constraint regions, an adaptive NN controller is constructed by introducing the asymmetric time-varying barrier Lyapunov function (TVBLF) and 2) the amount of the learning parameters is reduced by introducing a TVBLF at each step of the backstepping. Based on the Lyapunov stability analysis, it can be proven that all the signals in the closed-loop system are the semiglobal ultimately uniformly bounded and the time-varying full-state constraints are never violated. Finally, a numerical simulation is given, and the effectiveness of this adaptive control method can be verified.

Homeomorphism Mapping Based Neural Networks for Finite Time Constraint Control of a Class of Nonaffine Pure‐Feedback Nonlinear Systems

This paper proposes a new scheme for solving finite time neural networks adaptive tracking control issue for the nonaffine pure‐feedback nonlinear system. The procedure, based on homeomorphism mapping and backstepping, effectively deals with constraint control and design difficulty induced by pure‐feedback structure. The most outstanding novelty is that finite time adaptive law is proposed for training weights of neural networks. Furthermore, by combining finite time adaptive law and Lyapunov‐based arguments, a valid finite time adaptive neural networks controller design algorithm is presented to ensure that system is practical finite stable (PFS) rather than uniformly ultimately bounded (UUB). Because of using the finite time adaptive law to training weights of neural networks, the closed‐loop error system signals are in assurance of bounded in finite time. Benchmark simulations have well demonstrated effectiveness and efficiency of the proposed approach.

Direct Adaptive Neural Control Design for a Class of Nonlinear Multi Input Multi Output Systems

This paper proposes a direct adaptive neural control law for a class of affine nonlinear multi-input-multi-output (MIMO) systems of the form $\dot {x}=f(x)+G(x)u$ using feedback linearization when both $f(x)$ and $G(x)$ are to be estimated. It is challenging to estimate $f(x)$ , a vector, and $G(x)$ , a matrix, to be used in synthesizing the control law, simultaneously, because of the dimensional inconsistency arising with the available neural structures, which do not have multiple layers of outputs. This problem is addressed in this paper by exploiting the power of matrix vectorization and reshaping techniques using the Kronecker product. The strategy may be visualized as equivalent to the neural structure consisting of multiple layers of outputs that result from the appropriate manipulation of matrices corresponding to the proposed estimations. The weight update laws, for both the radial basis function neural networks that estimate both $f(x)$ and $G(x)$ , are derived such that the proposed control law achieves the twin objective of the derived tracking performance as well as closed-loop system stability in the sense of Lyapunov. The ratios $\alpha $ and $\beta $ are proposed in line with the widely used concept of Rayleigh’s quotient adopted in structural dynamics to evaluate the natural frequency of a system. The simulation results obtained from the use of a twin rotor MIMO system are presented here to demonstrate the feasibility and effectiveness of the proposed control law. The superiority of this approach lies in the development of suitable control law for a MIMO system in the absence of knowledge about the nonlinearities.

F40THE ANALYSIS APOE-DEPENDENT STEM CELL PLASTICITY AND STEM CELL AGING DURING DEVELOPMENT OF IPS CELL-DERIVED NEURAL PROGENITORS FROM DEMENTIA PATIENTS AND HEALTHY DONORS

This article is concerned with the problem of adaptive neural controller design for multi-input/multi-output nonlinear systems with input-saturations and disturbances. In the proposed design mechanism, we will take advantage of hyperbolic tangent functions to smooth the sharp corners of the input saturations and use Young’s inequality to handle the nonlinear terms derived from the deducing process, and meanwhile apply the intelligent algorithm to estimate the unknown nonlinearity via neural networks. Furthermore, the backstepping technique is used to complete the design of the controller and Lyapunov stability theory is employed to show that the whole closed-loop system is semi-global uniformly ultimately bounded and the tracking error is bounded subject to the small neighborhood of the origin. Finally, as a practical application of the researched design scheme, adaptive neural controller for a continuous stirred tank reactor is constructed.

Adaptive Neural Control for MIMO Pure-Feedback Nonlinear Systems With Periodic Disturbances.

In this paper, an adaptive neural control design method is presented for a class of multiple-input-multiple-output (MIMO) pure-feedback nonlinear systems with periodically time-varying disturbances appearing nonlinearly in unknown nonaffine functions. The nonaffine functions do not need to be differentiable, and the bounded condition of unknown nonaffine functions is relaxed such that only a more general semibounded assumption is required as the controllability condition of the considered MIMO pure-feedback system. To facilitate the control design, the gain functions are designed to be continuous and positive with the bounds being unknown functions. Furthermore, for handling with the difficulty caused by these unknown bounds, several appropriate compact sets are defined to obtain the bounds of gain functions. By utilizing Lyapunov analysis, all the variables of the resulting closed-loop system are proven to be semiglobally uniformly ultimately bounded, and the tracking error can converge to an arbitrarily small neighborhood around zero by choosing design parameters appropriately. The effectiveness of the proposed control algorithm is demonstrated by two simulations.

Adaptive Neural State-Feedback Tracking Control of Stochastic Nonlinear Switched Systems: An Average Dwell-Time Method.

In this paper, the problem of adaptive neural state-feedback tracking control is considered for a class of stochastic nonstrict-feedback nonlinear switched systems with completely unknown nonlinearities. In the design procedure, the universal approximation capability of radial basis function neural networks is used for identifying the unknown compounded nonlinear functions, and a variable separation technique is employed to overcome the design difficulty caused by the nonstrict-feedback structure. The most outstanding novelty of this paper is that individual Lyapunov function of each subsystem is constructed by flexibly adopting the upper and lower bounds of the control gain functions of each subsystem. Furthermore, by combining the average dwell-time scheme and the adaptive backstepping design, a valid adaptive neural state-feedback controller design algorithm is presented such that all the signals of the switched closed-loop system are in probability semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in probability. Finally, the availability of the developed control scheme is verified by two simulation examples.

Output-feedback control design for switched nonlinear systems: Adaptive neural backstepping approach

The tracking control is addressed for switched nonlinear systems with arbitrary switchings by adaptive neural approach via output feedback. The switched systems under consideration are composed of some subsystems in non-strict -feedback form. It is assumed that all the system state variables are unavailable, but the output variable is measurable. A switched nonlinear observer is set up to estimate those unmeasurable state variables. Convex combination method is utilized to determine the observer gain matrix so that the effect from those nonlinear terms can be well compensated for. By the feature of the basis vector functions of radial basis neural networks (RBF NN), a new observer-based adaptive neural backstepping control design scheme is presented for the switched nonlinear non-strict feedback systems. The multiple Lyapunov method is used to show the stability of the adaptive closed-loop systems. It is also proven that the tracking error converges to a small neighborhood around the original point under the action of the suggested controllers. Finally, a simulation example is studied to test the efficacy of the suggested control strategies.

Adaptive Neural Controller Design Scheme of Nonlinear Delayed Systems With Completely Unknown Nonlinearities and Non-Strict-Feedback Structure

This paper proposes a novel adaptive intelligent tracking controller design scheme for a type of nonlinear delayed systems with completely unknown nonlinearities and non-strict-feedback structure. In the backsteppping-based design architecture, the intelligent estimation technique is utilized to approximate the unknown nonlinear functions via neural networks, and Lyapunov–Krasovskii functionals are designed to deal with the unknown delay terms. The constructed adaptive intelligent controller guarantees the semi-global boundedness of the resulting closed-loop system and the system output eventually converges to a small neighborhood around the desired reference signal. In the end, the presented simulation results verify the effectiveness of the proposed design method.

Neural Observer and Adaptive Neural Control Design for a Class of Nonlinear Systems.

This paper addresses the problem of adaptive neural tracking control for nonlinear nonstrict-feedback systems. The state variables are immeasurable and only the system output is available. A neural observer is constructed to estimate these unknown system state variables. An observer-based adaptive neural tracking control scheme is developed via backstepping approach. It is shown that the designed controller guarantees that the system output well follows the desired reference signal, and meanwhile, other closed-loop signals remain bounded. Finally, two simulation examples are used to test our results.

Adaptive Backstepping-Based Neural Tracking Control for MIMO Nonlinear Switched Systems Subject to Input Delays.

This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.