Multi-Dimensional Taylor Network-Based Adaptive Output-Feedback Tracking Control for a Class of Nonlinear Systems

This paper presents a neural adaptive controller for a class of nonlinear system in the presence of input saturation and arbitrary unknown information by integrating the design framework of neural networks (NNs) with the dynamic surface control (DSC) and backstepping technique. NNs are directly used to deal with unknown nonlinear terms. By introducing a well-defined smooth function and a Nussbaum function, a novel robust adaptive control scheme is developed to guarantee the states of system to be semi-globally uniformly ultimately bounded (SGUUB). Owing to the introduction of DSC, the problem of ‘explosion of complexity’ inherent in the backstepping design is effectively eliminated. Simulation results demonstrate the effectiveness and simplicity of the proposed method.

This paper presents an adaptive multi-dimensional Taylor network (MTN) control approach for a class of nonlinear systems with unknown parameters. MTN is employed to identify unknown nonlinear characteristics existing in the system, and then a novel adaptive MTN tracking control method is proposed, via backstepping technique. In the controller design, double adaptive laws are designed and appropriate Lyapunov functions are chosen to overcome the difficulties caused by the unknown parameters. The designed controller can guarantee that all the variables in the closed-loop systems are bounded and the tracking error can be arbitrarily small. Finally, simulation results are presented to verify the effectiveness of the proposed approach.

In this paper, an inverse control scheme based on the novel dynamic network (multi-dimensional Taylor network (MTN)) is proposed for the real-time tracking control of nonlinear time-varying systems with noise disturbances. Utilized in this scheme are the three MTNs: the adaptive model identifier for system modeling, the adaptive inverse controller for inverse modeling, and the adaptive nonlinear filter for eliminating the noise disturbances, whose weights are modified by the variable forgetting factor recursive least squares (VFF-RLS), back propagation through model (BPTM), normalized least mean square (NLMS) algorithms, respectively. To avoid “compromise”, this scheme is designed into a structure wherein controlling the object dynamic response and eliminating the noise disturbances are implemented in two relatively independent processes. Furthermore, the weight-elimination algorithm is introduced for choice of effective regression items to avoid the dimension explosion, thus overcoming the shortcoming that the number of middle nodes needs to be determined before using the traditional neural network. After a certain number of training, the more streamlined MTNs are observed to contribute to satisfying the real-time requirements of software implementation and engineering application. To ensure that MTN inverse control is strict in theory, the general conditions for the existence of single-input/single-output (SISO) nonlinear inverse systems are identified. Simulation of the MTN inverse control is conducted to confirm the effectiveness of the proposed method.

In this paper, an novel adaptive tracking control is developed for a class of completely non-affine pure-feedback nonlinear systems using radial basis function neural networks (RBFNNs). Combining the dynamic surface control (DSC) technique and backstepping method, the explosion of complexity in the traditional backstepping design is avoided. Using mean value theorem and Young's inequality, only one learning parameter need to be tuned online in the whole controller design, and the computational burden is effectively alleviated. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system. Simulation results verify the effectiveness of the proposed approach.

In this study, the problem of adaptive multi‐dimensional Taylor network (MTN) control for single‐input single‐output (SISO) uncertain stochastic non‐linear systems is investigated. How to minimise the influence of randomness and uncertain non‐linearity for less complex computation, and how to improve the real‐time performance of the controller are of great significance. To this end, a control approach based on MTN is proposed for tracking control of stochastic non‐linear systems. MTNs are used to approximate the non‐linearities, and the backstepping technique is employed to construct the MTN controller (MTNC). MTNC involves only addition and multiplication, featuring desirable simplicity and real‐time performance. Stability of the system is guaranteed via Lyapunov approach, and it is proved that the proposed controller can guarantee that all signals of the closed‐loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighbourhood around the origin. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this study has good real‐time performance and control quality.

For switched nonlinear systems with output hysteresis, by working on multi-dimensional Taylor network (MTN), an adaptive control strategy is put forward, which can effectively solve the tracking control problem. Firstly, the modified Bouc–Wen hysteresis model is employed to cope with the nonlinear problem caused by output hysteresis. Secondly, the Nussbaum function is introduced into the control design process, and MTN is used to approach nonlinear structures. Thirdly, a novel network adaptive control strategy is constructed with the help of a common Lyapunov function, which can realize the tracking control and stability of the system simultaneously. It is worth noting that as a new type of neural network, MTN is first used for control of switched systems with output hysteresis. Finally, two simulation examples show that the proposed control strategy is effective.

Adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults based on dynamic surface technique

This paper focuses on the problem of adaptive output feedback tracking control for a class of non-strict-feedback nonlinear systems with unknown control coefficients. By employing a linear state transformation, the original system is transformed to a new system for which control design becomes feasible. Then, after the introduction of a simple input-driven observer, an adaptive output feedback controller which contains only one parameter is developed for such systems by using backstepping technique and variable separation method. The designed controller ensures that all the signals in the closed-loop systems are Semi-globally Uniformly Ultimately Bounded (SGUUB).

This paper focuses on the problem of multi-dimensional Taylor network (MTN)-based adaptive tracking control for a class of nonlinear systems with input constraints. As preliminaries, the saturation is first presented by a smooth function, and then a novel MTN-backstepping-based adaptive control method is designed on the basis of the Lyapunov stability theory. It is shown that the proposed control method can guarantee that all the signals in the closed-loop system are bounded and the tracking error converges to an arbitrarily small neighborhood around the origin. Finally, one example is given to illustrate the effectiveness of the proposed design approach.

Adaptive asymptotic tracking control of constrained nonlinear MIMO systems subject to unknown hysteresis input: A novel network-based strategy

This paper presents an adaptive neural tracking control approach for uncertain stochastic nonlinear time‐delay systems with input and output constraints. Firstly, the dynamic surface control (DSC) technique is incorporated into adaptive neural control framework to overcome the problem of ‘explosion of complexity’ in the control design. By employing a continuous differentiable asymmetric saturation model, the input constraint problem is solved. Secondly, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time‐delay terms, RBF neural network is utilized to identify the unknown systems functions, and barrier Lyapunov functions (BLFs) are designed to avoid the violation of the output constraint. Finally, based on adaptive backstepping technique, an adaptive neural control method is proposed, and it decreases the number of learning parameters. Using Lyapunov stability theory, it is proved that the designed controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two simulation examples are provided to further illustrate the effectiveness of the proposed approach.

MTN optimal control of MIMO non-affine nonlinear time-varying discrete systems for tracking only by output feedback

Adaptive tracking control for a class of switched uncertain nonlinear systems under a new state-dependent switching law

This paper is concerned with the problem of output feedback adaptive tracking control for a class of uncertain nonlinear time-delay systems (NTDS) with both uncertain output function and unknown control directions. By introducing a linear state transformation, the original system is transformed into a new system for which output feedback control design becomes feasible. Without the precise information on output function, an input-driven high-gain state observer is presented to estimate the unavailable states of the new system. Moreover, some radial basis function neural networks (RBFNNs) are employed to approximate the lumped unknown nonlinear functions during the procedure of control design. Then, by combining the Lyapunov–Krasovskii functional method, the Nussbaum gain function approach and the backstepping technique, a novel adaptive output feedback control scheme including only one parameter to be updated is developed for such systems. As a result, all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) while the tracking error can remain in a small neighbourhood of zero. Finally, two simulation examples are given to validate the effectiveness and applicability of the proposed design method.

An output feedback adaptive tracking scheme is proposed for a class of nonlinear systems with parameter uncertainty and input saturation. The unmeasured states are estimated by constructing filters, then dynamic surface control system is designed, which avoids explosion complexity of backstepping control. The effect of actuator saturation on system performance is compensated by neural network. It is shown that the proposed scheme can guarantee semi-global stability of the closed-loop system and the tracking error can be made arbitrarily small.KeywordsOutput feedback Dynamic surface control Input saturation Neural networks Adaptive control