Optimal output-feedback tracking of SISO stochastic nonlinear systems using multi-dimensional Taylor network

Adaptive fault tolerant tracking control for a class of stochastic nonlinear systems with output constraint and actuator faults

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.

This note is devoted to study the stabilization problem of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. By introducing the notation of input-to-state practical stability and an event-triggered strategy, we establish the input-to-state practically exponential mean-square stability of the suggested system. Moreover, we investigate the stabilization result by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities. Also, the lower bounds of interexecution times by the proposed event-triggered control method are obtained. Finally, an example is given to show the effectiveness of the proposed method. Compared with a large number of results for discrete-time stochastic systems, only a few results have appeared on the event-triggered control for continuous-time stochastic systems. In particular, there have been no published papers on the event-triggered control for continuous-time stochastic delay systems. This note is a first try to fill the gap on the topic.

This paper mainly focuses on output feedback practical tracking controller design for stochastic nonlinear systems with polynomial function growth conditions. Mostly, there are some studies on output feedback tracking control problem for general nonlinear systems with parametric certainty in existing achievements. Moreover, we extend it to stochastic nonlinear systems with parametric uncertainty and system nonlinear terms are assumed to satisfy polynomial function growth conditions which are more relaxed than linear growth conditions or power growth conditions. Due to the presence of unknown parametric uncertainty, an output feedback practical tracking controller with dynamically updated gains is constructed explicitly so that all the states of the closed-loop systems are globally bounded and the tracking error belongs to arbitrarily small interval after some positive finite time. An example illustrates the efficiency of the theoretical results.

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

A novel alleviating fuzzy control algorithm for a class of nonlinear stochastic systems in pure-feedback form

Motion control is an essential part of industrial machinery and manufacturing systems. In this article, the adaptive fuzzy controller is proposed for precision trajectory tracking control in biaxial X-Y motion stage system. The theoretical analyses of direct fuzzy control which is insensitive to parameter uncertainties and external load disturbances are derived to demonstrate the feasibility to track the reference trajectories. The Lyapunov stability theorem has been used to testify the asymptotic stability of the whole system, and all the signals are bounded in the closed-loop system. The intelligent position controller combines the merits of the adaptive fuzzy control with robust characteristics and learning ability for periodic command tracking of a servo drive mechanism. The simulation and experimental results on square, triangle, star, and circle reference contours are presented to show that the proposed controller indeed accomplishes the better tracking performances with regard to model uncertainties. It is observed that the convergence of parameters and tracking errors can be faster and smaller compared with the conventional adaptive fuzzy control in terms of average tracking error and tracking error standard deviation.

Backstepping-based decentralized bounded-H∞ adaptive neural control for a class of large-scale stochastic nonlinear systems

Decentralized stabilization of large-scale stochastic nonlinear systems with time-varying powers

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.

An approximation-based adaptive neural controller is constructed for uncertain stochastic nonlinear systems in nonstrict-feedback form appearing dead-zone and output constraint. Neural networks (NNs) are directly utilized to approximate the unknown nonlinear functions existing in systems. A barrier Lyapunov function is introduced to ensure that the trajectory of output is limited within a predetermined range. By integrating NNs into the backstepping technique, an adaptive neural controller is designed to guarantee all variables existing in the considered closed-loop system are semi-globally uniformly ultimately bounded, and by appropriately tuning several design parameters online, the tracking error can be converged to a small neighborhood of the origin. Simulations on a numerical example are given to demonstrate the effectiveness of the method proposed in this paper.

This paper investigates the stochastic distribution tracking problem while the probability density function (PDF) of the stochastic non-linear system output can be controlled to desired distribution. To achieve the control objective, a data- driven approach is proposed in which no information of the system model is required. The output PDF can be estimated by kernel density estimation (KDE) based on the collected system output data. Using the estimated PDF, the probability states can be obtained by sampling operation which can be used to re-characterise the PDF of the system output. Thus, the tracking performance can be achieved by PID control. The parametric selection of the controller has been analysed following the identified PDF dynamic model to assure the convergence of the system output. The effectiveness of the presented algorithm is illustrated by a numerical example.

In this paper, the output feedback adaptive multi-dimensional Taylor network (MTN) tracking control for a class of nonlinear systems with unmeasurable states is investigated. Firstly, a nonlinear state observer is designed to estimate the unmeasurable states, and then an adaptive MTN-based output-feedback control approach is developed via backstepping technique. Secondly, in view of the simple structure of MTN, the controller based on MTN has the advantages of simple structure and fast calculation speed. Thirdly, in order to avoid the “differential explosion” problem inherited from the backstepping design, dynamic surface control (DSC) technique is introduced in the process of controller design. The results demonstrate that this scheme guarantees the stability and tracking performance of the closed-loop system. Finally, simulation examples are given to reveal the viability of the proposed method.

This paper concerns the filtering problem of stochastic nonlinear systems that depend either on some external input (open-loop system) or on the system output (closed-loop system), through a controller. Such systems are denoted feedback systems. The following result is proven: for feedback systems, the minimum variance estimator belonging to a specific class of functions of the output in the open loop case has better or equal performance than the minimum variance estimator of the same class for the corresponding closed-loop system. Some consequences of this general result are illustrated together with a simple example.