Unknown Control Gain Functions Research Articles

Composite learning control of strict‐feedback nonlinear system with unknown control gain function

AbstractThe composite learning control with the heterogeneous estimator is proposed to deal with the multiple uncertainties of strict‐feedback nonlinear systems. The article applies the recorded data‐based neural learning and the disturbance observer (DOB) to learn the multiple uncertainties, including the nonlinear dynamics, the unknown control gain function (CGF), and the time‐varying disturbance. The lumped prediction error is constructed and included into the update law by neural approximation and disturbance observation. Furthermore, the asymmetric saturation nonlinearity (ASN) of the control input is represented by the smooth form model to ensure the input limitation, and a projection algorithm is adopted to avoid the singularity problem. The closed‐loop system stability is rigorously analyzed and the boundedness of the system tracking error is guaranteed. Through the tests of the third‐order nonlinear system and the autonomous underwater vehicle (AUV), it is observed that the proposed approach can improve the system tracking accuracy with the expected learning performance.

An Observer-Based Fuzzy Adaptive Consensus Control Method for Nonlinear Multiagent Systems

This article investigates the problem of fuzzy adaptive consensus tracking control for nonlinear multiagent systems with unknown nonlinear control gain functions. In the control design, fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics, and a distributed state observer is constructed to estimate the unmeasured states. Under the case of directed graph, by constructing the logarithm Lyapunov functions, an adaptive fuzzy distributed control method is presented, which removes the restrictive assumptions about the unknown control gain functions must be constants in traditional adaptive intelligent output feedback control methods. The developed control scheme cannot only ensure that all signals of the controlled system are semiglobal uniformly ultimately bounded, but also make the outputs of all the followers keep consensus with the output trajectory of the leader. Finally, simulation results are given to illustrate the effectiveness of the developed consensus control scheme and theorem.

Reinforcement learning‐based optimized backstepping control of nonlinear strict feedback system with unknown control gain function

AbstractThe article develops an optimized control via learning from the design idea of optimized backstepping (OB) technique for the nonlinear strict feedback systems containing the unknown dynamic and control gain functions. OB technique requires to deal with the actual and virtual controls of backstepping as the optimized solutions of corresponding subsystems so that the entire backstepping control is optimized. In the work, for achieving the optimization control, reinforcement learning (RL) of critic‐actor structure is constructed in every backstepping step on the basis of the neural network approximation of the Hamilton–Jacobi–Bellman equation's solution. Since the unknown nonlinear control gain function is considered, the complexity of control algorithm is greatly increased. However, the proposed RL is with the simple training laws, it can greatly alleviate the algorithm complexity for the optimized control. Finally, the feasibility of the method is demonstrated by both theory and simulation.

Predefined Time Synchronization Control for Uncertain Chaotic Systems.

In this study, the predefined time synchronization problem of a class of uncertain chaotic systems with unknown control gain function is considered. Based on the fuzzy logic system and varying-time terminal sliding mode control technology, the predefined time synchronization between the master system and the slave system can be realized by the proposed control method in this study. The simulation results confirm the theoretical analysis.

Fuzzy adaptive output feedback control for uncertain nonlinear systems with unknown control gain functions and unmodeled dynamics

In this work, the fuzzy adaptive robust output feedback control issues are investigated for single-input single-output (SISO) strict-feedback nonlinear systems. The controlled systems under consideration of this paper contain the unknown control gain functions, unmodeled dynamics and immeasurable states. The unknown nonlinear functions are be approximated by utilizing the fuzzy logic systems, and the immeasurable states are estimated by constructing a new fuzzy state observer. In order to handle the unknown control gain functions and the unmodeled dynamics problems, the Logarithm Lyapunov functions are constructed, under which a new fuzzy adaptive robust output feedback control scheme is proposed by using the adaptive backstepping control design technique and a dynamical signal function. The designed fuzzy adaptive control algorithm can ensure that the closed-loop system is semi-globally uniformly ultimately boundedness (SGUUB) and has the robustness to the unmodeled dynamics. Finally, a simulation example is considered to illustrate the availability of the designed controller.

Fuzzy adaptive dynamic surface control for strict-feedback nonlinear systems with unknown control gain functions

In this work, the fuzzy adaptive output feedback control is investigated for single-input single-output (SISO) uncertain nonlinear systems in strict-feedback form. The controlled systems under consideration of this work contain the immeasurable states and unknown control gain functions. The immeasurable states are estimated by constructing a fuzzy state observer, and the uncertain nonlinear functions are approximated by fuzzy logic systems. In order to settle the issue of ‘explosion of complexity’ inherent in the conventional backstepping design process, the ‘dynamic surface control’ (DSC) method is introduced. An observer-based fuzzy adaptive control algorithm is proposed by employing the adaptive backstepping control design technique and constructing the Logarithm Lyapunov functions. The designed fuzzy adaptive control scheme can settle the complexity problem of control scheme and insure that the closed-loop system is semi-globally uniformly ultimately boundedness (SGUUB), a simulation example is considered to illustrate the availability of the designed controller.

Fuzzy adaptive fault tolerant IGC method for STT missiles with time-varying actuator faults and multisource uncertainties

This paper studies the integrated guidance and control (IGC) problem for a class of skid-to-turn (STT) missiles subjected to rapidly changing actuator failures and coupled multisource uncertainties. Meanwhile, during interception, the target is allowed to possess unknown and changeable maneuver accelerations. By analyzing the dominating factors in the IGC system, a nonlinear uncertain strict-feedback system suffering from matched and mismatched uncertainties is utilized to describe the IGC dynamics. Furthermore, for each subsystem, the control gain functions and their boundaries are assumed unknown, which make it difficult to design the controllers. By using a hyperbolic tangent function and estimating the bounds of the lumped disturbances, the time-varying multisource uncertainties can be handled. To compensate the unknown nonlinearities existing in the IGC system, several fuzzy logic systems are established. Furthermore, a number of reciprocal adaptive laws are developed such that unwanted effects caused by the unknown control gain functions and changing actuator gain faults can be surmounted. As a result, a novel fault tolerant IGC structure is constructed and satisfactory hit-to-kill interception performance can be obtained. Finally, the numerical simulations are provided to verify the validity and advantage of the proposed method.

A combined backstepping and dynamic surface control to adaptive fuzzy state‐feedback control

SummaryThis paper studies an adaptive fuzzy dynamic surface control for a class of nonlinear systems with fuzzy dead zone, unmodeled dynamics, dynamical disturbances, and unknown control gain functions. The unknown system functions are approximated by the Takagi‐Sugeno–type fuzzy logic systems. There are 3 main features for the presented systematic design scheme. First, by adopting an integrated method, a novel adaptive fuzzy controller is constructed for the nonlinear system with fuzzy dead zone. Second, only 3 online learning parameters need to be tuned, which significantly reduces the computation burden. Third, the possible controller singularity problem in some of the existing adaptive control methods with feedback linearization techniques can be avoided. On the basis of the backstepping technique and dynamic surface control, all the signals of the closed‐loop system are guaranteed to be semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to illustrate the effectiveness of the proposed scheme.

Observer-based fuzzy adaptive fault control for a class of MIMO nonlinear systems

ABSTRACTIn this paper, the fault-tolerant control (FTC) problem is investigated for a class of multi-input multiple output nonlinear systems with time-varying delays, and an active FTC method is proposed. The controlled system contains unknown nonlinear functions, unknown control gain functions and actuator faults, which integrates time-varying bias and gain faults. Then, fuzzy logic systems are used to approximate the unknown nonlinear functions and unknown control gain functions, fuzzy adaptive observers are used for fault detection and isolation. Further, based on the obtained information, an accommodation method is proposed for compensating the actuator faults. It is shown that all the variables of the closed-loop system are semi-globally uniformly bounded, the tracking error converges to an arbitrary small neighbourhood of the origin. A simulation is given to demonstrate the effectiveness of the proposed approach.

Razumikhin–Nussbaum‐lemma‐based adaptive neural control for uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays

SUMMARYThis paper addresses the problem of adaptive neural control for a class of uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays. Major technical difficulties for this class of systems lie in: (1) the unknown control direction embedded in the unknown control gain function; and (2) the unknown system functions with unknown time‐varying delays. Based on a novel combination of the Razumikhin–Nussbaum lemma, the backstepping technique and the NN parameterization, an adaptive neural control scheme, which contains only one adaptive parameter is presented for this class of systems. All closed‐loop signals are shown to be 4‐Moment semi‐globally uniformly ultimately bounded in a compact set, and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed control schemes. Copyright © 2012 John Wiley & Sons, Ltd.

Adaptive neural control for a class of non-affine stochastic non-linear systems with time-varying delay: a Razumikhin–Nussbaum method

This study focuses on the problem of adaptive neural control for a class of uncertain non-affine stochastic non-linear systems with time-varying delay. Major technical difficulties for this class of systems lie in: (i) the unknown control direction embedded in the unknown control gain functions and (ii) the unknown system function with unknown time-varying delay. A novel Razumikhin–Nussbaum lemma is proposed to overcome the mentioned difficulties. Moreover, based on the Razumikhin functional approach, an adaptive neural controller is developed for this class of systems by exploring the application of Nussbaum functions to stochastic non-linear systems. The proposed design guarantees that all the error variables in the closed-loop systems are four-moment semi-globally uniformly ultimately bounded in a compact set, while the tracking error remains in a neighbourhood of the origin. The effectiveness of the proposed design is verified by simulation results.

Direct Adaptive Output Feedback CMAC Control with Unknown Control Gain for a Class of Nonlinear Systems

A direct adaptive output feedback CMAC (cerebellar model articulation controller) control based on only output measurements is proposed with unknown control gain function for a class of affine nonlinear systems. Therefore, it is needed to design a state observer to estimate unmeasured states of the systems. By using strictly positive-real Lyapunov theory, the stability of the closed-loop system can be guaranteed. Finally, simulation results for an inverted pendulum system show that the effect of the approximation error on the tracking error can be attenuated efficiently.

Adaptive neural network output feedback control for a class of non-affine non-linear systems with unmodelled dynamics

In this study, an output feedback-based adaptive neural controller is presented for a class of uncertain non-affine pure-feedback non-linear systems with unmodelled dynamics. Two major technical difficulties for this class of systems lie in: (i) the few choices of mathematical tools in handling the non-affine appearance of control in the systems, and (ii) the unknown control direction embedded in the unknown control gain functions, in great contrast to the standard assumptions of constants or bounded time-varying coefficients. By exploring the new properties of Nussbaum gain functions, stable adaptive neural network control is possible for this class of systems by using a strictly positive-realness-based filter design. The closed-loop system is proven to be semi-globally uniformly ultimately bounded, and the regulation error converges to a small neighbourhood of the origin. The effectiveness of the proposed design is verified by simulations.

Backstepping control for periodically time-varying systems using high-order neural network and Fourier series expansion

An adaptive backstepping tracking scheme is developed for a class of strict-feedback systems with unknown periodically time-varying parameters and unknown control gain functions. High-order neural network (HONN) and Fourier series expansion (FSE) are combined into a new function approximator to model each uncertain term in the system. The dynamic surface control (DSC) approach is used to solve the problem of ‘explosion of complexity’ in the backstepping design procedure. Nussbaum gain function (NGF) is employed to deal with the unknown control gain functions. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. Two simulation examples are provided to demonstrate the effectiveness of the control scheme designed in this paper.