Model-Reference Fuzzy Adaptive Control as a Framework for Nonlinear System Control

The paper presents a general methodology of adaptive control based on fuzzy model to deal with unknown plants. The problem of parameter estimation is solved using a direct approach, i.e. the controller parameters are adapted without explicitly estimating plant parameters. Thus, very simple adaptive and control laws are obtained using Lyapunov stability criterion. The generality of the approach is substantiated by Stone-Weierstrass theorem, which indicates that any continuous function can be approximated by fuzzy basis function expansion. In the sense of adaptive control, this implies the adaptive law with fuzzified adaptive control parameters. The proposed control algorithm may be viewed as an extension of classical adaptive control for linear plants, but compared to the latter it provides higher adaptation ability and consequently better performance if the plant is nonlinear. The global stability of the control system is assured and the tracking error converges to the residual set that depends on fuzzification properties. The main advantage of the approach is simplicity that suits control engineers since wide range of industrial processes can be controlled by the proposed method. In the paper, the control of heat exchanger is performed.     

Robust Adaptive Control of Robots Using Neural Network: Global Stability

A desired compensation adaptive law‐based neural network (DCAL‐NN) controller is proposed for the robust position control of rigid‐link robots. The NN is used to approximate a highly nonlinear function. The controller can guarantee the global asymptotic stability of tracking errors and boundedness of NN weights. In addition, the NN weights here are tuned on‐line, with no offline learning phase required. When compared with standard adaptive robot controllers, we do not require linearity in the parameters, or lengthy and tedious preliminary analysis to determine a regression matrix. The controller can be regarded as a universal reusable controller because the same controller can be applied to any type of rigid robots without any modifications. A comparative simulation study with different robust and adaptive controllers is included.     

A new model reference control architecture: Stability,performance, and robustness

In this paper, we develop a new model reference control architecture to effectively suppress system uncertainties and achieve a guaranteed transient and steady‐state system performance. Unlike traditional robust control frameworks, only a parameterization of the system uncertainty given by unknown weights with known conservative bounds is needed to stabilize uncertain dynamical systems with predictable system performance. In addition, the proposed architecture's performance is not dependent on the level of conservatism of the bounds of system uncertainty. Following the same train of thought as adaptive controllers that modify a given reference system to improve system performance, the proposed method is inspired by a recently developed command governor theory that minimizes the effect of system uncertainty by augmenting the input signal of the uncertain dynamical and reference systems. Specifically, a dynamical system, called a command governor, is designed such that its output is used to modify the input of both the controlled uncertain dynamical and reference systems. It is theoretically shown that if the command governor design parameter is judiciously selected, then the controlled system approximates the given original, unmodified reference system. The proposed approach is advantageous over model reference adaptive control approaches because linearity of the uncertain dynamical system is preserved through linear control laws, and hence, the closed‐loop performance is predictable for different command spectrums. Additionally, it is shown that the architecture can be modified for robustness improvements with respect to high frequency content due to, for example, measurement noise. Modifications can also be made in order to accommodate actuator dynamics and retain closed‐loop stability and predictable performance. The main contribution of this paper is the rigorous analysis of the stability and performance of a system utilizing the command governor framework. A numerical example is provided to illustrate the effectiveness of the proposed architecture. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive backstepping impact angle control with autopilot dynamics and acceleration saturation consideration

This paper presents a robust impact angle constraint guidance law for maneuvering target interception in the presence of autopilot dynamics and input saturation. The presented guidance law is designed on the basis of a combination of adaptive backstepping control technique and higher‐order sliding mode differentiator. Different from existing impact angle constraint guidance law using sliding mode control, the line‐of‐sight angular rate and impact angle tracking error are regulated by two different virtual control laws. Because the future course of action of the target, an independent entity, cannot be predicted beforehand, adaptive laws are introduced in guidance law derivation for disturbance rejection. Unlike dynamic surface control approach, higher‐order sliding mode differentiator is adopted here as an alternative way to obtain the derivatives of the virtual control laws, thus leading to the exact tracking performance of backstepping control. Detailed stability analysis shows that both the line‐of‐sight angular rate and impact angle error can be stabilized in a small region around zero asymptotically. Simulation results explicitly show that accurate interception is achieved with a wide range of impact angles. Copyright © 2017 John Wiley & Sons, Ltd.     

Adaptive and non-adaptive 'pole-placement' control of multivariable linear time-varying plants

In this paper, the adaptive and non-adaptive 'pole-placement' control problems are addressed for a class of indexinvariant multivariable linear time-varying plants. In the case where the plant parameters are completely known, it is shown that a 'pole-placement'-like control algorithm can be designed by solving a time-varying Diophantine equation. Furthermore, the tracking performance of such a controller can be improved by incorporating the internal model principle into the design. In the case where the plant parameters are only partially known, a gradient-based adaptive law with projection and normalization is employed to estimate the plant parameters on-line. An adaptive controller is then designed, based on these parameter estimates, and the stability properties of the adaptive closed-loop plant are established. The design and realization of both the adaptive and non-adaptive control laws is illustrated by means of a simple example.     

L1 adaptive output‐feedback control of multivariable nonlinear systems subject to constraints using online optimization

In this paper, an L₁ adaptive output‐feedback controller is developed for multivariable nonlinear systems subject to constraints using online optimization. In the L₁ adaptive architecture, an adaptive law will update the adaptive parameters that represent the nonlinear uncertainties such that the estimation error between the predicted state and the real state is driven to zero at every integration time step. Of course, neglection of the unknowns for solving the error dynamic equations will introduce an estimation error in the adaptive parameters. The magnitude of this error can be lessened by choosing a proper sampling time step. A control law is designed to compensate the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. Model predictive control is introduced to solve a receding horizon optimization problem with various constraints maintained. Numerical examples are given to illustrate the design procedures, and the simulation results demonstrate the availability and feasibility of the developed framework.     

Decentralised adaptive architectures for control of large-scale active–passive modular systems with stability and performance guarantees

ABSTRACT

Decentralised control of large-scale active–passive modular systems is considered in this paper. The considered class of large-scale systems consist of physically interconnected and generally heterogeneous modules, where local control signals can only be applied to a subset of these modules (i.e. active modules) and the rest do not admit any control signals (i.e. passive modules). Specifically, based on a set-theoretic model reference adaptive control approach predicated on restricted potential functions, we design and analyse decentralised command following control laws for each active module such that they can effectively perform their tasks in the presence of unknown physical interconnections between modules and module-level system uncertainties. The key feature of our framework allows the system error trajectories of the active modules to be contained within a-priori, user-defined compact sets. Thus, they are guaranteed to achieve strict performance guarantees, where this is of paramount importance for practical applications. In addition to our theoretical findings and research contributions, the efficacy of the proposed decentralised adaptive control architecture is demonstrated in an illustrative numerical example.     

多变量非线性系统的间接模糊输出反馈自适应控制

针对一类多输入多输出非线性不确定系统，提出一种基于观测器的模糊间接自适应控制方法，并基于李亚普诺夫函数方法，导出了输出反馈控制律以及参数的自适应律，证明了整个控制方案不但能保证闭环系统稳定，而且取得了良好的跟踪控制性能。     

Model-free adaptive control design for nonlinear discrete-time processes with reinforcement learning techniques

This paper deals with the model-free adaptive control (MFAC) based on the reinforcement learning (RL) strategy for a family of discrete-time nonlinear processes. The controller is constructed based on the approximation ability of neural network architecture, a new actor-critic algorithm for neural network control problem is developed to estimate the strategic utility function and the performance index function. More specifically, the novel RL-based MFAC scheme is reasonable to design the controller without need to estimate y(k+1) information. Furthermore, based on Lyapunov stability analysis method, the closed-loop systems can be ensured uniformly ultimately bounded. Simulations are shown to validate the theoretical results.     

Dynamical adaptive integral backstepping variable structure controller design for uncertain systems and experimental application

In this study, a dynamical adaptive integral backstepping variable structure control (DAIBVSC) system based on the Lyapunov stability theorem is proposed for the trajectory tracking control of a nonlinear uncertain mechatronic system with disturbances. In this control scheme, no prior knowledge is required on the uncertain parameters and disturbances because it is estimated by two types of dynamical adaptive laws. These adaptive laws are integrated into the dynamical adaptive integral backstepping control and variable structure control (VSC) parts of the DAIBVSC. The dynamical adaptive law in the dynamical adaptive integral backstepping control part updates parametric uncertainties, while the other in the VSC part adapts upper bounds of non‐parametric uncertainties and disturbances. In order to achieve a more robust output tracking and better parameter adaptation, the control system is extended by one integrator and sliding surface is augmented by an integral action. Experimental evaluation of the DAIBVSC is conducted with respect to performance and robustness to parametric uncertainties. Experimental results of the DAIBVSC are compared with those of a traditional VSC. The proposed DAIBVSC exhibits satisfactory output tracking performance, good estimation of the uncertain parameters and can reject disturbances with a chattering free control law. Copyright © 2017 John Wiley & Sons, Ltd.     

基于参数估计误差的鲁棒自适应律设计及验证

针对传统自适应控制系统设计的自适应律参数收敛慢进而影响控制系统瞬态性能的问题,研究一类新的基于参数估计误差修正的鲁棒自适应律设计.首先引入滤波操作给出参数估计误差的提取方法,构建出含参数估计误差修正项的自适应律,进而将该自适应律用于控制器设计和分析中,可同时实现控制误差和参数估计误差指数收敛.对比分析了几类传统自适应律和所提出自适应律的收敛性和鲁棒性,并给出了保证参数收敛所需持续激励条件的一种直观、简便的在线判别方法.数值仿真及基于自制三自由度直升机系统俯仰轴实验结果表明,基于参数误差修正的自适应律及控制器可得到优于传统自适应方法的跟踪控制和参数估计性能.     

一类关于不确定性机器人的鲁棒控制策略

基于计算力矩结构,研究参数和结构不确定的机器人轨迹跟踪的鲁棒控制策略.其 特点是利用了机器人不确定动力学的集中包络函数,在该包络函数已知的情况下,设计的非 线性连续补偿控制律能够有效消除系统的不确定性影响,保证系统达到三种不同的稳定性结 果.另外,在该包络函数参数未知时,还没计了一个新颖的在线辨识器,可保证系统指数意义 下的渐近收敛或一致有界.     

一类非线性多变量系统的多模型自适应解耦控制

针对一类多变量离散时间非线性动态系统。分别设计线性鲁棒自适应解耦控制律和神经网络非线性自适应解耦控制律．根据指定的性能指标,通过它们之间的切换对系统进行控制．理论分析和仿真结果表明,该控制策略不但可以保证闭环系统BIBO稳定,而且能够改善系统的性能．     

Supervisory control of air–fuel ratio in spark ignition engines

The problem of air–fuel ratio stabilization in spark ignition engines is addressed in this paper. The proposed strategy consists of proper switching among two control laws to improve quality of the closed-loop system. The first control law is based on an a priori off-line identified engine model and ensures robust and reliable stabilization of the system at large, while the second control law is adaptive, it provides on-line adaptive adjustment to the current fluctuations and improves accuracy of the closed-loop system. The supervisor realizes a switching rule between these control laws providing better performance of regulation. Results of implementation on two vehicles are reported and discussed.     

Passivity and robust PI control of the air supply system of a PEM fuel cell model

Fuel cells are electrochemical devices that convert the chemical energy of a gaseous fuel directly into electricity. They are widely regarded as potential future stationary and mobile power sources. The response of a fuel cell system depends on the air and hydrogen feed, flow and pressure regulation, and heat and water management. In this paper, the study is concentrated on the control of the air subsystem that feeds the fuel cell cathode with oxygen—whose dynamics is described with a widely accepted nonlinear model. Due to the complexity of this model, the model-based controllers that have been proposed for this application are designed using its linear approximation at a given equilibrium point, which might lead to conservative stability margin estimates for the usually wide operating ranges of the system. On the other hand, practitioners propose the use of simple proportional or proportional–integral controllers around the compressor flow, which ensures good performance in most applications. In this paper we provide the theoretical justification to this scheme, proving that this output variable has the remarkable property that the linearization (around any admissible equilibrium) of the input–output map is strictly passive. Hence, the controllers used in applications yield (locally) asymptotically stable loops—for any desired equilibrium point and all values of the controller gains. Ensuring stability for all tuning gains overcomes the inherent conservativeness of linearized dynamics analysis, and assures the designer on the current use of robust, high performance loops. Instrumental to prove the passivity property is the exploitation of some monotonicity characteristics of the system that stem from physical laws.     

Uniting local and global controllers for uncertain nonlinear systems: beyond global inverse optimality

This paper provides a solution to a new problem of global robust control for uncertain nonlinear systems. A new recursive design of stabilizing feedback control is proposed in which inverse optimality is achieved globally through the selection of generalized state-dependent scaling. The inverse optimal control law can always be designed such that its linearization is identical to linear optimal control, i.e. optimal control, for the linearized system with respect to a prescribed quadratic cost functional. Like other backstepping methods, this design is always successful for systems in strict-feedback form. The significance of the result stems from the fact that our controllers achieve desired level of ‘global’ robustness which is prescribed a priori. By uniting locally optimal robust control and global robust control with global inverse optimality, one can obtain global control laws with reasonable robustness without solving Hamilton–Jacobi equations directly.     

Adaptive control of Hammerstein–Wiener nonlinear systems

The Hammerstein–Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein–Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.     

Extended filtering high‐gain output feedback controller for a class of uncertain nonlinear systems subject to external disturbances

In this article, an extended filtering high‐gain output feedback controller is developed for a class of uncertain nonlinear systems subject to external disturbances. The nonlinearities under consideration satisfy a semiglobal Lipschitz condition. The proposed control architecture integrates the extended state observer (ESO), high gain, and low‐pass filter together. None of them is used alone. The ESO can not only estimate the unknown internal state, but also deliver a good property of disturbance rejection simultaneously due to the presence of high gain. Since the high gain deteriorates the robustness of the system, a low‐pass filtering mechanism is added in the control law to filter away aggressive signals and recover the robustness. The filtering control law is designed to compensate the nonlinear uncertainties and deliver a good tracking performance with guaranteed stability. The matched uncertainties are canceled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. Since the virtual reference system defines the best performance that can be achieved by the closed‐loop system, the uniform performance bounds are derived for the states and control signals via comparison. Numerical examples are provided to illustrate the effectiveness of the novel design via comparisons with the model reference adaptive control method and L₁ adaptive controller.     

Mixed H2/H∞ robust model predictive control with saturated inputs

In this paper, we investigate the mixed H₂/H_∞ robust model predictive control (RMPC) for polytopic uncertain systems, which refers to the infinite horizon optimal guaranteed cost control (OGCC). To fully use the capability of actuators, we adopt a saturating feedback control law as the control strategy of RMPC. As the saturating feedback control law can be effectively represented by the convex hull of a group of auxiliary linear feedback laws, the auxiliary feedback laws allow us to design the actual feedback control law without consideration of the input constraints directly to achieve the improved performance. Moreover, we suggest the relative weights on the actual and auxiliary feedback laws to the RMPC, which in turn improves the closed-loop system performance. Furthermore, an off-line design of the proposed RMPC is also developed to make it more practical. Numerical studies demonstrate the effectiveness of the proposed algorithm.