Multiple-model-and-neural-network-based nonlinear multivariable adaptive control

A multivariable adaptive controller feasible for implementation on distributed computer systems (DCS) is presented for a class of uncertain nonlinear multivariable discrete time systems. The adaptive controller is composed of a linear adaptive controller, a neural network nonlinear adaptive controller and a switching mechanism. The linear controller can provide boundedness of the input and output signals, and the nonlinear controller can improve the performance of the system. The purpose of using the switching mechanism is to obtain the improved system performance and stability simultaneously. Theory analysis and simulation results are presented to show the effectiveness of the proposed method.     

Nonlinear multivariable adaptive control using multiple models and neural networks

In this paper, a multivariable adaptive control approach is proposed for a class of unknown nonlinear multivariable discrete-time dynamical systems. By introducing a k-difference operator, the nonlinear terms of the system are not required to be globally bounded. The proposed adaptive control scheme is composed of a linear adaptive controller, a neural-network-based nonlinear adaptive controller and a switching mechanism. The linear controller can assure boundedness of the input and output signals, and the neural network nonlinear controller can improve performance of the system. By using the switching scheme between the linear and nonlinear controllers, it is demonstrated that improved performance and stability can be achieved simultaneously. Theory analysis and simulation results are presented to show the effectiveness of the proposed method.     

一类离散时间非线性系统的多模型自适应控制

针对一类离散时间非线性被控对象,根据模型参数的变化范围,对被控对象建立多个模型,并针对每一模型设计控制器.基于模型的估计误差建立指标切换函数,每一采样时刻,利用指标切换函数选择最优模型,并将基于此模型的控制器切换为当前控制器.采用局部化技术,保证在不损失控制品质的同时,减少多模型自适应控制器的计算量.可以证明,多控制器相互切换时闭环系统是稳定的,同时由于多个模型的存在,控制品质得到了极大的改善.     

Nonlinear adaptive control using multiple identification models

A multiple model adaptive controller is proposed for nonlinear systems in parametric-strict-feedback form. By running in parallel multiple identification models and designing a suitable switching scheme, some models close to the real plant can be selected quickly, so that transient performance can be improved significantly. Global asymptotic stability of the closed-loop switching system is proved. A simulation example is given to demonstrate the effectiveness of the proposed multiple model adaptive controller.     

The changing face of adaptive control: The use of multiple models

Adaptive systems that continuously monitor their own performance and adjust their control strategies to improve it, have been studied for over 50 years. The theory of such systems is now commonly referred to as classical adaptive control. Such control is now well established and is found to be satisfactory when the uncertainty in the system to be controlled (i.e. the plant) is small.During the past 15 years several attempts were made to extend this general methodology to systems with large uncertainties, by using multiple models to identify the plant. Among these, two general methods based on “switching” and “switching and tuning” have emerged as the leading contenders. Recently, a radically different approach was proposed by the authors (Han & Narendra, 2010b), in which the multiple models are used to play a significantly larger role in the decision making process, resulting in substantial improvement in performance.In this paper, which is tutorial in nature, the three methods based on multiple models are critically examined. At the same time, alternative methods using fixed and adaptive models are also proposed. In all cases, detailed simulation studies of adaptation in different environments are presented. Theoretical explanations are given, where available, for the wide spectrum of performances observed in the simulation studies.     

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．     

On near optimal neural control of multiple-input nonlinear systems

It has been a common consensus that general techniques for stabilization of nonlinear systems are available only for some special classes of nonlinear systems. Control design for nonlinear systems with uncertain components is usually carried out on a per system basis, especially when physical control constraints, and certain control performance measures such as optimum time control are imposed. Elegant adaptive control techniques are difficult to apply to this type of problems. A new neural network based control design is proposed and presented in this paper to deal with a special class of uncertain nonlinear systems with multiple inputs. The desired system dynamics are analyzed and utilized in the process of the proposed intelligent control design. The theoretical results are provided to justify the design procedures. The simulation study is conducted on a second-order bilinear system with two inputs and uncertainties on its parameters. The simulation results indicate that the proposed design approach is effective.     

An adaptive disturbance rejection control scheme for multivariable nonlinear systems

An adaptive disturbance rejection control scheme is developed for uncertain multi-input multi-output nonlinear systems in the presence of unmatched input disturbances. The nominal output rejection scheme is first developed, for which the relative degree characterisation of the control and disturbance system models from multivariable nonlinear systems is specified as a key design condition for this disturbance output rejection design. The adaptive disturbance rejection control design is then completed by deriving an error model in terms of parameter errors and tracking error, and constructing adaptive parameter-updated laws and adaptive parameter projection algorithms. All closed-loop signals are guaranteed to be bounded and the plant output tracks a given reference output asymptotically despite the uncertainties of system and disturbance parameters. The developed adaptive disturbance rejection scheme is applied to turbulence compensation for aircraft fight control. Simulation results from a benchmark aircraft model verify the desired system performance.     

Dissipative-based adaptive neural control for nonlinear systems

A dissipative-based adaptive neural control scheme was developed for a class of nonlinear uncertain systems with unknown nonlinearities that might not be linearly parameterized. The major advantage of the present work was to relax the requirement of matching condition, i.e., the unknown nonlinearities appear on the same equation as the control input in a state-space representation, which was required in most of the available neural network controllers. By synthesizing a state-feedback neural controller to make the closed-loop system dissipative with respect to a quadratic supply rate, the developed control scheme guarantees that the L2-gain of controlled system was less than or equal to a prescribed level. And then, it is shown that the output tracking error is uniformly ultimate bounded. The design scheme is illustrated using a numerical simulation.     

多变量自适应极点配置对偶控制的研究

针对参数未知的多变量差分方程形式的系统,首先利用Kalman滤波器进行参数辨识,根据确定性等价原理对系统进行极点配置;然后利用极点配置得到的非对偶控制器作为标称输入,其对应的输出作为标称输出,进而根据双指标准则进行对偶控制器的设计;最后给出一个仿真实例,验证该算法的可行性和有效性.     

多变量系统的非理想解耦自适应控制

将非理想解耦方法与一种简单的、具有较好鲁棒性的模型参考自适应控制策略相结合 ,提出了一类不确定系统的非理想解耦自适应控制方法。该方法在保证系统稳定的前提下 ,使解耦控制器作最大限度的解耦。仿真结果表明该控制器控制效果良好。     

Robust adaptive control of linearizable nonlinear single input systems with guaranteed error bounds

In this paper, a nonlinear robust adaptive control algorithm is designed and analyzed for a class of single-input nonlinear systems with unknown nonlinearities. The controller employs a single layer neural network to estimate the unknown plant nonlinearities on-line. The proposed controller is continuous and guarantees closed-loop semi-global stability and convergence of the tracking error to a small residual set. Furthermore, it handles the situation where the estimated plant becomes uncontrollable without any restrictive assumptions. In contrast to previous work on the same subject, the size of the residual tracking error can be specified a priori and is guaranteed by choosing certain design parameters. A procedure for choosing these parameters is presented. An example is used to demonstrate the performance and properties of the proposed scheme.     

Immersion and invariance adaptive control of linear multivariable systems

We show in this paper that it is possible to globally adaptively stabilize linear multivariable systems with reduced prior knowledge of the high-frequency gain. In particular, we relax the restrictive (nongeneric) symmetry condition usually required to solve this problem. Instrumental for the establishment of our result is the use of the new immersion and invariance approach to adaptive control recently proposed in the literature. The controllers obtained with this technique are not certainty equivalent—though smooth and without projections or overparameterizations—and the resulting Lyapunov functions contain cross-terms between the plant states and the parameter errors.     

Parameterization issues in multivariable adaptive control

This paper gives both an overview of multivariable adaptive control algorithms which have evolved to date and presents some new approaches to the design of indirect multivariable adaptive control systems. All algorithms are presented using a unified pole placement approach. Furthermore the emphasis is on parameterization issues such as: types of control structures necessary for implementation, required prior information necessary for implementation and techniques for reducing the size of the resulting parameter estimation problem.     

A direct method for robust adaptive nonlinear control with guaranteed transient performance

In this paper, the adaptive control problem is studied for a class of nonlinear systems in the presence of bounded disturbances. By utilizing a nice property of the studied systems, a novel Lyapunov-based control structure is developed, which avoids the possible control singularity problem in adaptive nonlinear control. The transient bounds of output tracking error are shown to be explicit functions of initial conditions and design parameters, and the control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulation study is provided to verify the theoretical results.     

The zero divisor problem of multivariable stochastic adaptive control

Stochastic adaptive minimum variance control algorithms require a division by a function of a recursively computed parameter estimate at each instant of time. In order that the analysis of these algorithms is valid, zero divisions must be events of probability zero. This property is established for the stochastic gradient adaptive control algorithm under the condition that the initial state of the system and all finite segments of its random disturbance process have a joint distribution which is absolutely continuous with respect to Lebesgue measure. This result is deduced from the following general result established in this paper: a non-constant rational function of a finite set of random variables {x₁},x_n} is absolutely continuous with respect to Lebesgue measure if the joint distribution function of {x₁,…,x_n} has this property.     

Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics

A neural network-based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unmodeled dynamics. By on-line approximating the unknown nonlinear functions and unmodeled dynamics by radial basis function (RBF) networks, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. It is proved that with the proposed control law, the closed-loop system is stable and the tracking error converges to zero in the presence of unmodeled dynamics and unknown nonlinearity. A simulation example is presented to demonstrate the method.     

Robust adaptive control of nonlinear non-minimum phase systems with uncertainties

This paper, presents a robust adaptive control method for a class of nonlinear non-minimum phase systems with uncertainties. The development of the control method comprises two steps. First, stabilization of the system is considered based on the availability of the output and internal dynamics of the system. The reference signal is designed to stabilize the internal dynamics with respect to the output tracking error. Moreover, a combined neuro-adaptive controller is proposed to guarantee asymptotic stability of the tracking error. Then, the overall stability is achieved using the small gain theorem. Next, the availability of internal dynamics is relaxed by using a linear error observer. The unmatched uncertainty is compensated using a suitable reference signal. The ultimate boundedness of the reconstruction error signals is analytically shown using an extension of the Lyapunov theory. The theoretical results are applied to a translational oscillator/rotational actuator model to illustrate the effectiveness of the proposed scheme.     

Adaptive switching control of discrete time nonlinear systems based on multiple models

We use the approach of “optimal” switching to design the adaptive control because the design among multiple models is intuitively more practically feasible than the traditional adaptive control in improving the performances. We prove that for a typical class of nonlinear systems disturbed by random noise, the multiple model adaptive switching control based on WLS(Weighted Least Squares) or projected-LS (Least Squares) is stable and convergent.