New approach to robust model reference adaptive control for a class of plants

Motivated by recent advances in designing robust adaptive controllers and in dealing with uncertain dynamical systems, a new model reference adaptive control which is robust to a class of unmodelled dynamics and bounded output disturbances in the case of relative degree one is presented. The implementation of the controllers includes a switching mechanism which plays a crucially important role in functions of stabilizing as well as tracking. It is shown that global stability of the overall system is achieved under no assumption of persistency of excitation, and tracking errors will converge to a residual set whose size can be directly related to the size of unmodelled dynamics and of output disturbances explicitly. In the ideal case, the residual set degenerates to a single null point and convergence can be achieved in finite time without any requirement of persistency of excitation.     

Model reference adaptive control for nonminimum phase systems

In this paper we define a new model reference adaptive control problem which allows a large amount of plant uncertainty. Instead of the usual goal of asymptotic error regulation, here we require that the limit superior of the magnitude of the error be less than a predefined constant times the limit superior of the magnitude of the external reference input. This provides a natural way to incorporate uncertainty which includes nonminimum phase systems.     

State-space approach to non-linear model reference adaptive control

A new method is developed for tracking in non-linear delay-differential systems when the exact knowledge of the system parameters are not known. The method is based on securing the stability in the state spaces of plant and reference models. The results obtained are quite general in nature and can be applied to many physical systems.     

A new approach to model reference adaptive control

In classical model reference adaptive control, the goal is to design a controller to make the closed-loop system act like a prespecified reference model in the face of significant plant uncertainty. Typically, the controller consists of an identifier (or tuner) which is used to adjust the parameters of a linear time-invariant (LTI) compensator, and under suitable assumptions on the plant model uncertainty it is proven that asymptotic matching is achieved. However, the controller is typically highly nonlinear, and the closed loop system can exhibit undesirable behavior, such as large transients or a large control signal, especially if the initial parameter estimates are poor. Furthermore, its ability to tolerate time-varying parameters is typically limited. Here, we propose an alternative approach. Rather than estimating the plant or compensator parameters, instead we estimate what the control signal would be if the plant parameters and plant state were known and the "ideal LTI compensator" were applied. We end up with a linear periodic controller. Our assumptions are reasonably natural extensions of the classical ones to the time-varying setting; we allow rapid parameter variations, although we add a compactness requirement. We prove that we can obtain arbitrarily good tracking, explore the benefits and limitations of the approach, and provide a simulation study.     

A model reference approach to safe controller changes in iterative identification and control

A controller change from a current controller which stabilises the plant to a new controller, designed on the basis of an approximate model of the plant and with guaranteed bounds on the stability properties of the true closed loop, is called a safe controller change. In this paper, we present a model reference approach to the determination of safe controller changes on the basis of approximate closed loop models of the plant and robust stability results in the ν-gap.     

Imperfect model reference adaptive control: deadbeat output error approach

It is well known that while the perfect model matching condition (i.e. unstable plant zeros must be zeros of the reference model) is not met, the model reference adaptive control cannot easily be implemented. In adaptive control systems, since the plant is assumed to be unknown previously, it is a difficult task to choose an adequate reference model such that the perfect model matching condition is guaranteed in every adaptive step. In this paper, a new design algorithm for model reference adaptive control systems is proposed to synthesize an adaptive controller such that the error between the reference model output and the plant output can vanish in a deadbeat manner. In this situation, the stringent matching condition can be relaxed in every adaptive step, so our design algorithm is also suitable for unstable or non-minimum phase systems. Several simulation results are presented to illustrate the good behaviour of our design algorithm.     

Adaptive control of nonminimum phase systems subject to unknownbounded disturbances

This paper presents a robust adaptive pole placement control scheme for continuous-time systems with bounded disturbances. The system may possibly be nonminimum phase and unstable. It is shown that for arbitrary bounded disturbances, a global asymptotical bounded-input/bounded-output (BIBO) stability is established through pole placement techniques without either introducing persistent excitation probing signals into the system or assuming any a priori knowledge on the plant parameters. Moreover, the disturbance upper bound is not assumed to be known. The system order is the only a priori knowledge required on the plant. The adaptive control law is free from singularities in the sense that the estimated plant model is always controllable     

基于虚拟参考反馈整定的改进无模型自适应控制

针对一类离散时间非线性系统, 提出一种基于虚拟参考反馈整定的改进无模型自适应控制方案. 首先, 利用动态线性化方法给出非线性系统的紧格式动态线性化模型; 然后, 基于优化技术设计控制算法和伪偏导数估计算法; 最后, 设计基于虚拟参考反馈整定的伪偏导数初值和重置值的估计算法. 该控制方案设计仅依赖于被控系统的输入和输出数据, 且能保证闭环系统的稳定性和收敛性. 仿真比较结果验证了所提出方法的有效性.

     

非定常参考模型的模型参考自适应控制系统（MRACS）设计

针对定常参考模型ＭＲＡＣＳ无法实现最优性能指标控制问题,提出了采用非定常参考模型的ＭＲＡＣＳ设计方法,使被控对象跟随最优性能指标下线性时变或非线性参考模型的设计问题得以实现。     

Direct model reference adaptive control using Kp = LDU factorization for multivariable discrete-time plants

For a large class of discrete-time multivariable plants with arbitrary relative degrees, the design and analysis of the direct model reference adaptive control scheme are investigated under less restrictive assumptions. The algorithm is based on a new parametrization derived from the high frequency gain matrix factorization Kp=LDU under the condition that the signs of the leading principal minors of/fp are known. By reproving the discrete-time Lp and L2σ norm relationship between inputs and outputs, establishing the properties of discrete-time adaptive law, defining the normalizing signal, and relating the signal with all signals in the closed-loop system, the stability and convergence of the discrete-time multivariable model reference adaptive control scheme are analyzed rigorously in a systematic fashion as in the continuous-time case.     

A reference model approach to stability analysis of neural networks

In this paper, a novel methodology called a reference model approach to stability analysis of neural networks is proposed. The core of the new approach is to study a neural network model with reference to other related models, so that different modeling approaches can be combinatively used and powerfully cross-fertilized. Focused on two representative neural network modeling approaches (the neuron state modeling approach and the local field modeling approach), we establish a rigorous theoretical basis on the feasibility and efficiency of the reference model approach. The new approach has been used to develop a series of new, generic stability theories for various neural network models. These results have been applied to several typical neural network systems including the Hopfield-type neural networks, the recurrent back-propagation neural networks, the BSB-type neural networks, the bound-constraints optimization neural networks, and the cellular neural networks. The results obtained unify, sharpen or generalize most of the existing stability assertions, and illustrate the feasibility and power of the new method.     

模型参考自适应控制在自动导向车中的应用

运用波波夫（POPOV）超稳定性理论，对自动导向车（AGV）的速度控制设计模型参考自适应控制系统。此控制系统可以抑制干扰，减小自动导向车运行偏差，使其沿着预定的轨迹运行。并通过仿真实验验证所设计系统的可行性。     

Identifier-tracking model reference adaptive control

Model reference adaptive control is a major design method for controlling plants with uncertain parameters. The primary objective of this paper is to develop a new design approach for a differentiator-free model reference adaptive control of a single-input single-output linear time-invariant plant. The proposed method, called the “Identifier-tracking model reference adaptive control”, uses a stacked identifier structure that is new to the field of adaptive control. The goal is to make the output of the plant asymptotically track the output of the first identifier, and then driving the output of the first identifier to track that of the second identifier, and so forth, up to the qth identifier where q is the relative degree of the plant. Lastly, the output of the qth identifier is forced to converge to that of the reference model. Simulation results show the superiority of the proposed method over the traditional model reference adaptive control with augmented error in terms of the transient response. Since the resulting control systems are non-linear and time-varying, the stability analysis of the overall system plays a central role in developing the theory.     

Robust model reference adaptive control

We propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed-loop adaptive control system with respect to unmodeled plant uncertainties. The robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law. The extra a priori information needed to design the adaptive law, are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function.     

Fuzzy model reference adaptive control

This paper investigates a fuzzy model reference adaptive controller (FMRAC) for continuous-time multiple-input-multiple-output (MIMO) nonlinear systems. The proposed adaptive scheme uses a Takagi-Seguno (TS) fuzzy adaptive system, which allows for the inclusion of a priori information in terms of qualitative knowledge about the plant operating points or analytical regulators (e.g., state feedback) for those operating points. A proportional-integral update law is used to obtain a fast parameters adaptation. Stability and robustness of this adaptive scheme are established using Lyapunov stability tools. The simulation results, for a two-link robot, confirm the performance of the proposed approach.     

Pre- and post-filtering approach to sensorless VSS speed control of a permanent magnet DC motor subject to Hammerstein and Wiener nonlinearities

In this paper, we propose a pre- and post-filtering approach to output feedback variable structure control of a permanent magnet DC servo motor under constant inertial load. The proposed control method is to regulate the motor speed by using the armature current measurement alone. Both the Hammerstein nonlinearity for the system input end and the Wiener nonlinearity for the output end are considered. With these static nonlinear functions carefully identified and their inverses fitted, the linearized model renders a simple dynamic mapping from the armature current to the sliding variable, which is designed as a dynamic function of the motor angular velocity. The pre-filter is the inverse of the Hammerstein function. The post-filter consists of two blocks in series: the inverse of the Wiener function and the concatenating dynamic filter, which is a linear relationship between the armature current and the sliding variable. The proposed method is robust against parameter variations in the electric subsystem such as the armature inductance and resistance.