离散时间间接型模型参考自适应控制的一种系统化的分析方法

This paper presents the design and analysis of indirect model reference adaptive control(MRAC)with normalized adaptive law for a class of discrete-time systems.The main work includes three parts.Firstly,the constructed plant parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms but also avoids the possibility of division by zero.Secondly,by finding the relationship between the plant parameter estimate and controller parameter estimate and using the properties of plant parameter estimate,the similar properties of controller parameter estimate are also established. Thirdly,based on the relationship properties between the normalizing signal and all the signals in the closed-loop system and on some important mathematical tools on discrete-time systems,as in the continuous-time case,a systematic stability and convergence analysis approach to the discrete indirect MRAC scheme is developed rigorously.     

离散时间直接型模型参考自适应控制

本文针对一类离散时间系统, 研究了具有规范化自适应律的直接型模型参考自适应控制 (MRAC). 我们重新证明了离散时间系统的输入与输出间的 Lp 范数与 L2δ 范数关系特性和离散时间的交换引理 1 与引理 2. 并建立了离散时间自适应律的性质, 定义了规范化信号, 把闭环系统中的所有信号与其建立联系. 从而, 正如连续时间系统一样, 以一种系统化的方法严格分析了离散时间 MRAC 方案的稳定性与收敛性.     

Gain Margins of Adaptive Control Systems

This paper presents a systematic study of the gain margins (GM) of adaptive control systems: the specification of the parameter range of a control gain matrix in a designed adaptive control system for maintaining the desired closed-loop signal boundedness and asymptotic tracking performance. It is proved that the GM is infinity for continuous-time direct model reference adaptive control (MRAC) schemes applied to multi-input, multi-output (MIMO) linear time-invariant (LTI) systems, while it is finite with an upper bound for the discrete-time case. The derived GM results are applicable to systems with adaptive nonlinear or pole placement control designs. Analytical GM result is also obtained for some indirect multivariable MRAC systems; in particular, the GM is infinity but with a lower bound for such systems. Methods for enlarging the GM by proper choices of design parameters are presented. Moreover, the effect of sample time on the GM of sampled-data adaptive control systems is studied, which establishes the relationship between the continuous-time and discrete-time GM results. A simulation example is provided to illustrate some of the theoretical results.      

A robust adaptive controller for Hammerstein nonlinear systems

Hammerstein nonlinear systems have appeared useful in modeling nonlinear processes encountered in engineering practice. Control algorithms may lead to unsatisfactory performance if the parametric model does not agree with the plant. To this end, this paper proposes a new robust adaptive control approach for discrete-time Hammerstein nonlinear systems which are more close to some industrial plants. The adaptive control law and recursive parameter estimation are updated by introducing the estimate of the model error as a feedback. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under mild conditions. Simulation examples including a continuous stirred tank reactor (CSTR) system are given to show the effectiveness of the obtained results.     

A discrete-time parameter estimation based adaptive actuator failure compensation control scheme

This article studies discrete-time adaptive failure compensation control of systems with uncertain actuator failures, using an indirect adaptive control method. A discrete-time model of a continuous-time linear system with actuator failures is derived and its key features are clarified. A new discrete-time adaptive actuator failure compensation control scheme is developed, which consists of a total parametrisation of the system with parameter and failure uncertainties, a stable adaptive parameter estimation algorithm, and an on-line design procedure for feedback control. This work provides a new design of direct adaptive compensation of uncertain actuator failures, using an indirect adaptive control method. Such an adaptive design ensures desired closed-loop system stability and tracking properties despite uncertain actuator failures. Simulation results are presented to show the desired adaptive actuator failure compensation performance.     

A modified model reference adaptive control scheme for improvedtransient performance

The author proposes a modified model reference adaptive control (MRAC) scheme aimed at improving the transient performance of adaptive systems while maintaining the ideal asymptotic properties possessed by standard MRAC. In the modified scheme, the estimation error, which is generated by the identification scheme, is used directly as a control signal to counteract errors resulting from the certainty equivalence design. It is shown that the modified scheme provides essentially the same stability and robustness properties as the standard adaptive MRAC approach but with the transient performance substantially improved. Simulation results are presented to illustrate the effectiveness of the proposed scheme     

Globally stabilizing adaptive control design for nonlinearly-parameterized systems

In this note, a new adaptive control design is proposed for nonlinear systems that are possibly nonaffine and contain nonlinearly parameterized unknowns. The proposed control is not based on certainty equivalence principle which forms the foundation of existing and standard adaptive control designs. Instead, a biasing vector function is introduced into parameter estimate; it links the system dynamics to estimation error dynamics, and its choice leads to a new Lyapunov-based design so that affine or nonaffine systems with nonlinearly parameterized unknowns can be controlled by adaptive estimation. Explicit conditions are found for achieving global asymptotic stability of the state, and the convergence condition for parameter estimation is also found. The conditions are illustrated by several examples and classes of systems. Besides global stability and estimation convergence, the proposed adaptive control has the unique feature that it does not contains any robust control part which typically overpowers unknown dynamics, may be conservative, and also interferes with parameter estimation.     

互质因子摄动系统最优е1鲁棒控制: 连续性与自适应控制

针对具有互质因子摄动和未知干扰的离散时间系统研究了一种自适应鲁棒控制策略. 本文的主要工作包括三个方面. 首先建立了互质因子摄动系统最优е1鲁棒控制设计的连续性. 然后,提出了一种带变死区的参数鲁棒估计投影算法. 最后, 结合所提出的参数估计算法和最优е1鲁棒控制,利用确定性等价原理提出了互质因子摄动系统的一种新的自适应鲁棒控制方法. 基于本文建立的е1优化设计的连续性, 证明了自适应鲁棒控制的全局稳定性,给出了自适应控制系统稳定性的后验可计算条件.     

Robust adaptive observers for nonlinear systems with boundeddisturbances

Since existing adaptive observers for nonlinear systems may generate unbounded parameter estimates in the presence of bounded disturbances, robust adaptive observers are presented which prevent parameter estimate drift. In addition the input-to-state stability of the error dynamics with respect to disturbances and parameter time-derivatives is guaranteed by generalizing a persistency of excitation result. Asymptotic convergence of state estimation errors is still achieved for systems in adaptive observer form when disturbances are not present, by a suitable extension of Barbalat's lemma     

Robust discrete-time set-based adaptive predictive control for nonlinear systems

The problem of robust adaptive predictive control for a class of discrete-time nonlinear systems is considered. First, a parameter estimation technique, based on an uncertainty set estimation, is formulated. This technique is able to provide robust performance for nonlinear systems subject to exogenous variables. Second, an adaptive MPC is developed to use the uncertainty estimation in a framework of min–max robust control. A Lipschitz-based approach, which provides a conservative approximation for the min–max problem, is used to solve the control problem, retaining the computational complexity of nominal MPC formulations and the robustness of the min–max approach. Finally, the set-based estimation algorithm and the robust predictive controller are successfully applied in two case studies. The first one is the control of anonisothermal CSTR governed by the van de Vusse reaction. Concentration and temperature regulation is considered with the simultaneous estimation of the frequency (or pre-exponential) factors of the Arrhenius equation. In the second example, a biomedical model for chemotherapy control is simulated using control actions provided by the proposed algorithm. The methods for estimation and control were tested using different disturbances scenarios.     

On the Lyapunov-based adaptive control redesign for a class of nonlinear sampled-data systems

Stabilization of the exact discrete-time models of a class of nonlinear sampled-data systems, with an unknown parameter, is addressed. Given a Lyapunov-based continuous-time adaptive controller that ensures some stability properties for the closed-loop system, a sufficient condition for the design of high order discrete-time controllers is given. The stability analysis is carried out considering the truncated Fliess series of the Lyapunov difference equation. Due to the appearance of power terms of the unknown parameter, the problem is reparameterized in a convex-like form and an estimation law for the new unknown parameter is derived with no need of overparametrization or projection techniques. Then, assuming appropriate conditions hold, high order controllers can be designed. The boundedness of the extended state vector is ensured under some conditions, for a sufficiently small sampling period. It is shown how increasing the controller order can improve system performance.     

Some comments on the use of normalization in robust adaptive control

This paper discusses the role of normalization with respect to robust parameter estimation for discrete-time adaptive control in the presence of unmodeled dynamics. It is pointed out that the normalizing signal may be brought into the adaptive law in two distinct ways; (i) via normalization of the regressor and the error signal in the standard parameter update law, and (ii) by replacement of the error signal with a function of the normalizing signal and the error. The convergence properties for both approaches are derived and shown to be similar.     

Model reference adaptive control using the delta operator

Reference is made to a recent paper by G.C. Goodwin, R. Lozano Leal, D.Q. Mayne, and R.H. Middleton (Automatica, vol.22, p.199-207, 1986), where it is shown that a cancellation of nonminimum-phase zeros appearing in discrete-time model reference adaptive control (MRAC) at a fast sampling rate can be easily avoided if the model to be identified is expressed in terms of the delta operator. A new proof of stability of the MRAC is given using the delta operator which, in contrast to the proof given in the above paper, does not require an assumption that a system consisting of a model determined by estimated parameters and a control law based on certainty equivalence principle is exponentially stable. A simple parameterization is proposed for the discrete-time MRAC using the delta operator which allows application of the usual (i.e. without dead zone) estimation algorithms     

离散时间系统间接自适应调节的稳定性分析

研究一类离散时间一阶线性系统的自适应调节器,采用不同的估计器分别结合修改的“必然等价”控制律,克服了当系统增益的估计值为零时可能丧失稳定性(或能控性)的困难,并指出Middleton and Kokotovic的有关论文[1]的一些实质性错误.对所设计的闭环系统的状态方程组获得显式解或相平面轨道的显式表达式,完全描述了这些自适应调节系统的非线性性质,并对某些情况下所估计的模型可能丧失稳定性的问题进行了分析,还探讨了这些结果对于具有未知控制方向和模型参数的离散时间高阶线性系统的间接自适应调节的意义.     

基于复合自适应律的直线电机自适应鲁棒控制

自适应鲁棒控制(ARC)能克服参数不确定性与扰动对系统的影响, 具有良好的输出跟踪性能. 然而常规ARC的参数估计值难以逼近真值. 为实现高性能的控制与准确的参数估计, 本文提出了基于复合自适应律的自适应鲁棒控制(CAARC). 该方法同时采用了输出误差与参数估计误差的相关信息构造自适应律, 具有比常规ARC更好的参数估计效果. 本文在理论上证明了CAARC的闭环稳定性与参数估计误差的收敛性, 并通过分析表明CAARC具有比常规ARC更好的输出跟踪性能, 最后通过仿真验证了该方法的有效性.     

Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

Without any prior knowledge of the physical bounds of unknown parameters and uncertain nonlinearities, an indirect adaptive robust controller is constructed for uncertain nonlinear time‐varying systems in a strict‐feedback form. Firstly, an adaptive strong robust controller is derived based on the command filtered adaptive backstepping approach. This controller not only can guarantee the boundedness of the closed‐loop system signals in the presence of time‐varying (TV) parameters and uncertain nonlinearities but also obviate the need to compute analytic derivatives of virtual control functions. Thus, the problem of “explosion of terms” in the standard adaptive backstepping technique is avoided. Through introduction of a simple adaptation law on the upper bound of uncertainties, a smooth robust control term is used to realize the disturbance attenuation. Afterwards, based on the nonlinear X‐swapping techniques, a modular approach in which the controller and the identifier can be designed separately is exploited. A novel algorithm is proposed to estimate the TV parameters accurately. By adopting the variation trend of the covariance matrix as an indicator of the driving signals' persistent excitation level, this online parameter estimation law is switched between a modified least‐squares algorithm and a gradient algorithm based on fixed σ‐modification. Finally, a series of properties on the asymptotic stability and the global uniform ultimate boundedness of the closed‐loop system is established. Simulation results verify the effectiveness of the suggested method.     

Globally stable model reference adaptive control based on fuzzy description of the plant

A novel fuzzy adaptive control algorithm is presented that belongs to direct model reference adaptive techniques based on a fuzzy (Takagi-Sugeno) model of the plant. The global stability of the overall system is proven, namely all the signals in the system remain bounded while the tracking error and estimated parameters converge to some residual set that depends on the size of disturbance and high-order parasitic dynamics. The hallmarks of the approach are its simplicity and transparency. The proposed algorithm is a straightforward extension of classical model reference adaptive control (MRAC) with a robust adaptive law to nonlinear systems described by fuzzy models. The performance of the approach was tested on a simulated plant and compared with the performance of a PI controller and a classical MRAC.     

Remarks on nonlinear adaptive observer design

A solution to the problem of state estimation for systems with unknown parameters is to use some on-line adaptation of the observer parameters. On the basis of various existing results for such adaptive observer designs, a unifying “adaptive observer form” is proposed in this paper. This form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters, as well as additional properties which further allow parameter estimation. As an example, it is shown how an adaptive observer can be designed for a class of state affine systems.     

On tuning leakage for performance-robust adaptive control

The behavior of a model reference adaptive control (MRAC) system is examined. The effect of the inclusion of leakage in the adaptive algorithm is studied, and the leakage mechanism of the σ-modification and the e₁-modification are discussed. A useful approximation is given for a particular MRAC problem for the small step-size average parameter estimate motion away from an arbitrary stabilizing adaptive controller parameterization. Arrow diagrams verify the conclusion that designer-selected leakage constants must be well chosen in relation to the unknown plant and environment to avoid bursting by an adaptive controller in the absence of adequate excitation by the external forcing function(s)