Adaptive decoupling of linear systems using multirate generalized sampled-data hold functions

An indirect adaptive controller synthesis algorithm is derivedfor the decoupling of linear multivariable time-invariant systemswith unknown parameters using multi-rate generalized sampled-datahold functions. Such controllers contain a multirate samplingmechanism with different sampling period at each system inputand two periodically varying modulating matrix functions. Thealgorithm proposed in the paper estimates the modulating functionson line, and ensures persistent excitation of the continuous-timeplant without making any assumption on the reference signals.The only prior knowledge needed is the minimality of the continuousand sampled system, known order, and a set of structural indices,namely the locally minimum controllability indices of the continuous-timepalnt.     

FLOATING QUANTIZATION EFFECTS ON MULTIRATE SAMPLED-DATA NONLINEAR CONTROL SYSTEMS

In this article,floating quantization effects on multirate sampled-data control systems are studied.It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable.Moreover,it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.     

Auxiliary model identification method for multirate multi-input systems based on least squares

This paper derives state-space models for multirate multi-input sampled-data systems. Based on the corresponding transfer function models, an auxiliary model based recursive least squares algorithm is presented to identify the parameters of the multirate systems from the multirate input–output data. Further, convergence properties of the proposed algorithm are analyzed. Finally, an illustrative example is given.     

An indirect adaptive pole place for MIMO systems based on multirate sampling of the plant output

The use of multirate-output controllers in order to achieveadaptive pole placement in linear multiple-input multiple-outputsystems with unknown parameters is investigated for the firsttime. Multirate-output controllers contain a multirate samplingmechanism with different sampling period at each system output.Such {acute} control allows us to assign the poles of the sampledclosed-loop system arbitrarily in desired locations, and doesnot make assumptions on the plant other than controllability,observability, and the knowledge of two sets of structural indices,namely the controllability and the observability indices. Anindirect adaptive control scheme based on these sampled-datacontrollers is proposed, which estimates the controller parameterson line. Using the proposed adaptive algorithm, the problemof adaptive pole placement is reduced to the determination ofa fictitious static state-feedback controller, due to the meritsof dynamic multirate-output controllers. Known techniques resortto the direct computation of dynamic controllers. The controllerdeterminations here is based on the transformation of the discreteanalogue of the systems under control to a phase-variable canonicalform prior to the applications of the control design procedure.The solution of the problem can be obtained by a quite simpleutilization of the concept of state similarity transformation,whereas known techniques usually require the solution of matrixpolynomial Diophantine equations. Moreover, persistent excitationof the continuous-time plant is provided without assuming anyspecial richness of the reference signals.     

Stochastic stability and robust control for sampled-data systems with Markovian jump parameters

In this paper, the problems of stochastic stability and robust control for a class of uncertain sampled-data systems are studied. The systems consist of random jumping parameters described by finite-state semi-Markov process. Sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented. The conditions for the existence of a sampled-data feedback control and a multirate sampled-data optimal control for the continuous-time uncertain Markovian jump systems are also obtained. The design procedure for robust multirate sampled-data control is formulated as linear matrix inequalities (LMIs), which can be solved efficiently by available software toolboxes. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques.     

输入通道有干扰多变量MRAC系统的全局稳定化控制

对具有未建模动态并且输入通道存在干扰的动态不确定多输入多输出(MIMO)模型参考自适应控制(MRAC)系统,应用输出反馈给出了一种变结构模型跟踪控制器设计．系统的已建模部分有大于1的任意相对阶且已建模部分阶的上界是未知的．通过引入辅助信号和带有记忆功能的正规化信号,以及适当选择控制器参数,保证了闭环系统的全局稳定性,且跟踪误差可调整到任意小．     

Normal form for linear systems with respect to its vector relative degree

For multi-input multi-output (MIMO) linear systems with existing vector relative degree a normal form is constructed. This normal form is not only structural simple but allows to characterize the system’s zero dynamics for the design of feedback controllers. A characterization of the zero dynamics in terms of the normal form is given.     

Analytical failure-detection using adpative,secondary observers

The problem of designing analytical failure-detection systems, using adaptive observers, is addressed in this paper. Failure-detection systems can be applied to linear multi-input, multi-output systems and are related to the examination of then-dimensional observer error vector which carries the necessary information on possible failures. This approach leads toward the design of highly sensitive failure detection systems, obtaining a unique fingerprint for every possible failure (abrupt or soft). In order to keep the observer's false-alarm rate under a certain specified value, it is necessary to have an acceptable matching between the observer model and the system parameters. It is shown here that properly designed adaptive observers are able to detect abrupt changes in the system (actuator, sensor failures, etc.) with adequate reliability. Conditions for convergence for the adaptive observer algorithm are obtained. Good tracking performance with small observer output errors, coupled with accurate and fast parameter identification in both deterministic and stochastic cases, is obtained.Dedicated to G. LeitmannThis research was supported by a National Research Council Associateship at NASA Ames Research Center. The author is indebted to both NRC and NASA Ames Research Center.     

输入通道有干扰多变量MRAC系统全局稳定化控制

对具有未建模动态且输入通道存在干扰的动态不确定多输入多输出(MIMO)模型参考自适应控制(MRAC) 系统，仅应用系统的输入输出量测数据给出了一种变结构模型跟踪控制器设计机制.通过辅 助信号和带有记忆功能的正规化信号,并适当选择控制器参数, 所提出的变结构控制 (VSC)能保证闭环系统的全局稳定性,且跟踪误差可调整到任意小.     

Robust finite-time convergence of chaotic systems via adaptive terminal sliding mode scheme

This paper investigates robust finite-time stabilization of a class of uncertain chaotic systems. A new terminal sliding mode (TSM) algorithm is proposed to steer the plant fast to zero within finite time. In particular, a new form of TSM is developed for multi-input and multi-output systems, and some criteria are presented to facilitate its control design. With adaption laws to identify uncertain parameters and unknown bounds on disturbances, the proposed terminal sliding mode controllers get rid of uncertainties and nonlinearities successfully. The closed-loop systems are provided with fast finite-time stability and strong robustness against uncertainties. Finally, numerical simulation of Lorenz system illustrates the effectiveness of this proposed control scheme.     

Multivariable RBF-ARX model-based robust MPC approach and application to thermal power plant

For a class of smooth nonlinear multivariable systems whose working-points vary with time and the future working-points knowledge are unknown, a combination of a local linearization and a polytopic uncertain linear parameter-varying (LPV) state-space model is built to approximate the present and the future system’s nonlinear behavior, respectively. The combination models are constructed on the basis of a matrix polynomial multi-input multi-output (MIMO) RBF-ARX model identified offline for representing the underlying nonlinear system. A min–max robust MPC strategy is designed to achieve the systems’ output-tracking control based on the approximate models proposed. The closed loop stability of the MPC algorithm is guaranteed by the use of time-varying parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). The effectiveness of the modeling and control methods proposed in this paper is illustrated by a case study of a thermal power plant simulator.     

Decentralized Adaptive Robust State Feedback for Uncertain Large-Scale Interconnected Systems with Time Delays

The problem of the decentralized robust control is considered for a class of large-scale time-varying systems withdelayed state perturbations and external disturbances in the interconnections. Here, the upper bounds of the delayed stateperturbations and external disturbances in the interconnections are assumed to be unknown. Adaptation laws areproposed to estimate such unknown bounds; by making use of the updated values of the unknown bounds, decentralized linear and nonlinear memoryless robust state feedback controllers are constructed. Based on Lyapunov stability theoryand Lyapunov–Krasovskii functionals, as well as employing the proposed decentralized nonlinear robust state feedback controllers, it is shown that the solutions of the resulting adaptive closed-loop large-scale time-delay system can be guaranteed to be uniformly bounded and that the states converge uniformly and asymptotically to zero. It is also shown that the proposed decentralized linear robust state feedback controllers can guarantee the uniform ultimate boundedness of the resulting adaptive closed-loop large-scale time-delay system. Finally, a numerical example is given to demonstrate the validity of the results.     

Robust output feedback sliding mode control for uncertain discrete time systems

This paper proposes a robust output feedback controller for a class of uncertain discrete-time, multi-input multi-output, linear, systems. This method, which is based on the combination of discrete-time sliding mode control (DTSMC) and Kalman estimator, ensures the stability, robustness and an output tracking against the modeling uncertainties at large sampling periods. For this purpose, an appropriate structure is considered for sliding surface and the Lyapunov theory for the mismatched uncertain system is then used to design its parameter. This problem leads to solve a set of linear matrix inequalities. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show the effectiveness of the proposed method in the presence of parameter uncertainties and external disturbances at large sampling periods.     

Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems

This paper describes an adaptive fuzzy sliding-mode control algorithm for controlling unknown or uncertain, multi-input multi-output (MIMO), possibly chaotic, dynamical systems. The control approach encompasses a fuzzy system and a robust controller. The fuzzy system is designed to mimic an ideal sliding-mode controller, and the robust controller compensates the difference between the fuzzy controller and the ideal one. The parameters of the fuzzy system, as well as the uncertainty bound of the robust controller, are tuned adaptively. The adaptive laws are derived in the Lyapunov sense to guarantee the asymptotic stability and tracking of the controlled system. The effectiveness of the proposed method is shown by applying it to some well-known chaotic systems.     

A low-order active fault-tolerant state space self-tuner for the unknown sampled-data nonlinear singular system using OKID and modified ARMAX model-based system identification

In this paper, we present two control schemes for the unknown sampled-data nonlinear singular system. One is an observer-based digital redesign tracker with the state-feedback gain and the feed-forward gain based on off-line observer/Kalman filter identification (OKID) method. The presented control scheme is able to make the unknown sampled-data nonlinear singular system to well track the desired reference signal. The other is an active fault tolerance state-space self-tuner using the OKID method and modified autoregressive moving average with exogenous inputs (ARMAX) model-based system identification for unknown sampled-data nonlinear singular system with input faults. First, one can apply the off-line OKID method to determine the appropriate (low-) order of the unknown system order and good initial parameters of the modified ARMAX model to improve the convergent speed of recursive extended-least-squares (RELS) method. Then, based on modified ARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown sampled-data nonlinear singular system with immeasurable system state. Moreover, in order to overcome the interference of input fault, one can use a fault-tolerant control scheme for unknown sampled-data nonlinear singular system by modifying the conventional self-tuner control (STC). The presented method can effectively cope with partially abrupt and/or gradual system input faults. Finally, some illustrative examples including a real circuit system are given to demonstrate the effectiveness of the presented design methodologies.     

A hierarchical structure of observer-based adaptive fuzzy-neural controller for MIMO systems

An observer-based adaptive controller developed from a hierarchical fuzzy-neural network (HFNN) is employed to solve the controller time-delay problem for a class of multi-input multi-output (MIMO) non-affine nonlinear systems under the constraint that only system outputs are available for measurement. By using the implicit function theorem and Taylor series expansion, the observer-based control law and the weight update law of the HFNN adaptive controller are derived. According to the design of the HFNN hierarchical fuzzy-neural network, the observer-based adaptive controller can alleviate the online computation burden. Moreover, the common adaptive controller is utilized to control all the MIMO subsystems. Hence, the number of adjusted parameters of the HFNN can be further reduced. In this paper, we prove that the proposed observer-based adaptive controller can guarantee that all signals involved are bounded and that the outputs of the closed-loop system track asymptotically the desired output trajectories.     

A two-sided Arnoldi algorithm with stopping criterion and MIMO selection procedure

In this paper we introduce a two-sided Arnoldi method for the reduction of high order linear systems and we propose useful extensions, first of all a stopping criterion to find a suitable order for the reduced model and secondly, a selection procedure to significantly improve the performance in the multi-input multi-output (MIMO) case. One application is in micro-electro-mechanical systems (MEMS). We consider a thermo-electric micro thruster model, and a comparison between the commonly used Arnoldi algorithm and the two-sided Arnoldi is performed.     

An Algebraic Method for Pole Placement in Multivariable Systems

This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance.     

Funnel Control for Linear DAEs

We study funnel control for linear differential-algebraic multi-input multi-output systems which are not necessarily regular. We show that the funnel controller (that is a static nonlinear output error feedback) achieves - for a special class of right-invertible systems with asymptotically stable zero dynamics - tracking of a reference signal by the output signal within a pre-specified performance funnel. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Algebraic Method for Pole Placement in Multivariable Systems

This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance.