Intelligent Control of Discrete Linear Systems Based on a Supervised Adaptive Multiestimation Scheme

A pole-placement based adaptive controller synthesised from a multiestimation scheme is designed for linear plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterisation of the adaptive controller in real time. The basic usefulness of the proposed scheme is to improve the transient response so that the closed-loop stability is guaranteed. The switching process is subject to a minimum dwelling or residence time within which the supervisor is not allowed to switch between the multiple estimation schemes. The high level supervision is based on the multiestimation identification scheme. The residence time condition guarantees the closed-loop stability. The above higher level switching structure is on-line supervised by a closed-loop tracking error based algorithm. This second supervision on-line tunes the free design parameters which appear as time varying weights in the loss function of the above switching structure. Thus, the closed-loop behaviour, compared to the constant parameter case one, is improved when the design parameter is not tightly initialised. Both supervisors are hierarchically organised in the sense that they act on the system at different rates. Furthermore, a projection algorithm has been considered in the estimation scheme in order to include a possible a priori knowledge of the estimates parameter vector value in the estimation algorithm.     

Parameter Estimation Algorithms for Hierarchical Distributed Systems

There has been a great deal of research activity in the area of identification of distributed parameter systems over the past two decades. An extensive treatment of off-line schemes ( e.g. , output least squares, estimation error, etc. ) together with a comprehensive survey of the literature can be found in the monograph by Banks and Kunisch [4] . In the case of on-line, or adaptive, schemes, the available literature is less extensive and more recent ( Isermann et al . [7] ). The on-line methods give estimates recursively as the measurements are obtained within the time limit imposed by the sampling period. These include recursive projection algorithm ( Baumeister et al. [5] ), recursive least squares algorithm ( Glentis et al . [6] ), on-line excitation algorithms ( Ludwig et al. [8] ), etc . In this paper an equivalent 2nd order dynamical system is formulated from a given trajectory representing the pattern to be recognised and simulated in order to estimate the parameters for hierarchical distributed systems using 1st and 2nd order dynamics. Recommendations for the best estimation strategy are given.     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

Stability and operating constraints of adaptive LMS-based feedback control

The filtered-X LMS algorithm has enjoyed widespread usage in both adaptive feedforward and feedback controller architectures. For feedforward controller designs the filtered-X LMS algorithm has been shown to exhibit unstable divergence for plant estimation errors in excess of ±90°. Typical implementations of this algorithm in adaptive feedback controllers such as filtered-U and filtered-E have previously been assumed to conform to these same identification constraints. Here we present two instability mechanisms that can arise in filtered-E control that violate the 90° error assumption: feedback loop instabilities and LMS algorithm divergence. Analysis of the adaptive feedback system indicates that the conventionally interpreted plant estimation error can be arbitrarily small yet induce algorithm divergence; while other cases may have very large estimation errors and feedback loops cause controller instability. These analytical observations are supported by simulations. The implications of the actual plant estimation error, calculated here for the filtered-E controller, are extended to practical constraints placed on applications including filtered-U, on-line system identification, and self-excited system control.     

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.     

On minimal error entropy stochastic approximation

Information-theoretic concepts are developed and employed to obtain conditions for a minimax error entropy stochastic approximation algorithm to estimate the state of a non-linear discrete time system baaed on noisy linear measurements of the state. Two recursive suboptimal error entropy estimation procedures are presented along with an upper bound formula for the resulting error entropy. A simple example is utilized to compare the optimal and suboptimal error entropy estimators and the minimum mean Square error linear estimator.     

Recursive identification for Hammerstein–Wiener systems with dead-zone input nonlinearity

A new recursive algorithm is proposed for the identification of a special form of Hammerstein–Wiener system with dead-zone nonlinearity input block. The direct motivation of this work is to implement on-line control strategies on this kind of system to produce adaptive control algorithms. With the parameterization model of the Hammerstein–Wiener system, a special form of model estimation error is defined; and then its approximate formula is given for the following derivation. Based on these, a recursive identification algorithm is established that aims at minimizing the sum of the squared parameter estimation errors. The conditions of uniform convergence are obtained from the property analysis of the proposed algorithm and an adaptive setting method for a weighted factor in the algorithm is given, which enhances the convergence of the proposed algorithm. This algorithm can also be used for the identification of the Hammerstein systems with dead-zone nonlinearity input block. Three simulation examples show the validity of this algorithm.     

Minimum entropy filtering for multivariate stochastic systems with non-Gaussian noises

In this note, a minimum entropy filtering algorithm is presented for a class of multivariate dynamic stochastic systems, which are represented by a set of time-varying difference equations and are subjected to the multivariate non-Gaussian stochastic inputs. Several new concepts including the hybrid random vector, hybrid probability and hybrid entropy are firstly established to describe the probabilistic property of the estimation errors. New relationships are provided between the probability density functions (PDFs) of the multivariate stochastic input and output for different mapping cases. Recursive algorithms are then proposed to design the real-time sub-optimal filter so that the hybrid entropy of the estimation error can be minimized. Finally, an improved algorithm is provided through the on-line tuning of the weighting matrices so as to guarantee the local stability of the error system.     

基于误差通道并行建模的主动控制系统

提出了基于误差通道并行在线建模算法的主动控制系统,该系统同时采用3个自适应滤波器,并且通过引入一个延迟单元,以保证滤波器解的唯一性。数学分析和仿真实验结果表明,该控制算法能获取误差通道的无偏估计,并可降低主动降噪系统总体代价。     

模型在线辨识方法及其应用

本文提出了一种有效的非线性模型和参数在线估计方法。为了实现模型在线辨识，本文根据误差性能指标，给出了模型判据及计算式。根据递推加权最小二乘算法和优选判据，导出了模型和参数同时在线估计的有效算法。为了提高计算效率和数值稳定性，模型辨识和参数辨识均采用了Ｕ－Ｄ分解方法。新方法可用于飞行器非线性气动模型和参数的实时估计。实际应用结果表明，使用该方法可以有效地确定多项式、样条函数模型结构，参数辨识的结果满     

On-line system identification with an adjustable estimation interval

On-line system identification with an adjustable estimation interval based on a continuous-time model is developed. The algorithm of interval selection depends on measurement noise, adaptive gain, and modelling error. Parameter estimation is carried out using recursive formulae via a weighted least-squares estimation. Illustrative examples are presented to show the potential of this method.     

基于小波神经网络的加工过程自适应控制

把信息熵、小波分析和神经网络相结合,提出了基于小波神经网络的加工过程自适应控制系统及其自适应控制算法。提出并定义了广义熵方误差函数,在理论上证明了广义熵方误差函数的有效性。用广义熵方误差函数准则取代BP算法的均方误差准则,用自适应地搜索小波基函数和自适应地调整小波的尺度参数、平移参数和神经网络权值的方法对参数变化的切削力进行在线控制。仿真结果表明,该系统响应快,无超调,比传统的加工过程神经网络自适应控制具有更好的控制效果。     

Adaptive control of a Wiener type system: application of a pH Neutralization reactor

In this paper the problem of on-line identification and adaptive control of a Wiener type non-linear system is studied. First, a Wiener model is defined whose linear and non-linear parts are described using Laguerre and piecewise linear basis functions, respectively. Then, an adaptive identification algorithm for this model is presented. A local convergence analysis for the adaptive identification is performed. The model obtained is used to adapt the parameters of a controller designed for the specific structure of the model. The complete scheme is applied to a simulation of a pH neutralization reactor subject to several perturbations. The results show the improved behaviour of the proposed scheme compared with other approaches found in the literature.     

Stable on-line parameter identification with general knowledge on level of information noise discrete-time case

An on-line parameter identification problem is posed and solved for discrete-time systems with general knowledge on the level of the inherent information noise. The knowledge can be the bound on either the magnitude or the finite-index ^p norm, pε[1, ∞), of the noise. Based on the knowledge, a switching type gradient algorithm (or called gradient algorithm with dead zone) is proposed to estimate the parameters of the system from the available input-output data. In spite of the existence of the noise, this on-line algorithm guarantees that the estimation error is monotonically decreasing, and the parameter estimate is convergent to a steady-state value under a mild condition. Furthermore, the algorithm is stable in the sense that the estimation error will converge to zero as the bound on the noise gradually diminishes.     

Robustness index for adaptive control based on pole-zero placement

A robustness index for adaptive control is proposed. The control algorithm is based on pole-zero placemen!. Parameter estimation via weighted least-squares recursive formulas is presented. By using the index, effects of the modelling error on the performance of the adaptive control system are indicated. If the index is less than one, the system is stable. Proper on-line control is obtained.     

Modified adaptive robust control system design

The robust control design problem is studied for a class of uncertain dynamical systems. The uncertainty of the system is time varying. The only assumption on the uncertainty is that it is bounded. No statistical property of the uncertainty is ever assumed and utilized. The robust control does not need the a priori estimation on the bound of uncertainty. An adaptive algorithm for the on-line estimation of the bound is constructed and the robust control is only dependent on this estimation. The adaptive algorithm is a modification of previous work by Corless and Leitmann (1983). The advantages of this new algorithm include a constant control design parameter (which should have been time varying previously) and the applicability to linear systems with mismatched uncertainty and measurement noise.     

On-line identification and control of multivariablc discrete-time systems based on a transformed model

Recursive algorithms for on-line combined identification and control of linear discrete-time multivariable systems is presented. A variant of the observable canonical model with one-way coupling form of the state model is used to develop a solution of the problem. Exploiting the canonical structure of the model, the proposed solution turns out to be simpler than that obtained by El-Sherief (1983) and moreover, a combined decentralized state and parameter estimation based control scheme can be developed in three stages. In Stage I, the parameters of the system matrices are estimated by a recursive least-square algorithm or by a normalized stochastic approximation algorithm in decoupled manner. These parameters are then employed for state estimation in Stage 2 using a centralized conventional Kalman filter or by a decentralized adaptive Kalman filter which in turn reduces instrumentation and telemetry costs. Estimated parameters and states are then utilized in Stage 3 to implement the square-root based control law along with the good numerical behaviour of the control problem. The proposed algorithms are tested by considering an example of a third-order state-space model.     

Recursive subspace identification subject to relatively slow time-varying load disturbance

In this paper, a recursive subspace identification method is proposed to identify linear time-invariant systems subject to load disturbance with relatively slow dynamics. Using the linear superposition principle, the load disturbance response is decomposed from the deterministic-stochastic system response in the form of a time-varying parameter. To ensure unbiased estimation of the deterministic system matrices, a recursive least-squares (RLS) identification algorithm is established with a fixed forgetting factor, while another RLS algorithm with an adaptive forgetting factor is constructed based on the output prediction error to quickly track the time-varying parameter of load disturbance response. By introducing a deadbeat observer to represent the deterministic system response, two extended observer Markov parameter matrices are constructed for recursive estimation. Consequently, the deterministic matrices are retrieved from the identified system Markov parameter matrices. The convergence of the proposed method is analysed with a proof. Two illustrative examples are shown to demonstrate the effectiveness and merit of the proposed identification method.     

Genetic adaptive state estimation

A genetic algorithm (GA) uses the principles of evolution, natural selection, and genetics to offer a method for parallel search of complex spaces. This paper describes a GA that can perform on-line adaptive state estimation for linear and nonlinear systems. First, it shows how to construct a genetic adaptive state estimator where a GA evolves the model in a state estimator in real time so that the state estimation error is driven to zero. Next, several examples are used to illustrate the operation and performance of the genetic adaptive state estimator. Its performance is compared to that of the conventional adaptive Luenberger observer for two linear system examples. Next, a genetic adaptive state estimator is used to predict when surge and stall occur in a nonlinear jet engine. Our main conclusion is that the genetic adaptive state estimator has the potential to offer higher performance estimators for nonlinear systems over current methods.     

Fault estimation for T-S fuzzy Markovian jumping systems based on the adaptive observer

The adaptive fault estimation problem is studied for a class of stochastic Markovian jumping systems (MJSs) with time delays and nonlinear parameters. By means of Takagi-Sugeno fuzzy models, the dynamics of observer error generator and the fuzzy error dynamical system are constructed. Based on the selected Lyapunov-Krasovskii functional framework, the adaptive fault estimation algorithm is proposed to enhance the rapidity and accuracy performance of fault estimation. In terms of linear matrix inequalities techniques, a sufficient condition on the existence of the adaptive observer is presented and proved. Moreover, the presented results are also extended to multiple time-delayed nonlinear MJSs. A numerical example is given at last to illustrate the effectiveness of the proposed approach.