Recursive Prediction Error Algorithm Research Articles

On the development and application of a continuous-discrete recursive prediction error algorithm

Recursive state and parameter reconstruction is a well-established field in control theory. In the current paper we derive a continuous-discrete version of recursive prediction error algorithm and apply the filter in an environmental and biological setting as a possible alternative to the well-known extended Kalman filter. The framework from which the derivation is started is the so-called ‘innovations-format’ of the (continuous time) system model, including (discrete time) measurements. After the algorithm has been motivated and derived, it is subsequently applied to hypothetical and ‘real-life’ case studies including reconstruction of biokinetic parameters and parameters characterizing the dynamics of a river in the United Kingdom. Advantages and characteristics of the method are discussed.

Alstom selected for Canadian hydro plant

An application of a multivariable state-space adaptive controller to a turbo-generator set is considered in this paper. The turbo-generator, consisting of an air pressure turbine and a synchronous generator, is a typical electromechanical system, which exhibits highly nonlinear behaviour and non-negligible couplings between electrical and mechanical control loops. Especially if the plant is not connected to the rigid 50 Hz grid, the control task for varying load in different operating points is quite difficult. Great fluctuations of the central pressure pump cause the turbo-generator to work in a noisy environment as well. The parameters of the state-space model are identified directly using the recursive prediction error algorithm, which estimates also the system states. Based on the estimated parameters and states, the adaptive controller is determined through state feedback. The optimal control strategy is comissioned for designing the state controller. The results of real-time control experiments of the turbo-generator demonstrate the feature and applicability of the designed multivariable state-space adaptive controller.

An Adaptive Optimal Autopilot Using the Recursive Prediction Error Method

This paper presents a new type of ship autopilot applying the linear quadratic gaussian (LQG) optimal control algorithm linked to the recursive prediction error (RPE) algorithm. The RPE method is used to online estimate of unknown parameters of a multivariate auto-regressive exogenous (MARX) model. Full-scale experiments for the optimal autopilot were quite successful and gave excellent results. It has been found that the RPE method is a good method to online identify the ship steering dynamics and the optimal autopilot has very good steering characteristics. Choices of the design parameters determine the steering characteristics of the optimal autopilot.

Hybrid multilayered perceptron networks

This paper introduces a modified multilayered perception network (MLP) called the Hybrid Multilayered Perceptron (HMLP) network to improve the performance of a MLP network. The convergence rate of the proposed network is further improved by proposing a modified version of the recursive prediction error algorithm as the training algorithm. The capability of the proposed network architecture trained using the modified recursive prediction error algorithm was demonstrated using simulated and real data sets. The results indicated that the proposed network provides a significant improvement over a standard MLP network. These additional linear input connections do not significantly increase the complexity of the MLP network since the connections are linear. In fact, by using the linear input connections, the number of hidden nodes required by the standard MLP network model can be reduced, which will also reduce computational load. The performance of the HMLP network was also compared with Radial Basis Function (RBF) and Hybrid Radial Basis Function (HRBF) networks. It was found that the proposed HMLP network was much more efficient than both RBF and HRBF networks.

逐次予測誤差法を用いた極配置制御型オートパイロットに関する研究

This paper presents a new method of designing a self-tuning pole assignment (PA) type of autopilot for ships. The design method applies the recursive prediction error (RPE) algorithm as an online estimator linking to the self-tuning pole assignment algorithm to construct an adaptive autopilot. Main tasks of designing a robust pole assignment type of autopilot are to model the ship dynamic system in an suitable form and to construct the control algorithm. To calculate control gains of the pole assignment control type of autopilot is often based on the ship steering dynamic coefficients identified by an appropriate online estimation method. The new design method is developed from the design method of the conventional pole assignment type of autopilot which was proposed by D.H. Nguyen et al. by applying the recursive least squares (RLS) algorithm linking to the pole assignment control algorithm. Full-scale experiments aboard the training ship at sea are briefly described. The pole assignment type of autopilot using the RPE method has good steering characteristics for course-keeping and course-changing control of ship.

Pseudolinear neural networks based nonlinear system modeling and control

Pseudo-linear neural networks (PNN) based modeling and control strategy for a class of nonlinear dynamic systems is proposed. The training of the PNN is implemented by using a recursive prediction error (RPE) algorithm. The control strategy is based on one-step-ahead prediction, in which a direct controller design for an affine nonlinear system and the second order based optimization for a general nonlinear system are adopted. The stability of the closed loop control system is investigated, and some sufficient conditions for the local asymptotic stability are derived. The some simulated examples showed the good results of proposed control strategies in this paper.

Adaptive IIR filtering using QR matrix decomposition

In this correspondence, an approach to adaptive IIR filtering based on a pseudo-linear regression and applying an iterative QR matrix decomposition is developed. In simulations, the algorithm has shown a high stability and excellent convergence properties. The derivation of the IIR-QR adaptive filter is straightforward, and the computational complexity of the algorithm is comparable with the FIR-QR adaptive algorithm of the same order and less than gradient-based adaptive IIR filters such as the simplified-gradient recursive prediction error (RPE) algorithm. Fast versions of O(N) computational complexity are readily available.

Identification of model structure for photosynthesis and respiration of algal populations

The paper introduces a methodology for model evaluation based upon (i) a controlled random search algorithm used for calibration and (ii) a recursive prediction error algorithm used as a verification tool. The method is applied to a case study in north west Georgia involving the dynamic simulation of a population of algae in a standing body of water. Efforts to identify a model structure for the dissolved oxygen dynamics associated with photosynthesis and respiration are made, with some success.

Tuning the stator resistance of induction motors using artificial neural network

Tuning the stator resistance of induction motors is very important, especially when it is used to implement direct torque control (DTC) in which the stator resistance is a main parameter. In this paper, an artificial network (ANN) is used to accomplish tuning of the stator resistance of an induction motor. The parallel recursive prediction error and backpropagation training algorithms were used in training the neural network for the simulation and experimental results, respectively. The neural network used to tune the stator resistance was trained on-line, making the DTC strategy more robust and accurate. Simulation results are presented for three different neural-network configurations showing the efficiency of the tuning process. Experimental results were obtained for one of the three neural-network configurations. Both simulation and experimental results showed that the ANN have tuned the stator resistance in the controller to track actual resistance of the machine.

Identification of model structure for photosynthesis and respiration of algal populations

The paper introduces a methodology for model evaluation based upon (i) a controlled random search algorithm used for calibration and (ii) a recursive prediction error algorithm used as a verification tool. The method is applied to a case study in north west Georgia involving the dynamic simulation of a population of algae in a standing body of water. Efforts to identify a model structure for the dissolved oxygen dynamics associated with photosynthesis and respiration are made, with some success.

Extending the response range of an optical fibre pH sensor using an artificial neural network

An artificial neural network (ANN) has been applied for the analysis of the response of an optical fibre pH sensor. The optrode was based on a 3,4,5,6-tetrabromophenol sulphonephthalein indicator, which was covalently bound onto aminopropyl glass beads, then packed at the tip of a bifurcated fibre-optic bundle. A three layer feed forward network was used and network training was performed using the recursive prediction error (RPE) algorithm. It was found that an optimised network with 13 hidden neurons was highly accurate in predicting the response of the optical pH sensor, with the worst interpolation error of 0.08 pH for test data set and 0.07 pH for measuring unknown buffer solutions. Overall, the application of ANN enabled the extension of the useful pH response range of the sensor from its narrow linear range (pH 5.0–7.25) to the full calibration response (pH 2.51–9.76).

Design of a multivariable state-space adaptive controller, and its application to a turbogenerator pilot plant

An application of a multivariable state-space adaptive controller to a turbogenerator set is considered in this paper. The turbo-generator, consisting of an air pressure turbine and a synchronous generator, is a typical electromechanical system, which exhibits highly nonlinear behaviour and non-negligible couplings between electrical and mechanical control loops. Especially if the plant is not connected to the rigid 50 Hz grid, the control task for varying loads at different operating points is quite difficult. Great fluctuations of the central pressure pump cause the turbo-generator to work in a noisy environment as well. The parameters of the state-space model are identified directly, using the recursive prediction error algorithm, which also estimates the system states. Based on the estimated parameters and states, the adaptive controller is determined through state feedback. The optimal control strategy is commissioned for designing the state controller. The results of real-time control experiments on the turbogenerator demonstrate the features and applicability of the designed multivariable state-space adaptive controller.

Structured modeling and state estimation in a fermentation process: Lipase production by Candida rugosa

A simple structured mathematical model coupled with a methodology of state and parameter estimation is developed for lipase production by Candida rugosa in batch fermentation. The model describes the system according to the following qualitative observations and hypothesis: Lipase production is induced by extracellular oleic acid present in the medium. The acid is transported into the cell where it is consumed, transformed, and stored. Lipase is excreted to the medium where it is distributed between the available oil-water interphase and aqueous phase. Cell growth is modulated by the intracellular substrate concentration. Model parameters have been determined and the whole model validated against experiments not used in their determination. The estimation problem consists in the estimation of three state variables (biomass, intra- and extracellular substrate) and two kinetic parameters by using only the on-line measurement provided by exhaust gas analysis. The presented estimation strategy divides the complex problem into three subproblems that can be solved by stable algorithms. The estimation of biomass (X) and the specific growth rate (mu), is achieved by a recursive prediction error algorithm using the on-line measurement of the carbon dioxide evolution rate. mu is then used to perform an estimation of intracellular substrate and the other kinetic parameter related to substrate transport (A) by an adaptive observer. Extracellular substrate is then evaluated by means of the estimated values of intracellular substrate and biomass through the material balance of the reactor. Simulation and experimental tests showed good performance of the developed estimator, which appears suitable to be used for process control and monitoring. (c) 1995 John Wiley & Sons, Inc.

Identification of Hidden Markov Models with Grouped State Values

This paper presents a recursive prediction error algorithm which addresses the problem of computational complexity for on-line identification of hidden Markov models (HMMs). The particular class of HMMs considered has state-values which are clustered into groups. This allows a reformulation of the Markov model and results in a sub-optimal reduced order identification scheme. Actually, an exact definition of clustering is not discussed, rather, a general identification technique is presented for which the computational requirements are greatly reduced when the state-values are divided in some way into groups. The applicability to certain types of cluster patterns is tested via simulation studies.

Design of a Multivariable State-Space Adaptive Controller and Its Application to a Turbo-Generator Pilot Plant

An application of a multivariable state-space adaptive controller to a turbo-generator set is considered in this paper. The turbo-generator, consisting of an air pressure turbine and a synchronous generator, is a typical electromechanical system, which exhibits highly nonlinear behaviour and non-negligible couplings between electrical and mechanical control loops. Especially if the plant is not connected to the rigid 50 Hz grid, the control task for varying load in different operating points is quite difficult. Great fluctuations of the central pressure pump cause the turbo-generator to work in a noisy environment as well. The parameters of the state-space model are identified directly using the recursive prediction error algorithm, which estimates also the system states. Based on the estimated parameters and states, the adaptive controller is determined through state feedback. The optimal control strategy is comissioned for designing the state controller. The results of real-time control experiments of the turbo-generator demonstrate the feature and applicability of the designed multivariable state-space adaptive controller.

A block gradient-based algorithm for adaptive IIR filtering

This paper presents a new block gradient-based adaptive algorithm for Infinite Impulse Response (IIR) adaptive filters. In contrast with the Recursive Prediction Error (RPE) algorithm, the proposed algorithm employs more accurate gradient estimates. The gradients are calculated based on sampled data blocks, within which the filter coefficients are kept constant. The proposed approach is characterised by improved steady-state performance and reduced computational complexity when compared with the conventional RPE algorithm.

An innovation representation for nonlinear systems with application to parameter and state estimation

An innovation model is derived for a nonlinear stochastic system described by a state variable representation. The problem of state and system parameter estimation is solved through identification of the innovation model. A recursive prediction error (RPE) algorithm is derived for the joint system parameter and state estimation through minimization of the innovation variance (MIV). The algorithm is robust against the use of an erroneous model. Convergence and stability properties of the algorithm are also analyzed. In order to ensure stability, the algorithm needs an on-line stability check at each iteration.

Identification of rudder—yaw and rudder—roll steering models by using recursive prediction error techniques

AbstractLinear and non‐linear recursive prediction error (RPE) methods have been employed for the purpose of identification of the dynamics of ship rudder—yaw and —roll motions. The evaluations of the goodness of model structures have been carried out by comparing simulated outputs from the identified model with real measurements. In the linear case Nomoto's first‐order model has been initially considered for the transfer functions between rudder—yaw and —sway, with a second‐order model for rudder—roll with coupling effects considered only between sway—yaw and —roll. Identification results have shown that such a model is not appropriate. Changing the model to second‐order between rudder—sway and —yaw and further considering the coupling effects between roll angle—sway and —yaw shows that a significant improvement is achieved, while the coupling effect between yaw and roll appears negligible. In the nonlinear case effects due to various non‐linear terms have been studied with the non‐linear RPE algorithm.

Analytic first and second derivatives for the recursive prediction error algorithm's log likelihood function

This note improves on a method for computing analytic derivatives of the likelihood function of a discrete, linear, time invariant Gaussian state-space system and extends it to handle correlation between the state transition and measurement noise terms and to compute the analytic Hessian matrix. >

A multilayered neural net controller using direct learning algorithm

This paper describes a recent study on the application of neural networks to dynamic system control. We consider two learning algorithms: the error backpropagation algorithm and the parallel recursive prediction error algorithm. The proposed method is an on-line approach of a multilayered neural network controller which does not require any information about the system dynamics. Lengthy training of the controller might be eliminated using the proposed approach. The implementation aspects of the proposed approaches to dynamic system control are discussed by case studies.