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The problem of curse-of-dimensionality in finite state and action Markov decision processes is considered using iterative clustering of closed-loop data and repeated discretization of the state space process model. The performance of the control design approach is demonstrated using a multi-input van der Vusse continuous stirred tank reactor control benchmark. It is demonstrated that the finite state description provides a simple implementation of Bayesian state estimation using cell filters, and dynamic programming gives means to conduct optimization of closed-loop performance of a nonlinear stochastic multidimensional chemical plant.

This paper deals with regulation control on the basis of genealogical decision trees (GDTs). GDTs are a population-based random search technique for solving sequential multimodal and multivariable trajectory tracking problems, when gradient information is not available or does not exist. A direct application of GDT results in an open-loop control. In this paper, feedback regulation based on GDT is considered. In the proposed scheme, GDTs are used for solving off-line a number of predictive control problems; a finite set of initial states is then constructed from these simulations, for each of which an optimal control sequence has been computed. Natural handling of missing state vector measurements is provided. Numerical examples dealing with the van der Vusse CSTR illustrate the feasibility and the efficiency of this feedback control algorithm. A discussion on alternative approaches and a numerical comparison with the Markov-decision-process-based optimal policy are provided. Copyright © 2008 John Wiley & Sons, Ltd.

An application of a linear quadratic self-tuning control approach to a pulsed liquid-liquid extraction column is described. The control algorithm is derived from the minimization of a quadratic cost function. The resulting Riccati equation is iterated until the closed-loop poles belong to a predefined stability domain included in the unit circle. Based upon the certainty equivalence principle, the adaptive control algorithm involves a parameter identification procedure and a feedback control law which uses the estimated parameters. Several experiments are carried out on a pulsed liquid-liquid extraction column. Such extractors are being increasingly used in several industries because they are not energy-consuming and they lead to high product purity. The column considered has the same dimensions as those currently used in fine chemical processes. The control objective is to optimize the column behaviour. The selected control variables are the pulse frequency and the conductivity measured at the bottom of the column. The experiments have been carried out with a mixture of water and toluene. The physical model developed for the column is too complex to use for control purposes. To represent the complex behaviour of the column, a single-input/single-output discrete-time linear model was adopted. The parameters in the model are estimated on-line with normalized data. The forgetting factor is also adjusted to maintain a constant trace of the estimator gain matix. The results obtained show the ability of this algorithm to improve the efficiency of the process considered. Finally, some details on practical implementation are provided.

The identification of multiple-input single-output Wiener models is considered in this paper. The non-linear memoryless part is described by a parametrized steady state model. In this paper two representations for the linear dynamic part that preserve the unit steady state gain are discussed and compared: finite step response and transfer function with a feedback polynomial. The steps necessary for estimating the parameters of the Wiener model are presented. In the simulation examples with data from a pneumatic valve model, distillation column model and a pilot pump-valve system, the performance of the approach is examined, and the use of various kinds of non-linear black-box and grey-box structure for the modelling of the static part is illustrated.

This paper deals with the design and analysis of a modified version of the Bush-Mosteller reinforcement scheme applied by partners in a zero-sum repeated game with random pay-offs. The suggested study is based on the learning automata paradigm and a limiting average reward criterion is tackled to analyse the arising Nash equilibrium. No information concerning the distribution of the pay-off is a priori available. The novelty of the suggested adaptive strategy is related to the incorporation of a 'normalization procedure' into the standard Bush-Mosteller scheme to provide a possibility to operate not only with binary but also with any bounded rewards of a stochastic nature. The analysis of the convergence (adaptation) as well as the convergence rate (rate of adaptation) are presented and the optimal design parameters of this adaptive procedure are derived. The obtained adaptation rate turns out to be of o(n 1/3 ).

This paper concerns process modelling using fuzzy neural networks. In distributed logic processors (DLP) the rule base is parameterised. The DLP derivatives required by gradient-based training methods are given, and the recursive prediction error method is used to adjust the model parameters. The power of the approach is illustrated with a modelling example where NOx-emission data from a full-scale fluidised-bed combustion district heating plant are used. The method presented in this paper is general, and can be applied to other complex processes as well.

The paper concerns the estimation under constraints of the parameters of distributed logic processors (DLP). This optimization problem under constraints is solved using stochastic approximation techniques. DLPs are fuzzy neural networks capable of representing nonlinear functions. They consist of several logic processors, each of which performs a logical fuzzy mapping. A simulation example, using data collected from an industrial fluidized bed combustor, illustrates the feasibility and the performance of this training algorithm.

A long-range predictive control strategy using artificial neural networks ( ANNs) is represented. Both unconstrained and constrained control problems are considered. In this control scheme a recurrent ANN and a multilayer feedforward ANN are used. The recurrent ANN is used as a multi-step ahead predictor. For training this network the backpropagation through the time is used. The control action is provided by the multilayer feedforward ANN which uses the predictions of the output of the process to be controlled. The weights of this ANN are estimated at each control step using a stochastic approximation ( SA) algorithm by minimizing a quadratic control objective which is based on a series of the future predictions and future control actions, and by preventing violations of process constraints. To demonstrate the feasibility and the performance of this control scheme, a continuous biochemical reactor and a fixed bed tubular chemical reactor are chosen as realistic nonlinear case studies. Simulation...

A new algorithm for training the parameters of a distributed logic processor is suggested, based on learning automata. A fuzzy inference system is implemented on a multilayer perceptron platform. Various possibilities for assigning learning automata are discussed and two assignment strategies are proposed. The behaviour of the resulting algorithm is illustrated using flue-gas NO/sub x/ emission data measured from an industrial-size fluidised-bed combustor.

The behaviour of a stochastic automaton operating in an S-model environment is described. The environment response takes an arbitrary value in the closed segment [0, 1] (continuous response). The learning automaton uses a reinforcement scheme to update its action probabilities on the basis of the reaction of the environment. The complete set of actions is divided into a collection of non-empty subsets. The action set is changing from instant to instant. Each action set is selected according to a given probability distribution. Convergence and convergence rate results are presented. These results have been derived using quasimartingales theory.

This paper concerns the adaptive selection of the optimal order of linear regression models using a variable-structure stochastic learning automaton. The Alaike criterion is derived for stationary and non-stationary cases, and it is shown that the optimal order minimizes a loss function corresponding to the evaluation of this criterion. The order of the regression model belongs to a finite set. Each order value is associated with an action of the automaton. The Bush-Mosteller reinforcement scheme with normalized automaton input is used to adjust the probability distribution. Simulation results illustrate the feasibility and performance of this model order selection approach

This paper deals with the optimization of an autogenous grinding circuit using a random search technique. This technique is based on a hierarchical structure of learning automata operating in a random environment constituted by the autogenous circuit to be optimized. The ore feed rate to the mill is considered as the control variable while the mass flow rate of the concentrate of the subsequent separation process constitutes the controlled variable. The variation domain of the manipulated variables is discretized into a set of regions which are associated to the actions of the automata of the last level of the hierarchical learning system. A probability is associated to each action (region). The learning system selects one of the available actions and, based on the response of the environment, modifies the strategy (the probabilities associated to the set of actions) using an adaptation procedure called reinforcement scheme. Numerical results illustrate the feasibility and the performance of this self-adjusting optimization algorithm.

Autogenous grinding is characterized by non-linearities, time-varying dynamics and a high level of uncertainties, conditions which usually originate from the variability of the ore feed characteristics (hardness and grade). These characteristics make this grinding operation particularly appealing for some type of knowledge-based control. This paper discusses the application of the dynamic matrix control algorithm to an autogenous grinding operation. This control algorithm is a long-range predictive control algorithm which has been successfully applied to other processes. The study was carried out using an empirical simulator calibrated with industrial data. The simulation results were compared to those obtained using PID and learning controllers. The ability of the dynamic matrix control to improve the efficiency of this complex and highly sensitive process is clearly demonstrated.

Some critical computations in pole-placement design and in that of many model reference adaptive systems are described. These numerical problems are associated with the resolution of the diophantine equation. They occur when the assumption of no common poles and zeros is violated. Regularization techniques which cope with ill-conditioning are presented. The resulting algorithm combines a standard indirect pole-placement adaptive control algorithm and a dimension-free regularization procedure of the design equations, thus avoiding the pole-zero cancellation problem and yet retaining the other properties of the algorithm. The application of this control scheme in a pulsed liquid-liquid extraction column is described. The control objective is to optimize the column behaviour. Extraction columns are subject to changes in feed compositions, feed flow-rates, physical properties of the solvent (the extractor) and the solute (liquid mixture) and various disturbances. The column exhibits highly non-linear and time...

This paper presents a study on the control of a fluidized bed catalytic reactor. In this study, the model reference adaptative control algorithm with independent tracking and regulation objectives as presented by Landau-Lozano (1981) has been investigated. The purpose of the control is to maintain the temperature of the reactor as near as possible to a desired set value (490°C). Some of the heat produced as a result of the exothermal reaction tacking place between propylene, ammonia and oxygen is carried away by a ventilator. The control action is based on a simple mathematical lower order with time varying unknown parameters. This method of control results in a significantly improved control for both servo and regulatory control.

This paper aims at extending some results concerning the calculation of the residence time for linear systems to continuous flow nonlinear multidimensional systems. It is shown that the solution of a nonlinear system is equivalent to the solution of a linear system with time-varying parameters. An algorithm for calculating the residence time for nonlinear systems is developed. Simulation results dealing with three examples show the feasibility and performance of this proposed algorithm. However, this algorithm can be applied to other processes as well.