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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.

Simulation-based non-linear active suspension control design for MacPherson systems is considered. A nonlinear dynamic model for the MacPherson suspension system is derived. The model nonlinearities and the dynamic behaviour of the system is illustrated by simulations. The design of controllers and state estimators using finite state Markov models is briefly outlined, and applied for nonlinear active suspension control system. The study illustrates the potential of the finite Markov chains approach in non-linear active suspension control, emphasizing the possibility to move computational load due to simulations to off-line design.

Cognition and control processes share many similar characteristics, and decisionmaking and learning under the paradigm of multiple models has increasingly gained attention in both fields. The controlled finite Markov chain (CFMC) approach enables to deal with a large variety of signals and systems with multivariable, nonlinear, and stochastic nature. In this article, adaptive control based on multiple models is considered. For a set of candidate plant models, CFMC models (and controllers) are constructed off-line. The outcomes of the CFMC models are compared with frequentist information obtained from on-line data. The best model (and controller) is chosen based on the Kullback–Leibler information. This approach to adaptive control emphasizes the use of physical models as the basis of reliable plant identification. Three series of simulations are conducted: to examine the performace of the developed Matlab-tools; to illustrate the approach in the control of a nonlinear nonminimum phase van der Vusse CSTR plant; and to examine the suggested model selection method for the adaptive control.

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.

Polynomial artificial neural networks (PANN) have been shown to be powerful for forecasting nonlinear time series. The training time is small compared to the time used by other algorithms of artificial neural networks and the capacity to compute relations between the inputs and outputs represented by every term of the polynomial. In this paper a new structure of polynomial is presented that improves the performance of this type of network considering only non-integers exponents. The architecture adaptation uses genetic algorithm (GA) to find the optimal architecture for every example. Some examples of sunspots and chaotic time series are presented.

The goal of this paper is to design a new control algorithm for open-loop control of complex systems. This control approach is based on a genealogical decision tree for both regulation and tracking control problems. The idea behind this control strategy consists of associating Gaussian distributions to both the norms of the control actions and the tracking errors. This stochastic search model can be interpreted as a simple genetic particle evolution model with a natural birth and death interpretation. It converges on probability. A numerical example dealing with the control of a fluidized bed combustion power plant illustrates the feasibility and the performance of this control algorithm.

A new control algorithm for open-loop control of complex systems is suggested. The approach is based on a genealogical decision tree for tracking control problems. The idea behind this control strategy consists of associating Gaussian distributions to both the norms of the control actions and the tracking errors. This stochastic search model can be interpreted as a simple genetic particle evolution model with a natural birth and death interpretation. It converges in probability. A numerical example illustrates the feasibility and the performance of this control algorithm.

A distributed Wiener logic processor model structure is considered. Each fuzzy Wiener model consists of a succession of a linear dynamic part and a static steady-state (non-linear) logical part. The model structure and the necessary gradients required by gradient-based parameter estimation methods are given. Parameter projection and a modified threshold method are discussed. A simulation example illustrates the approach in the identification of a nonlinear, non-minimum phase CSTR process where a van der Vusse reaction takes place.

This paper presents an algorithm for optimization. This algorithm is based on a team of learning stochastic automata. Each automaton is characterized by two actions providing a binary output (0 or 1). The action of the team of automata consists of a digital number which represents the environment input. The probability distribution associated which each automaton is adjusted using a modified version of the Bush-Mosteller reinforcement scheme. This adaptation scheme uses a continuous environment response and a time-varying correction factor. A normalization procedure is used in order to preserve the probability measure. The asymptotic properties of this optimization algorithm are presented. A numerical example illustrates the feasibility and the performance of this optimization algorithm.

Modelling of dynamic non-linear processes using the Wiener approach is considered. Models are constructed based on sampled measurements from the process, as well as a priori information of the characteristics of the process. Prior information is expressed by a set of constraints, which leads to an optimisation problem of parameter estimation under constraints. Modelling of a two-tank system Illustrates the performance of the approach

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 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.

Control is a subject that heavily relies on mathematics and physics. High level theoretical treatments are more easily understood and digested when accompanied by concrete examples. In this study, two important phenomena, namely linearization and integration are chosen as two cases that are important in industrial processes. Examples of teaching approaches are demonstrated around these two cases. Some simple examples are chosen, for easy demonstration, without the loss of generality. The approaches are believed to be effective in teaching engineering students and especially engineers working in industry.

This paper considers the use of adaptive learning systems for multimodal functions optimization and process control. The learning system collects and processes the available data to achieve the desired control objective. The environment where the automaton operates corresponds to the function to be optimized (the process to be controlled) which is assumed to be unknown function of a single parameter x. The admissible region of x (control variable) is quantized into N levels. These levels are associated with the actions of the automaton. The set of these actions is further decomposed into nonempty subsets. The action set is changing from instant to instant. At each time an action set is selected according to a probability distribution. The action and the action set probabilities are adjusted using learning algorithms (reinforcement schemes). This optimization and control approach is tested using two numerical examples (multimodal function and a chemical reactor). However, the concept can be applied to other examples as well. Simulation results illustrate the feasibility and the performance of this adaptive automaton.

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.

Wiener type of models consist of linear dynamics followed by a static non-linear part. In this paper, a restricted class of Wiener models is considered where the static mapping represents a steady-state model for the process. A Wiener model structure is suggested for the identification of a MISO steady-state static model with linear FIR (finite impulse response) dynamics for each input. Unit steady-state gain is obtained by using a reduced FIR model, consisting of a unit gain plus FSR (finite step response) dynamics. The necessary derivatives required by gradient-based parameter estimation techniques are given. Simulation examples with data from a distillation column model and a pump-valve system, using sigmoid neural networks to model the non-linearities, illustrate the behaviour of the approach.

This paper presents a constrained predictive control strategy using artificial neural networks (ANN). In this control scheme two ANN are used. The recurrent ANN is used as a multi-step ahead predictor. The control action is provided by the multilayer feedforward ANN. 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. Simulation results demonstrate the usefulness and the robustness of this predictive control 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 process modelling based on fuzzy logic neural networks. Fuzzy systems are implemented in the form of distributed logic processors. Derivatives required by gradient descent training methods are given, and recursive prediction error training method is used to adjust the model parameters. The approach is illustrated with a modelling example where nitrogen emission (x) data from a fluidized-bed combustion district heating plant is used. The method presented in this paper is general, and can be applied to other complex processes as well.