Mathematical modelling and optimal multivariable control of chemical processes

This work reports the developnent of a mathenatical model and distributed, multi variable computer-control for a pilot plant double-effect climbing-film evaporator. A distributed-parameter model of the plant has been developed and the time-domain model transformed into the Laplace domain. The model has been further transformed into an integral domain conforming to an algebraic ring of polynomials, to eliminate the transcendental terms which arise in the Laplace domain due to the distributed nature of the plant model. This has made possible the application of linear control theories to a set of linear-partial differential equations. The models obtained have well tracked the experimental results of the plant. A distributed-computer network has been interfaced with the plant to implement digital controllers in a hierarchical structure. A modern rnultivariable Wiener-Hopf controller has been applled to the plant model. The application has revealed a limitation condition that the plant matrix should be positive-definite along the infinite frequency axis. A new multi variable control theory has emerged fram this study, which avoids the above limitation. The controller has the structure of the modern Wiener-Hopf controller, but with a unique feature enabling a designer to specify the closed-loop poles in advance and to shape the sensitivity matrix as required. In this way, the method treats directly the interaction problems found in the chemical processes with good tracking and regulation performances. Though the ability of the analytical design methods to determine once and for all whether a given set of specifications can be met is one of its chief advantages over the conventional trial-and-error design procedures. However, one disadvantage that offsets to some degree the enormous advantages is the relatively complicated algebra that must be employed in working out all but the simplest problem. Mathematical algorithms and computer software have been developed to treat some of the mathematical operations defined over the integral domain, such as matrix fraction description, spectral factorization, the Bezout identity, and the general manipulation of polynomial matrices. Hence, the design problems of Wiener-Hopf type of controllers and other similar algebraic design methods can be easily solved.

Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

Fully probabilistic control design in an adaptive critic framework

Optimal stochastic controller pushes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design (FPD) uses probabilistic description of the desired closed loop and minimizes Kullback-Leibler divergence of the closed-loop description to the desired one. Practical exploitation of the fully probabilistic design control theory continues to be hindered by the computational complexities involved in numerically solving the associated stochastic dynamic programming problem. In particular very hard multivariate integration and an approximate interpolation of the involved multivariate functions. This paper proposes a new fully probabilistic contro algorithm that uses the adaptive critic methods to circumvent the need for explicitly evaluating the optimal value function, thereby dramatically reducing computational requirements. This is a main contribution of this short paper.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Kárnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.

Stochastic control strategies and adaptive critic methods

Adaptive critic methods have common roots as generalizations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, nonlinear and nonstationary environments. In this study, a novel probabilistic dual heuristic programming (DHP) based adaptive critic controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) adaptive critic method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterized by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the critic network is then calculated and shown to be equal to the analytically derived correct value.

Probability distribution modelling to improve stability in nonlinear MIMO control

We consider the direct adaptive inverse control of nonlinear multivariable systems with different delays between every input-output pair. In direct adaptive inverse control, the inverse mapping is learned from examples of input-output pairs. This makes the obtained controller sub optimal, since the network may have to learn the response of the plant over a larger operational range than necessary. Moreover, in certain applications, the control problem can be redundant, implying that the inverse problem is ill posed. In this paper we propose a new algorithm which allows estimating and exploiting uncertainty in nonlinear multivariable control systems. This approach allows us to model strongly non-Gaussian distribution of control signals as well as processes with hysteresis. The proposed algorithm circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider.

A methodology for analysis and control of discrete event dynamic systems

The rapid developments in computer technology have resulted in a widespread use of discrete event dynamic systems (DEDSs). This type of system is complex because it exhibits properties such as concurrency, conflict and non-determinism. It is therefore important to model and analyse such systems before implementation to ensure safe, deadlock free and optimal operation. This thesis investigates current modelling techniques and describes Petri net theory in more detail. It reviews top down, bottom up and hybrid Petri net synthesis techniques that are used to model large systems and introduces on object oriented methodology to enable modelling of larger and more complex systems. Designs obtained by this methodology are modular, easy to understand and allow re-use of designs. Control is the next logical step in the design process. This thesis reviews recent developments in control DEDSs and investigates the use of Petri nets in the design of supervisory controllers. The scheduling of exclusive use of resources is investigated and an efficient Petri net based scheduling algorithm is designed and a re-configurable controller is proposed. To enable the analysis and control of large and complex DEDSs, an object oriented C++ software tool kit was developed and used to implement a Petri net analysis tool, Petri net scheduling and control algorithms. Finally, the methodology was applied to two industrial DEDSs: a prototype can sorting machine developed by Eurotherm Controls Ltd., and a semiconductor testing plant belonging to SGS Thomson Microelectronics Ltd.

The factors affecting the optimal performance of eddy-current machines

This thesis presents an examination of the factors which influence the performance of eddy-current machines and the way in which they affect optimality of those machines. After a brief introduction to the types of eddy-current machine considered, the applications to which these machines are put are examined. A list of parameters by which to assess their performance is obtained by considering the machine as part of a system. in this way an idea of what constitutes an optimal machine is obtained. The third chapter then identifies the factors which affects the performance and makes a quantitative evaluation of the effect. Here the various alternative configurations and components are compared with regard to their influence on the mechanical, electromagnetic, and thermal performance criteria of the machine. Chapter four contains a brief review of the methods of controlling eddy-current machines by electronic methods using thyristors or transistors as the final control element. Where necessary, the results of previous workers in the field of electrical machines have been extended or adapted to increase the usefulness of this thesis.

The role of stochasticity in an information-optimal neural population code

In this paper we consider the optimisation of Shannon mutual information (MI) in the context of two model neural systems The first is a stochastic pooling network (population) of McCulloch-Pitts (MP) type neurons (logical threshold units) subject to stochastic forcing; the second is (in a rate coding paradigm) a population of neurons that each displays Poisson statistics (the so called 'Poisson neuron'). The mutual information is optimised as a function of a parameter that characterises the 'noise level'-in the MP array this parameter is the standard deviation of the noise, in the population of Poisson neurons it is the window length used to determine the spike count. In both systems we find that the emergent neural architecture and; hence, code that maximises the MI is strongly influenced by the noise level. Low noise levels leads to a heterogeneous distribution of neural parameters (diversity), whereas, medium to high noise levels result in the clustering of neural parameters into distinct groups that can be interpreted as subpopulations In both cases the number of subpopulations increases with a decrease in noise level. Our results suggest that subpopulations are a generic feature of an information optimal neural population.

Neural network enhanced self tuning adaptive control application for non-linear control of dynamic systems

The main theme of research of this project concerns the study of neutral networks to control uncertain and non-linear control systems. This involves the control of continuous time, discrete time, hybrid and stochastic systems with input, state or output constraints by ensuring good performances. A great part of this project is devoted to the opening of frontiers between several mathematical and engineering approaches in order to tackle complex but very common non-linear control problems. The objectives are: 1. Design and develop procedures for neutral network enhanced self-tuning adaptive non-linear control systems; 2. To design, as a general procedure, neural network generalised minimum variance self-tuning controller for non-linear dynamic plants (Integration of neural network mapping with generalised minimum variance self-tuning controller strategies); 3. To develop a software package to evaluate control system performances using Matlab, Simulink and Neural Network toolbox. An adaptive control algorithm utilising a recurrent network as a model of a partial unknown non-linear plant with unmeasurable state is proposed. Appropriately, it appears that structured recurrent neural networks can provide conveniently parameterised dynamic models for many non-linear systems for use in adaptive control. Properties of static neural networks, which enabled successful design of stable adaptive control in the state feedback case, are also identified. A survey of the existing results is presented which puts them in a systematic framework showing their relation to classical self-tuning adaptive control application of neural control to a SISO/MIMO control. Simulation results demonstrate that the self-tuning design methods may be practically applicable to a reasonably large class of unknown linear and non-linear dynamic control systems.

Optimal design for correlated processes with input-dependent noise

Optimal design for parameter estimation in Gaussian process regression models with input-dependent noise is examined. The motivation stems from the area of computer experiments, where computationally demanding simulators are approximated using Gaussian process emulators to act as statistical surrogates. In the case of stochastic simulators, which produce a random output for a given set of model inputs, repeated evaluations are useful, supporting the use of replicate observations in the experimental design. The findings are also applicable to the wider context of experimental design for Gaussian process regression and kriging. Designs are proposed with the aim of minimising the variance of the Gaussian process parameter estimates. A heteroscedastic Gaussian process model is presented which allows for an experimental design technique based on an extension of Fisher information to heteroscedastic models. It is empirically shown that the error of the approximation of the parameter variance by the inverse of the Fisher information is reduced as the number of replicated points is increased. Through a series of simulation experiments on both synthetic data and a systems biology stochastic simulator, optimal designs with replicate observations are shown to outperform space-filling designs both with and without replicate observations. Guidance is provided on best practice for optimal experimental design for stochastic response models. © 2013 Elsevier Inc. All rights reserved.

Probabilistic synchronisation of pinning control

This paper is concerned with synchronization of complex stochastic dynamical networks in the presence of noise and functional uncertainty. A probabilistic control method for adaptive synchronization is presented. All required probabilistic models of the network are assumed to be unknown therefore estimated to be dependent on the connectivity strength, the state and control values. Robustness of the probabilistic controller is proved via the Liapunov method. Furthermore, based on the residual error of the network states we introduce the definition of stochastic pinning controllability. A coupled map lattice with spatiotemporal chaos is taken as an example to illustrate all theoretical developments. The theoretical derivation is complemented by its validation on two representative examples.