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Stochastic control theory is introduced and its importance relative to control science in general is discussed. It is noted that although most practical control problems are stochastic in some sense, stochastic control theory has found few successful applications. One of the major reasons for this dearth of practical applications is considered to be the difficulty of finding optimal solutions for most stochastic control problems. Consequently, suboptimal solutions are usually necessary and it is shown that the determination of useful suboptimal solutions depends largely on an understanding of the structure of stochastic control laws. It is observed that the basic result about the structure of stochastic control laws is that stochastic controllers perform two functions, estimation and control implementation. The mathematical form of the first function is updating equations while the mathematical form of the second function is the control policy. It is observed that it is the possible interaction between the two functions of estimation and control implementation which causes stochastic control policies to differ from deterministic control policies. It is shown that this interaction can occur in two ways: (i) the accuracy of the estimation can affect the control policy; (ii) the control policy can affect the rate at which uncertainty is reduced. The effects of the possible interaction on stochastic control policies is investigated by studying three classes of stochastic control problems, those that are certainty equivalent, neutral and separable. A consideration of the relationship between these three properties leads to the conclusion that stochastic control policies have three components: (i) the certainty equivalent policy; (ii) caution; (iii) probing and that the functions of these components are (i) to produce the required plant behaviour, (ii) to take into account the fact that the accuracy of the estimation can affect the control policy, (iii) to take advantage of the fact that the control policy can affect the rate at which uncertainty is reduced. Two of the components of stochastic control policies, caution and probing, describe the effect of the possible interaction between estimation and control implementation. The properties of these components are determined through several simple examples. It is noted that the caution component is more easily determined exactly than is the probing component; however, the exact form of the probing component is possibly not very important. Two simulations of simple stochastic control problems are reported. The first of these concerns the 'known gain problem' and clearly demonstrates that the advantages given by the application of stochastic control theory increase rapidly as the length of the process controlled increases. The second simulation is of the more complex 'unknown constant gain problem' and demonstrates the importance of caution. Caution is necessary if large and very costly errors are to be avoided while probing is necessary particularly for longer processes to reduce uncertainty. It is shown that a control policy called the neutral control policy which includes the optimal amount of caution but which has no probing component is more easily derived than is the optimal control policy. It is seen from the second simulation that the neutral control policy with a very simple additive probing term is a good suboptimal control policy. It is conjectured that neutral-plus-probing control policies may prove very useful as suboptimal policies for a large number of stochastic control problems.

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The possibility to manipulate the purely noise-induced behaviour in the large ensemble of globally coupled excitable systems is central to my research work. We employ globally coupled noise-driven FitzHugh-Nagumo units as a prototype of excitable system, which serve as a rough model of a neural network. Such a network is capable of demonstrating various kinds of behaviour with non-synchronized or synchronized units, with the mean field demonstrating periodic or chaotic small oscillations, or periodic or aperiodic spiking. Delayed feedback control applied through the mean field is shown capable of manipulating the basic features of the network behaviour, namely, to induce or suppress collective synchrony, to regularize the system behaviour in both synchronous and non-syncrhonous states, to shift the basic time scales of oscillations. These results are relevant to the control of unwanted behaviour in neural networks.

The control of systems with time-delay elements is reviewed. The differences between continuous and sampled-data control are discussed. A control method (for digitally controlled systems) is proposed based on the method due to O. J. Smith for continuously-controlled systems with a single delay. The effects of imperfections in the system model, and the effects of disturbance to the system are described and analysed. The method is extended for cascaded and other systems where the effect of delays is inseparable from the plant dynamics. Simulation studies using a hybrid computer are presented and discussed, in particular the effect of the use of short and extended shift registers for the simulation of pure time-delays is given detailed treatment.

Sensitivity theory and optimal control theory have been applied to the analysis and optimisation of the performance of a single machine power system. System sensitivity was used as a design criterion and as a method of optimisation and analysis. Both dynamic sensitivity and eigenvalue sensitivity have been considered. Systematic methods have been developed for the optimisation of the performance and sensitivity of linear and non-linear dynamic systems using sensitivity functions. These methods have been successfully applied to optimise the transient performance of conventional synchronous generators employing suboptimal excitation control and integrated excitation and steam-flow control. It was found that the suboptimal controls derived furnished substantial improvement in transient performance of the system under a wide range of operating conditions and varying parameters, A. comprehensive sensitivity analysis of the conventional generator has been mode which provides valuable insight into the sensitivity and dynamic characteristics of the system and forms a complementary study to the optimisation studies. The optimal and suboptimal excitation control of a dual-excited synchronous generator has also been investigated and it was found that substantial overall improvement were achieved by the optimal and suboptimal controls in the generator performance both under small and large disturbance conditions.

We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to meet demand, the requirement for simultaneous availability of resources means that a network may nevertheless be unstable. We show that instability occurs through a poor control strategy, and that, for a variety of network topologies, only small modifications to control strategies are required in order to ensure stability. For control strategies which possess a natural monotonicity property, we give some new results for the classification of the corresponding Markov processes, which lead to conditions both for stability and for instability. Finally, we study the effect of variation of call size distribution on stationary distributions and stability.

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Structural test rigs may incorporate between 1 and 30 hydraulic actuators each providing a load or displacement control. A closed loop PID controller is most commonly used to provide displacement or load control. Normally, industrial controllers provide a relatively high operational bandwidth of the actuator and a good performance within its operational range. The problem arises when the load is changing over a considerable range and sometimes in an unexpected manner. This causes undesirable interaction between actuators and results in degradation of the reference signal tracking. The controller proposed in this thesis is designed to meet aforementioned challenges facing the control system for modern multi-axis rigs: to reach satisfactory reference signal tracking without the need for iteration and robust performance in the presence of interactions and disturbances. The controller is a novel extension of the Model Reference Adaptive Control method known as Minimal Control Synthesis (MCS). It is arranged to function seamlessly through integration with a conventional test rig controller. Furthermore the controller employs important features which allow model following behaviour of the hydraulic cylinder and, to a large extent, to compensate for the actuator dynamics by the inverse model extension. A theoretical tool has been proposed for the analysis of the adaptation dynamics of the controller. A multi-axis scheme for the controller utilises a decentralised approach which implies individual control of each cylinder of the multi-axis system with coupling effects treated as disturbances, which should be attenuated by the adaptive controller. Experimental studies for single-axis and multi-axis variants of the control scheme were conducted on a six-axis MAST. Very good dynamic performance was demonstrated relative to a standard industrial controller. However, it was found that the bandwidth and disturbance attenuation property of the controller were compromised to some degree because it was not feasible to include acceleration feedback signal in the controller structure.