Improved robust control of nonlinear stochastic systems using uncertain models

We introduce a technique for quantifying and then exploiting uncertainty in nonlinear stochastic control systems. The approach is suboptimal though robust and relies upon the approximation of the forward and inverse plant models by neural networks, which also estimate the intrinsic uncertainty. Sampling from the resulting Gaussian distributions of the inversion based neurocontroller allows us to introduce a control law which is demonstrably more robust than traditional adaptive controllers.

Robust control of nonlinear stochastic systems by modelling conditional distributions of control signals

We introduce a novel inversion-based neuro-controller for solving control problems involving uncertain nonlinear systems that 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. In this work a novel robust inverse control approach is obtained based on importance sampling from these distributions. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The performance of the new algorithm is illustrated through simulations with example systems.

Distributed control of computer communication systems

Flow control in Computer Communication systems is generally a multi-layered structure, consisting of several mechanisms operating independently at different levels. Evaluation of the performance of networks in which different flow control mechanisms act simultaneously is an important area of research, and is examined in depth in this thesis. This thesis presents the modelling of a finite resource computer communication network equipped with three levels of flow control, based on closed queueing network theory. The flow control mechanisms considered are: end-to-end control of virtual circuits, network access control of external messages at the entry nodes and the hop level control between nodes. The model is solved by a heuristic technique, based on an equivalent reduced network and the heuristic extensions to the mean value analysis algorithm. The method has significant computational advantages, and overcomes the limitations of the exact methods. It can be used to solve large network models with finite buffers and many virtual circuits. The model and its heuristic solution are validated by simulation. The interaction between the three levels of flow control are investigated. A queueing model is developed for the admission delay on virtual circuits with end-to-end control, in which messages arrive from independent Poisson sources. The selection of optimum window limit is considered. Several advanced network access schemes are postulated to improve the network performance as well as that of selected traffic streams, and numerical results are presented. A model for the dynamic control of input traffic is developed. Based on Markov decision theory, an optimal control policy is formulated. Numerical results are given and throughput-delay performance is shown to be better with dynamic control than with static control.

Variational Markov Chain Monte Carlo for Bayesian smoothing of non-linear niffusions

In this paper we develop set of novel Markov chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. Flexible blocking strategies are introduced to further improve mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample, applications the algorithm is accurate except in the presence of large observation errors and low observation densities, which lead to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient.

Computerised control of cellular manufacturing systems

This thesis reviews the existing manufacturing control techniques and identifies their practical drawbacks when applied in a high variety, low and medium volume environment. It advocates that the significant drawbacks inherent in such systems, could impair their applications under such manufacturing environment. The key weaknesses identified in the system were: capacity insensitive nature of Material Requirements Planning (MRP); the centralised approach to planning and control applied in Manufacturing Resources Planning (MRP IT); the fact that Kanban can only be used in repetitive environments; Optimised Productivity Techniques's (OPT) inability to deal with transient bottlenecks, etc. On the other hand, cellular systems offer advantages in simplifying the control problems of manufacturing and the thesis reviews systems designed for cellular manufacturing including Distributed Manufacturing Resources Planning (DMRP) and Flexible Manufacturing System (FMS) controllers. It advocates that a newly developed cellular manufacturing control methodology, which is fully automatic, capacity sensitive and responsive, has the potential to resolve the core manufacturing control problems discussed above. It's development is envisaged within the framework of a DMRP environment, in which each cell is provided with its own MRP II system and decision making capability. It is a cellular based closed loop control system, which revolves on single level Bill-Of-Materials (BOM) structure and hence provides better linkage between shop level scheduling activities and relevant entries in the MPS. This provides a better prospect of undertaking rapid response to changes in the status of manufacturing resources and incoming enquiries. Moreover, it also permits automatic evaluation of capacity and due date constraints and hence facilitates the automation of MPS within such system. A prototype cellular manufacturing control model, was developed to demonstrate the underlying principles and operational logic of the cellular manufacturing control methodology, based on the above concept. This was shown to offer significant advantages from the prospective of operational planning and control. Results of relevant tests proved that the model is capable of producing reasonable due date and undertake automation of MPS. The overall performance of the model proved satisfactory and acceptable.

Some aspects of the solution of non-linear differential equations

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Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

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.

Neural network control of a gas turbine

In this paper we explore the practical use of neural networks for controlling complex non-linear systems. The system used to demonstrate this approach is a simulation of a gas turbine engine typical of those used to power commercial aircraft. The novelty of the work lies in the requirement for multiple controllers which are used to maintain system variables in safe operating regions as well as governing the engine thrust.

Simulation and control of a stepping motor

Open-loop operatlon of the stepping motor exploits the inherent advantages of the machine. For near optimum operation: in this mode, however, an accurate system model is required to facilitate controller design. Such a model must be comprehensive and take account of the non-linearities inherent in the system. The result is a complex formulation which can be made manageable with a computational aid. A digital simulation of a hybrid type stepping motor and its associated drive circuit is proposed. The simulation is based upon a block diagram model which includes reasonable approximations to the major non-linearities. The simulation is shown to yield accurate performance predictions. The determination of the transfer functions is based upon the consideration of the physical processes involved rather than upon direct input-outout measurements. The effects of eddy currents, saturation, hysteresis, drive circuit characteristics and non-linear torque displacement characteristics are considered and methods of determining transfer functions, which take account of these effects, are offered. The static torque displacement characteristic is considered in detail and a model is proposed which predicts static torque for any combination of phase currents and shaft position. Methods of predicting the characteristic directly from machine geometry are investigated. Drive circuit design for high efficiency operation is considered and a model of a bipolar, bilevel circuit is proposed. The transfers between stator voltage and stator current and between stator current and air gap flux are complicated by the effects of eddy currents, saturation and hysteresis. Frequency response methods, combined with average inductance measurements, are shown to yield reasonable transfer functions. The modelling procedure and subsequent digital simulation is concluded to be a powerful method of non-linear analysis.

Statnote 19: non-linear regression: fitting an exponential curve to data

Non-linear relationships are common in microbiological research and often necessitate the use of the statistical techniques of non-linear regression or curve fitting. In some circumstances, the investigator may wish to fit an exponential model to the data, i.e., to test the hypothesis that a quantity Y either increases or decays exponentially with increasing X. This type of model is straight forward to fit as taking logarithms of the Y variable linearises the relationship which can then be treated by the methods of linear regression.

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

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.