The aim of the project is to investigate the possibilities of the application of neural networks to the control of dynamical systems. Currently the design of control systems relies heavily upon an explicit mathematical model of the system. However, such an model is often very difficult and sometimes impossible to find. For this reason conventional control systems are usually based on a linearised and highly simplified mathematical model of the dynamics of the system. Experiences of the research groups involved show that neural networks, which are able to learn a non-linear model from examples, can succesfullv be applied for the control of non-linear systems. A second advantage is that neural networks are adaptive, in the sense that they keep learning during operation. This allows for continuous improvement of the controller while in operation.
However, little is known about the stability and robustness of control systems containing neural networks. Convergence has been proven for simple systems, but for complex systems neural networks have to genereralize well in high dimensional spaces. In this project we make the link between accuricy of function approximation with a neural network and the stability of the system. If this is achieved, neural control can be applied to real-world applications.
The project focusses on two control architectures: model-based predictive control and reinforcement learning. In the predictive control scheme neurocomputational methods will be applied for modelling the system. The aim is to develop a robust model-based (predictive) control scheme using a nonlinear (neural network) model. Of particular importance is that when bounds can be given on the modelling error, robust control schemes for such systems must be developed which lead to a guaranteed stable control system.
In reinforcement learning, neurocomputational methods are used to estimate a measure of utility (the future costs or reinforcement) directly by a neural network instead of deriving these costs from a (neural) model. Convergence properties of reinforcement learning have been proven, but only for a restricted class of representations for the critic, i.e. look-up tables. For more complex applications these look-up tables are inadequate, and representations which have larger generalization capacities (such as neural networks) are needed. The effect of this on the convergence properties is investigated in the project.
For both approaches the accuracy of function approximation with artificial neural networks is crucial. Both groups have strong experience with the issue of function approximation with neural networks and methods have been developed which are able to determine the optimal number of hidden units or network architecture. In the project we will specifically investigate the relationship between bounds on the network error and stability of the system.
At the start of the project we will start with the identification and control of some simple simulated systems (the choice of which will be guided by the users group) and develop a theoretical framework on the effect of the accuracy of function approximation on the stability of the system. In a later stage of the project, developed methodologies will be applied to specific control problems of the users group. Results will be compared with performance of conventional methods.

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