The Secretary of State for Defence in Her Britannic Majesty's Government

The Secretary of the State for Defence in Her Britannic Majesty's

Robin Jones

Martin Johnson

David S Broomhead

John G McWhirter

Terence John Shepherd

Kevin Dennis Ridley

Digital processor for simulating operation of a parallel processing array

A dynamical system analyser (10) incorporates a computer (22) to perform a singular value decomposition of a time series of signals from a nonlinear (possibly chaotic) dynamical system (14). Relatively low-noise singular vectors from the decomposition are loaded into a finite impulse response filter (34). The time series is formed into Takens' vectors each of which is projected onto each of the singular vectors by the filter (34). Each Takens' vector thereby provides the co-ordinates of a respective point on a trajectory of the system (14) in a phase space. A heuristic processor (44) is used to transform delayed co-ordinates by QR decomposition and least squares fitting so that they are fitted to non-delayed co-ordinates. The heuristic processor (44) generates a mathematical model to implement this transformation, which predicts future system states on the basis of respective current states. A trial system is employed to generate like co-ordinates for transformation in the heuristic processor (44). This produces estimates of the trial system's future states predicted from the comparison system's model. Alternatively, divergences between such estimates and actual behavior may be obtained. As a further alternative, mathematical models derived by the analyser (10) from different dynamical systems may be compared.

Dynamical system analyzer

A dynamical system analyzer (10) incorporates a computer (22) to perform a singular value decomposition of a time series of signals from a nonlinear (possibly chaotic) dynamical system (14). Relatively low-noise singular vectors from the decomposition are loaded into a finite impulse response filter (34). The time series is formed into Takens' vectors each of which is projected onto each of the singular vectors by the filter (34). Each Takens' vector thereby provides the co-ordinates of a respective point on a trajectory of the system (14) in a phase space. A heuristic processor (44) is used to transform delayed co-ordinates by QR decomposition and least squares fitting so that they are fitted to non-delayed co-ordinates. The heuristic processor (44) generates a mathematical model to implement this transformation, which predicts future system states on the basis of respective current states. A trial system is employed to generate like co-ordinates for transforation in the heuristic processor (44). This produces estimates of the trial system's future states predicted from the comparison system's model. Alternatively, divergences between such estimates and actual behavior may be obtained. As a further alternative, mathematical models derived by the analyzer (10) from different dynamical systems may be compared.

A heuristic processor incorporates a digital arithmetic unit arranged to compute the squared norm of each member of a training data set with respect to each member of a set of centers, and to transform the squared norms in accordance with a non-linear function to produce training .phi. vectors. A systolic array arranged for QR decomposition and least means squares processing forms combinations of the elements of each .phi. vector to provide a fit to corresponding training answers. The form of combination is then employed with like-transformed test data to provide estimates of unknown results. The processor is applicable to provide estimated results for problems which are non-linear and for which explicit mathematical formalisms are unknown.

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Worcester, United Kingdom

Robin Jones