Other Projects

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Non-uniform Small Gain Theorems

Consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This, however, is neither a necessary requirement, nor is it always useful. Systems may, for instance, be inherently unstable (e.g. intermittent, itinerant, meta-stable) or the problem statement may include requirements that cannot be satisfied with stable solutions. This is often the case in general optimization problems and in nonlinear parameter identification or adaptation. Conventional techniques for these cases rely either on detailed knowledge of the system's vector-fields or require boundeness of its states. The presently proposed method relies only on estimates of the input-output maps and steady-state characteristics. The method requires the possibility of representing the system as an interconnection of a stable, contracting, and an unstable, exploratory part.

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Adaptation in Nonlinear Dynamical Systems

We propose a solution to the problem of adaptive control and parameter estimation in systems with unstable target dynamics. Models of uncertainties are allowed to be nonlinearly parameterized, and required to be smooth and monotonic functions of linear functionals of the parameters. The mere assumption of existence of nonlinear operator gains for the target dynamics is sufficient to guarantee that system solutions are bounded, reach a neighborhood of the target set, and the mismatches between the modeled uncertainties and their compensator converge to zero. With respect to parameter convergence, a standard persistent excitation condition suffices to ensure that it is exponential. When a weaker, nonlinear version of persistent excitation is satisfied, asymptotic convergence is guaranteed. The spectrum of possible applications ranges from tyre-road slip control to asynchronous message transmission in spiking neural oscillators.

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Efficient Visual Intelligence Technologies

The project aims at developing computationally efficient methods, algorithms and tools in the area of intelligent image processing. Examples include but are not limited to efficient real-time object detection, recognition, and false positives suppression in live video streams. In this project, we focus on dealing with computational and theoretical issues imposed by inherent high-dimensionality of data, scarceness of samples, data uncertainty, and robustness to groups of transformations.

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Department of Mathematics
University of Leicester
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Undergraduate: mathsug@le.ac.uk
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