
Regularised LeastSquares Regression with InfiniteDimensional Output Space
We present some learning theory results on reproducing kernel Hilbert sp...
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Metric on random dynamical systems with vectorvalued reproducing kernel Hilbert spaces
The development of a metric on structural datagenerating mechanisms is ...
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Handling Hard Affine SDP Shape Constraints in RKHSs
Shape constraints, such as nonnegativity, monotonicity, convexity or su...
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Balanced Reduction of Nonlinear Control Systems in Reproducing Kernel Hilbert Space
We introduce a novel datadriven order reduction method for nonlinear co...
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Koopman Linearization for DataDriven Batch State Estimation of ControlAffine Systems
We present the Koopman State Estimator (KoopSE), a framework for modelf...
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Kernel Methods for the Approximation of Nonlinear Systems
We introduce a datadriven order reduction method for nonlinear control ...
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Random features for adaptive nonlinear control and prediction
A key assumption in the theory of adaptive control for nonlinear systems...
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Control Occupation Kernel Regression for Nonlinear ControlAffine Systems
This manuscript presents an algorithm for obtaining an approximation of nonlinear high order control affine dynamical systems, that leverages the controlled trajectories as the central unit of information. As the fundamental basis elements leveraged in approximation, higher order control occupation kernels represent iterated integration after multiplication by a given controller in a vector valued reproducing kernel Hilbert space. In a regularized regression setting, the unique optimizer for a particular optimization problem is expressed as a linear combination of these occupation kernels, which converts an infinite dimensional optimization problem to a finite dimensional optimization problem through the representer theorem. Interestingly, the vector valued structure of the Hilbert space allows for simultaneous approximation of the drift and control effectiveness components of the control affine system. Several experiments are performed to demonstrate the effectiveness of the approach.
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