A sensitivity approach to optimal spline robot trajectories
Automatica (Journal of IFAC)
Approximate state-feedback linearization using spline functions
Automatica (Journal of IFAC)
Brief paper: Periodic smoothing splines
Automatica (Journal of IFAC)
Brief paper: Fast computation of smoothing splines subject to equality constraints
Automatica (Journal of IFAC)
Input estimation in nonlinear dynamical systems using differential algebra techniques
Automatica (Journal of IFAC)
The marginal likelihood for parameters in a discrete Gauss-Markovprocess
IEEE Transactions on Signal Processing
Brief Optimal trajectory planning and smoothing splines
Automatica (Journal of IFAC)
Brief Regularization networks for inverse problems: A state-space approach
Automatica (Journal of IFAC)
On the ill-conditioning of subspace identification with inputs
Automatica (Journal of IFAC)
Regularization networks: fast weight calculation via Kalman filtering
IEEE Transactions on Neural Networks
Brief paper: Fast computation of smoothing splines subject to equality constraints
Automatica (Journal of IFAC)
Hi-index | 22.15 |
The issue of constructing periodic smoothing splines has been recently formulated as a controlled two point boundary value problem which admits a state-space description. In the context of minimum norm problems in Hilbert spaces, it has been shown that the solution is the sum of a finite number of basis functions and can be obtained with a number of operations which scales with the cube of the sum of the number of measurements and boundary constraints. In this paper we consider a more general class of variational problems subject to equality constraints which contains the periodic smoothing spline problem as a special case. Using the theory of reproducing kernel Hilbert spaces we derive a solution to the problem which has the same computational complexity as that recently proposed. Next, assuming that the problem admits a state-space representation, we obtain an algorithm whose complexity is linear in the number of measurements. We also show that the solution of the problem admits the structure of a particular regularization network whose weights can be computed in linear time. Closed form expressions for the basis functions associated with the periodic cubic smoothing spline problem are finally derived.