Abstract
Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate relevant matrices and some relevant quantities such as the topological entropy. An application to stabilization via algebraic Riccati equations is included by viewing a control system as an autonomous system in an extended space of states and control inputs. Kernel methods are the main techniques used in this paper and the approach is illustrated via a series of numerical examples. The advantage of using kernel methods is that they allow to perform function approximation from data and, as illustrated in this paper, allow to approximate linear discrete-time autonomous and control systems from data.
Highlights
This paper discusses several problems in dynamical systems and control, where methods from learning theory are used in the state space of linear systems
In the control case, estimation of the relevant matrices for a linear control system is done by viewing a linear control system as a dynamical system in the extended space of states and control inputs
This paper has introduced the algorithm A based on kernel methods to identify a stable linear dynamical system from a time series
Summary
This paper discusses several problems in dynamical systems and control, where methods from learning theory are used in the state space of linear systems. This is in contrast to previous approaches in the frequency domain [10, 11]. The approach used in these papers is based on embedding a nonlinear system in a high (or infinite) dimensional reproducing kernel Hilbert space (RKHS) where linear theory is applied. To illustrate this approach, consider a polynomial in R , p(x) = + x + x2 where , , are real numbers. A preliminary version of this article appeared in Hamzi and Colonius [9]
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