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This paper presents a system identification technique for systems whose output is asymptotically periodic under constant inputs. The model used for system identification is a discrete-time Lure model consisting of asymptotically stable linear dynamics, a time delay, a washout filter, and a static nonlinear feedback mapping. For all sufficiently large scalings of the loop transfer function, these components cause divergence under small signal levels and decay under large signal amplitudes, thus producing an asymptotically oscillatory output. A bias-generation mechanism is used to provide a bias in the oscillation. The contribution of the paper is a least-squares technique that estimates the coefficients of the linear model as well as the parameterization of the continuous, piecewise-linear feedback mapping.
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global asymptotic stab
In this paper, we discuss several concepts of the modern theory of discrete integrable systems, including: - Time discretization based on the notion of Backlund transformation; - Symplectic realizations of multi-Hamiltonian structures; - Interr
The visibility of the two-photon interference in the Franson interferometer serves as a measure of the energy-time entanglement of the photons. We propose to control the visibility of the interference in the second-order coherence function by impleme
Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a second-ord
This paper introduces an algorithm for discovering implicit and delayed causal relations between events observed by a robot at arbitrary times, with the objective of improving data-efficiency and interpretability of model-based reinforcement learning