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A fundamental challenge in learning an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. We formulate a mathematical definition of what it means to safely learn a dynamical system by…
Recent studies highlight the importance of persistently exciting condition in single signal sequence for model identification and data-driven control methodologies. However, maintaining prolonged excitation in control signals introduces…
Common criteria used for measuring performance of vibrating systems have one thing in common: they do not depend on initial conditions of the system. In some cases it is assumed that the system has zero initial conditions, or some kind of…
Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of…
Lancaster (2002} proposes an estimator for the dynamic panel data model with homoskedastic errors and zero initial conditions. In this paper, we show this estimator is invariant to orthogonal transformations, but is inefficient because it…
In contrast to regular ordinary differential equations, the problem of accurately setting initial conditions just emerges in the context of differential-algebraic equations where the dynamic degree of freedom of the system is smaller than…
A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…
In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It…
We develop a new approximative estimation method for conditional Shapley values obtained using a linear regression model. We develop a new estimation method and outperform existing methodology and implementations. Compared to the sequential…
This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. The advantage of adaptivity in this context is the ability to focus more resources on regions of space where signal…
Solutions to the interval observation problem for delayed impulsive and switched systems with $L_1$-performance are provided. The approach is based on first obtaining stability and $L_1/\ell_1$-to-$L_1/\ell_1$ performance analysis…
To make predictions or design control, information on local sensitivity of initial conditions and state-space contraction is both central, and often instrumental. However, it is not always simple to reliably determine instability fields or…
In chaotic dynamical systems, a number of rare trajectories with low level of chaoticity are embedded in chaotic sea, while extraordinary unstable trajectories can exist even in weakly chaotic regions. In this study, a quantitative method…
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…
The effect of small noise in a smooth dynamical system is negligible on any finite time interval. Here we study situations when it persists on intervals increasing to infinity. Such asymptotic regime occurs when the system starts from…
Event-based methods carefully select when to transmit information to enable high-performance control and estimation over resource-constrained communication networks. However, they come at a cost. For instance, event-based communication…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
We present a reformulation of unsteady turbulent flow simulations. The initial condition is relaxed and information is allowed to propagate both forward and backward in time. Simulations of chaotic dynamical systems with this reformulation…
A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on…
A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them -- such as global vegetation -- are inherently non-stationary, for example due to strong…