Related papers: Predictability of Observables of Dynamical Systems

For linear control systems, the usual state feedback stabilizability has two components: one is a continuous observation mode (i.e., to observe solutions continuously in time), and the other is a class of feedback laws (which is usually the…

Habituation - a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld - is universally observed in living systems from animals to unicellular…

The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…

This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…

This work deals with the problem of designing observers for the estimation of a single function of the states for discrete-time nonlinear systems. Necessary and sufficient conditions for the existence of lower order functional observers…

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…

Stability is required for real world controlled systems as it ensures that those systems can tolerate small, real world perturbations around their desired operating states. This paper shows how stability for continuous systems modeled by…

It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…

Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…

A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…

Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…

We derive an exact deterministic nonlinear observer to compute the continuous state of an inertial navigation system based on partial discrete measurements, the so-called strapdown problem. Nonlinear contraction is used as the main analysis…

The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…

Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional…

Temporal-difference (TD) networks are a class of predictive state representations that use well-established TD methods to learn models of partially observable dynamical systems. Previous research with TD networks has dealt only with…

We study the problem of designing interval-valued observers that simultaneously estimate the system state and learn an unknown dynamic model for partially unknown nonlinear systems with dynamic unknown inputs and bounded noise signals.…

For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the…

We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…