Related papers: Structural, Dynamical and Symbolic Observability: …
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…
To understand and explain process behaviour we need to be able to see it, and decide its significance, i.e. be able to tell a story about its behaviours. This paper describes a few of the modelling challenges that underlie monitoring and…
Modern learning systems increasingly interact with data that evolve over time and depend on hidden internal state. We ask a basic question: when is such a dynamical system learnable from observations alone? This paper proposes a research…
Linear observed systems on manifolds are a special class of nonlinear systems whose state spaces are smooth manifolds but possess properties similar to linear systems. Such properties can be characterized by preintegration and exact…
Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…
This work highlights the duality between state estimation methods and model predictive control. A predictive controller, observed control, is presented that uses this duality to efficiently compute control actions with linear time-horizon…
The topic of identification of dynamic systems, has been at the core of modern control , following the fundamental works of Kalman. Realization Theory has been one of the major outcomes in this domain, with the possibility of identifying a…
Accurate knowledge of the state variables in a dynamical system is critical for effective control, diagnosis, and supervision, especially when direct measurements of all states are infeasible. This paper presents a novel approach to…
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…
We consider the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. First a number of foundational results on…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the…
Observability quantification is a key problem in dynamic network sciences. While it has been thoroughly studied for linear systems, observability quantification for nonlinear networks is less intuitive and more cumbersome. One common…
This paper proposes a novel approach for designing functional observers for nonlinear systems, with linear error dynamics and assignable poles. Sufficient conditions for functional observability are first derived, leading to functional…
This work attempts to discuss the observability of linear time-invariant systems with event-triggered measurements. A new notion of observability, namely, $\epsilon$-observability is defined with parameter $\epsilon$, which relates to the…
The goal of this article is twofold. Firstly, nonlinear system identification is introduced to a wide audience, guiding practicing engineers and newcomers in the field to a sound solution of their data driven modeling problems for nonlinear…
The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches…
How to recognise whether an observed person walks or runs? We consider a dynamic environment where observations (e.g. the posture of a person) are caused by different dynamic processes (walking or running) which are active one at a time and…
In this paper we propose a new observability property for nonautonomous linear control systems in finite dimension: the nonuniform complete observability, which is more general than the uniform complete observability. A dual relationship is…
The Koopman representation is an infinite dimensional linear representation of linear or nonlinear dynamical systems. It represents the dynamics of output maps (aka observables), which are functions on the state space whose evaluation is…