Related papers: Optimal high-level descriptions of dynamical syste…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…
State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
In this paper, we use Time Scale Calculus (TSC) to formulate and solve pharmacokinetic models exploring multiple dose dynamics. TSC is a mathematical framework that allows the modeling of dynamical systems comprising continuous and discrete…
Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…
The new method is considered for identifying the perfect (optimal) scenario of climate engineering operations based on the optimal control theory. The application of this approach is demonstrated using zero-dimensional energy-balance…
Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups.…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…
Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general…
Stability landscapes are useful for understanding the properties of dynamical systems. These landscapes can be calculated from the system's dynamical equations using the physical concept of scalar potential. Unfortunately, for most…
Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
This paper presents a new predictive second order sliding controller (PSSC) formulation for setpoint tracking of constrained linear systems. The PSSC scheme is developed by combining the concepts of model predictive control (MPC) and second…
The widely-accepted intuition that the important properties of solids are determined by a few key variables underpins many methods in physics. Though this reductionist paradigm is applicable in many physical problems, its utility can be…
Dynamic surface control (DSC) method uses high gain filters to avoid the "explosion of complexity" issue inherent in backstepping based controller designs. As a result, the closed loop system and filter dynamics possess time scale…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…