Related papers: Ensemble Observability of Linear Systems
We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be…
We consider a class of uncertain linear time-invariant overparametrized systems affected by bounded disturbances, which are described by a known exosystem with unknown initial conditions. For such systems an exponentially stable extended…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
A new method involving particle diagrams is introduced and developed into a rigorous framework for carrying out embedded random matrix calculations. Using particle diagrams and the attendant methodology including loop counting it becomes…
Ensemble pruning, selecting a subset of individual learners from an original ensemble, alleviates the deficiencies of ensemble learning on the cost of time and space. Accuracy and diversity serve as two crucial factors while they usually…
We introduce a new multivariate statistical problem that we refer to as the Ensemble Inverse Problem (EIP). The aim of EIP is to invert for an ensemble that is distributed according to the pushforward of a prior under a forward process. In…
Reconstructing the density fluctuations in the early Universe that evolved into the distribution of galaxies we see today is a challenge of modern cosmology [ref.]. An accurate reconstruction would allow us to test cosmological models by…
Observables in random tensor theory are polynomials in the entries of a tensor of rank $d$ which are invariant under $U(N)^d$. It is notoriously difficult to evaluate the expectations of such polynomials, even in the Gaussian distribution.…
This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…
The optimal instant of observation of astrophysical phenomena for objects that vary on human time-sales is an important problem, as it bears on the cost-effective use of usually scarce observational facilities. In this paper we address this…
In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system.…
We investigate the task of controlling ensembles of initial and terminal state vectors of parameter-dependent linear systems by applying parameter-independent open loop controls. Necessary, as well as sufficient, conditions for ensemble…
Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow,…
Many navigation problems can be formulated as observer design on linear observed systems with a two-frame group structure, on which an invariant filter can be implemented with guaranteed consistency and stability. It's still unclear how…
Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time-ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are…
In this paper, we tackle the long-standing challenges of ensemble control analysis and design using a convex-geometric approach in a Hilbert space setting. Specifically, we formulate the control of linear ensemble systems as a convex…
We introduce in the paper a novel observability problem for a continuum ensemble of nonholonomic control systems with unknown population density. We address the problem by focussing on a prototype of such ensemble system, namely, the…
A novel approach to solve the problem of distributed state estimation of linear time-invariant systems is proposed in this paper. It relies on the application of parameter estimation-based observers, where the state observation task is…