Related papers: Transfer Operator Based Approach for Optimal Stabi…
The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…
Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
In this paper, we provide a systematic approach for the design of stabilizing feedback controllers for nonlinear control systems using the Koopman operator framework. The Koopman operator approach provides a linear representation for a…
The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…
There are multiple ways in which a stochastic system can be out of statistical equilibrium. It might be subject to time-varying forcing; or be in a transient phase on its way towards equilibrium; it might even be in equilibrium without us…
The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. Barriers to transport, which mitigate mixing, are currently the subject of intense…
We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to…
In this paper we investigate the action of self-consistent transfer operators (STOs) on Birkhoff cones and give sufficient conditions for stability of their fixed points. Our approach relies on the order preservation properties of STOs that…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
We propose a parameterization of a nonlinear dynamic controller based on the recurrent equilibrium network, a generalization of the recurrent neural network. We derive constraints on the parameterization under which the controller…
A novel adaptive control approach is proposed to solve the globally asymptotic state stabilization problem for uncertain pure-feedback nonlinear systems which can be transformed into the pseudo-affine form. The pseudo-affine pure-feedback…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM…
The aim of this paper is to present a new fast-convergent numerically stable space-time adaptive processing (STAP) algorithm derived using a novel technique of feedback orthogonalization. The main advantages of this approach lie in its…