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This paper presents a new formulation for model-free robust optimal regulation of continuous-time nonlinear systems. The proposed reinforcement learning based approach, referred to as incremental adaptive dynamic programming (IADP),…
Advances in the variational approach to the $n$-body problem have led to significant progress in celestial mechanics, uncovering new types of possible orbits. In this paper, critical points of the Lagrangian action associated with the…
The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…
This paper introduces an advanced Lyapunov stability analysis for an attitude observer that has been developed on the special orthogonal group. In particular, when the attitude observer is constructed based on multiple direction…
We develop the theory of discrete time Lagrangian mechanics on Lie groups, originated in the work of Veselov and Moser, and the theory of Lagrangian reduction in the discrete time setting. The results thus obtained are applied to the…
The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift…
We present a relaxation-based method to bound expectation values on the steady state of dissipative many-body quantum systems described by master equations of the Lindblad form. Instead of targeting to represent the entire state, we promote…
Rayleigh-Taylor (RT) instability commonly arises in compressible systems with time-dependent acceleration in practical applications. To capture the complex dynamics of such systems, a two-component discrete Boltzmann method is developed to…
It is quite often claimed, and correctly so, that linear methods cannot achieve global stability results for attitude control, and conversely that nonlinear control is essential in order to achieve (almost) globally stable tracking of…
We present a numerical method to approximate the long-time asymptotic solution $\rho_\infty(t)$ to the Lindblad master equation for an open quantum system under the influence of an external drive. The proposed scheme uses perturbation…
The problem of sampling according to the probability distribution minimizing a given free energy, using interacting particles unadjusted kinetic Langevin Monte Carlo, is addressed. In this setting, three sources of error arise, related to…
A Lagrangian formalism is developed for a general nondissipative quasiperiodic nonlinear wave with trapped particles in collisionless plasma. The adiabatic time-averaged Lagrangian density $\mcc{L}$ is expressed in terms of the…
This paper presents a novel online capable method for simultaneous estimation of human motion in terms of segment orientations and positions along with sensor-to-segment calibration parameters from inertial sensors attached to the body. In…
A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian…
The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional.…
Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a…
We study the long-time behavior of solutions to a measure-valued selection-mutation model that we formulated in \cite{CLEVACK}. We establish permanence results for the full model, and we study the limiting behavior even when there is more…
Stochastic filters for on-line state estimation are a core technology for autonomous systems. The performance of such filters is one of the key limiting factors to a system's capability. Both asymptotic behavior (e.g.,~for regular…
A dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \to \varnothing$ with a given rate when they are within a finite radius of interaction. The system is described in terms of the…
This paper considers the problem of simultaneous estimation of the attitude, position and linear velocity for vehicles navigating in a three-dimensional space. We propose two types of hybrid nonlinear observers using continuous angular…