Related papers: Lyapunov-based Low-thrust Optimal Orbit Transfer: …
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
Optimal Transport is a popular distance metric for measuring similarity between distributions. Exact algorithms for computing Optimal Transport can be slow, which has motivated the development of approximate numerical solvers (e.g. Sinkhorn…
We study the optimal transport problem for pairs of stationary finite-state Markov chains, with an emphasis on the computation of optimal transition couplings. Transition couplings are a constrained family of transport plans that capture…
We introduce a new algorithm to solve constrained nonlinear optimal control problem, with an emphasis on low-thrust trajectory in highly nonlinear dynamics. The algorithm, dubbed Pontryagin-Bellman Differential Dynamic Programming (PDDP),…
Iterative gradient-based optimization algorithms are widely used to solve difficult or large-scale optimization problems. There are many algorithms to choose from, such as gradient descent and its accelerated variants such as Polyak's Heavy…
The feedback linearization method is further developed for the controller design on general nonlinear systems. Through the Lyapunov stability theory, the intractable nonlinear implicit algebraic control equations are effectively solved, and…
We study optimal transportation of measures on compact manifolds for costs defined from convex Lagrangians. We prove that optimal transportation can be interpolated by measured Lipschitz laminations, or geometric currents. The methods are…
Optimal transport (OT) is a central framework for modeling distribution shifts. Because OT compares distributions directly in input space, a well-designed ground metric between observations is essential to ensure that the optimizer does not…
We leverage second-order information for tuning of inverse optimal controllers for a class of discrete-time nonlinear input-affine systems. For this, we select the input penalty matrix, representing a tuning knob, to yield the Hessian of…
The orbit tracking of free-evolutionary target system in closed quantum systems is studied in this paper. Based on the concept of system control theory, the unitary transformation is applied to change the time-dependent target function into…
Future multi-spacecraft missions require robust autonomous trajectory optimization capabilities to ensure safe and efficient rendezvous operations. This capability hinges on solving non-convex optimal control problems in real-time, although…
Dynamical structures in the circular restricted three-body problem (CR3BP) are fundamental for designing low-energy transfers, as they aid in analyzing phase space transport and designing desirable trajectories. One of these dynamical…
This paper introduces a new approach to solving the thrust allocation problem using the maneuvering problem in the maritime domain for fully actuated vessels. The method uses a control Lyapunov function to create a nonlinear reference…
Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…
This article presents an adaptive nonlinear delayed feedback control scheme for stabilizing the unstable periodic orbit of unknown fractional-order chaotic systems. The proposed control framework uses the Lyapunov approach and sliding mode…
This paper presents a new method for synthesizing stochastic control Lyapunov functions for a class of nonlinear stochastic control systems. The technique relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman partial…
We propose a new method for the approximate solution of the Lyapunov equation with rank-$1$ right-hand side, which is based on extended rational Krylov subspace approximation with adaptively computed shifts. The shift selection is obtained…
We present a computational approach for the design of continuous low thrust transfers around an asteroid. These transfers are computed through the use of a reachability set generated on a lower dimensional Poincar\'e surface. Complex, long…
A number of applications to interplanetary trajectories have been recently proposed based on deep networks. These approaches often rely on the availability of a large number of optimal trajectories to learn from. In this paper we introduce…
Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the…