Related papers: Data-Driven Stochastic Optimal Control in Reproduc…
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…
In this work, we address optimization problems where the objective function is a nonlinear function of an expected value, i.e., compositional stochastic {strongly convex programs}. We consider the case where the decision variable is not…
The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an…
This paper describes the optimal selection of a control policy to program the steady state of controlled nonlinear systems with hyperbolic fixed points. This work is motivated by the field of synthetic biology, in which saddle points are…
Model predictive control strategies require to solve in an sequential manner, many, possibly non-convex, optimization problems. In this work, we propose an interacting stochastic agent system to solve those problems. The agents evolve in…
We present a novel approach for the control of uncertain, linear time-invariant systems, which are perturbed by potentially unbounded, additive disturbances. We propose a \emph{doubly robust} data-driven state-feedback controller to ensure…
This paper builds on the theoretical foundations for dynamic mode decomposition (DMD) of control-affine dynamical systems by leveraging the theory of vector-valued reproducing kernel Hilbert spaces (RKHSs). Specifically, control Liouville…
We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…
This work reformulates language generation as a stochastic optimal control problem, providing a unified theoretical perspective to analyze autoregressive and diffusion models and explain their limitations (Efficiency-Fidelity Paradox,…
The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…
This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…
We a controlled system driven by a coupled forward-backward stochastic differential equation (FBSDE) with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential…
The optimal control of distribution networks often requires monitoring and communication infrastructure, either centralized or distributed. However, most of the current distribution systems lack this kind of infrastructure and rely on…
In this paper, we study optimal stochastic control problems for stochastic systems driven by non-Markov sub-diffusion $B_{L_t}$, which have the mixed features of deterministic and stochastic controls. Here $B_t$ is the standard Brownian…
Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can still be tackled through Riccati equations. Remarkably, we…
This paper mainly establishes the finite-horizon stochastic bounded real lemma, and then solves the $H_{\infty}$ control problem for discrete-time stochastic linear systems defined on the separable Hilbert spaces, thereby unifying the…
This paper addresses the problem of learning the optimal control policy for a nonlinear stochastic dynamical system with continuous state space, continuous action space and unknown dynamics. This class of problems are typically addressed in…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
We consider deterministic infinite horizon optimal control problems with nonnegative stage costs. We draw inspiration from learning model predictive control scheme designed for continuous dynamics and iterative tasks, and propose a rollout…
We propose a data-driven control method for systems with aleatoric uncertainty, for example, robot fleets with variations between agents. Our method leverages shared trajectory data to increase the robustness of the designed controller and…