Related papers: State-space models through the lens of ensemble co…
Based on Pontryagin Maximum Principle (PMP), this paper established a generalized PMP aiming at non-feedback control system with stochastic initial conditions. We proved the conclusion and show its coming back to PMP when the randomness…
Many practical applications of control require that constraints on the inputs and states of the system be respected, while optimizing some performance criterion. In the presence of model uncertainties or disturbances, for many control…
This paper develops a comprehensive framework for optimal control of systems governed by fractional backward stochastic evolution equations (FBSEEs) in Hilbert spaces. We first establish a stochastic maximum principle (SMP) as a necessary…
We study a continuous time stochastic optimal control problem under partial observations that are available only at discrete time instants. This hybrid setting, with continuous dynamics and intermittent noisy measurements, arises in…
State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…
Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…
This work investigates the selection of high-quality pre-training data from massive corpora to enhance LMs' capabilities for downstream usage. We formulate data selection as a generalized Optimal Control problem, which can be solved…
In this paper, we consider a class of stochastic control problems for stochastic differential equations with random coefficients. The control domain need not to be convex but the control process is not allowed to enter in diffusion term.…
In this paper, we present a framework for solving continuous optimal control problems when the true system dynamics are approximated through an imperfect model. We derive a control strategy by applying Pontryagin's Minimum Principle to the…
We prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a stochastic partial differential equation driven by a finite dimensional Wiener process. The equation is formulated in a semi-abstract form…
State Space Models (SSMs) have emerged as a potent tool in sequence modeling tasks in recent years. These models approximate continuous systems using a set of basis functions and discretize them to handle input data, making them well-suited…
We provide an improvment of the maximum principle of Pon-tryagin of the optimal control problems, for a system governed by an ordinary differential equation, in presence of final constraints, in the setting of the piece-wise differentiable…
Reward fine-tuning of diffusion and flow models and sampling from tilted or Boltzmann distributions can both be formulated as stochastic optimal control (SOC) problems, where learning an optimal generative dynamics corresponds to optimizing…
State Space Models (SSMs) have emerged as a promising alternative to the popular transformer-based models and have been increasingly gaining attention. Compared to transformers, SSMs excel at tasks with sequential data or longer contexts,…
This paper studies multiobjective optimal control problems in the continuous-time framework when the space of states and the space of controls are infinite-dimensional and with lighter smoothness assumptions than the usual ones. The paper…
State Space Model (SSM) is a mathematical model used to describe and analyze the behavior of dynamic systems. This model has witnessed numerous applications in several fields, including control theory, signal processing, economics and…
State space models (SSMs) have gained attention by showing potential to outperform Transformers. However, previous studies have not sufficiently addressed the mechanisms underlying their high performance owing to a lack of theoretical…
This paper explores the controllability and state tracking of ensembles from the perspective of optimal transport theory. Ensembles, characterized as collections of systems evolving under the same dynamics but with varying initial…
Without exact knowledge of the true system dynamics, optimal control of non-linear continuous-time systems requires careful treatment under epistemic uncertainty. In this work, we translate a probabilistic interpretation of the Pontryagin…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…