Related papers: State-space models through the lens of ensemble co…
Recent State Space Models (SSMs) such as S4, S5, and Mamba have shown remarkable computational benefits in long-range temporal dependency modeling. However, in many sequence modeling problems, the underlying process is inherently modular…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
In this paper we give a new approach to introduce switching strategies in a special class of optimal multiprocesses. Defined as the set of partitions of the time interval, switching strategies become the character of a classical control.…
Ensemble control offers rich and diverse opportunities in mathematical systems theory. In this paper, we present a new paradigm of ensemble control, referred to as distributional control, for ensemble systems. We shift the focus from…
In this paper, we prove a Pontryagin Maximum Principle for constrained optimal control problems in the Wasserstein space of probability measures. The dynamics, is described by a transport equation with non-local velocities and is subject to…
We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type…
From a mathematical point of view self-organization can be described as patterns to which certain dynamical systems modeling social dynamics tend spontaneously to be attracted. In this paper we explore situations beyond self-organization,…
Despite the promising performance of state space models (SSMs) in long sequence modeling, limitations still exist. Advanced SSMs like S5 and S6 (Mamba) in addressing non-uniform sampling, their recursive structures impede efficient SSM…
We prove that Moore machines can be exactly realized as state-space models (SSMs), establishing a formal correspondence between symbolic automata and these continuous machine learning architectures. These Moore-SSMs preserve both the…
We present a Pontryagin maximum principle for discrete time optimal control problems with (a) pointwise constraints on the control actions and the states, (b) frequency constraints on the control and the state trajectories, and (c)…
We discuss a mathematical framework for analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in study of optimization for partial differential equations with some symmetry. It is shown that some…
Recurrent State-space models (RSSMs) are highly expressive models for learning patterns in time series data and system identification. However, these models assume that the dynamics are fixed and unchanging, which is rarely the case in…
We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as ${\Gamma}$-limits of optimal control problems subject to ODE…
The quantum control of spin-correlated radical pairs (SCRPs) holds promise for the targeted manipulation of magnetic field effects, with potential applications ranging from the design of noise-resilient quantum information processors to…
We establish an algorithm to learn feedback maps from data for a class of robust model predictive control (MPC) problems. The algorithm accounts for the approximation errors due to the learning directly at the synthesis stage, ensuring…
Our work is devoted to the study of Pontryagin's stochastic maximum principle for a mean-field optimal control problem under Peng's $G$-expectation. The dynamics of the controlled state process is given by a stochastic differential equation…
In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a…
This paper presents an indirect data-driven output feedback controller synthesis for nonlinear systems, leveraging Structured State-space Models (SSMs) as surrogate models. SSMs have emerged as a compelling alternative in modelling…
This article concerns an optimal crowd motion control problem in which the crowd features a structure given by its organization into N groups (participants) each one spatially confined in a set. The overall optimal control problem consists…
In this paper we study optimal advertising problems that models the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we…