Related papers: Data-Driven Stochastic Optimal Control using Linea…
This paper presents a novel data-driven stochastic MPC design for discrete-time nonlinear systems with additive disturbances by leveraging the Koopman operator and a distributionally robust optimization (DRO) framework. By lifting the…
In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…
In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In…
The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems…
Predictive control of power electronic systems always requires a suitable model of the plant. Using typical physics-based white box models, a trade-off between model complexity (i.e. accuracy) and computational burden has to be made. This…
This paper introduces a method for data-driven control based on the Koopman operator model predictive control. Unlike exiting approaches, the method does not require a dictionary and incorporates a nonlinear input transformation, thereby…
This survey collects, within a unified framework, various results (primarily by the authors themselves) on the use of Deterministic Infinite-Dimensional Optimal Control Theory to address applied economic models. The main aim is to…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
We present a data-driven method for spectral analysis of the Koopman operator based on direct construction of the pseudo-resolvent from time-series data. Finite-dimensional approximation of the Koopman operator, such as those obtained from…
Stochastic optimal control problems for Hamiltonian dynamics on graphs have wide-ranging applications in mechanics and quantum field theory, particularly in systems with graph-based structures. In this paper, we establish the existence and…
Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…
This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…
This study investigates a stochastic production planning problem with a running cost composed of quadratic production costs and inventory-dependent costs. The objective is to minimize the expected cost until production stops when inventory…
With the growing global emphasis on sustainability and the implementation of contemporary environmental policies, photovoltaic (PV) generation is playing an increasingly important role in modern power systems, while its intrinsic…
We study optimal control problems governed by abstract infinite dimensional stochastic differential equations using the dynamic programming approach. In the first part, we prove Lipschitz continuity, semiconcavity and semiconvexity of the…
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
Controlling robots with strongly nonlinear, high-dimensional dynamics remains challenging, as direct nonlinear optimization with safety constraints is often intractable in real time. The Koopman operator offers a way to represent nonlinear…
In a recent article, we presented a framework to control nonlinear partial differential equations (PDEs) by means of Koopman operator based reduced models and concepts from switched systems. The main idea was to transform a control system…