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The famous proof of the Pontryagin maximum principle for control problems on a finite horizon bases on the needle variation technique, as well as the separability concept of cones created by disturbances of the trajectories. In this…
We consider the optimal control problem of minimizing some quadratic functional over all possible solutions of an internally controlled multi-dimensional heat equation with a periodic terminal state constraint. This problem has a unique…
In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric…
In this work, we introduce a novel strategy for tackling constrained optimization problems through a modified penalty method. Conventional penalty methods convert constrained problems into unconstrained ones by incorporating constraints…
The necessary conditions for an optimal control of a stochastic control problem with recursive utilities is investigated. The first order condition is the the well-known Pontryagin type maximum principle. When the optimal control satisfying…
We propose a novel reformulation of the stochastic optimal control problem as an approximate inference problem, demonstrating, that such a interpretation leads to new practical methods for the original problem. In particular we characterise…
The problem of resource allocation of nonlinear networked control systems is investigated, where, unlike the well discussed case of triggering for stability, the objective is optimal triggering. An approximate dynamic programming approach…
We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a…
Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum…
Recent work linking deep neural networks and dynamical systems opened up new avenues to analyze deep learning. In particular, it is observed that new insights can be obtained by recasting deep learning as an optimal control problem on…
This paper considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modelled by a nonlinear state-space model, but where the model parameters, state and…
Many engineering tasks require solving families of nonlinear constrained optimization problems, parametrized in setting-specific variables. This is computationally demanding, particularly, if solutions have to be computed across strongly…
This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling…
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
Synthesizing optimal controllers for dynamical systems often involves solving optimization problems with hard real-time constraints. These constraints determine the class of numerical methods that can be applied: computationally expensive…
We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for…
Physics-Informed Neural Networks (PINNs) have revolutionized solving differential equations by integrating physical laws into neural networks training. This paper explores PINNs for open-loop optimal control problems (OCPs) with incomplete…
Infinite-time nonlinear optimal regulation control is widely utilized in aerospace engineering as a systematic method for synthesizing stable controllers. However, conventional methods often rely on linearization hypothesis, while recent…