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Hybrid optimal control problems are studied for a general class of hybrid systems where autonomous and controlled state jumps are allowed at the switching instants and in addition to terminal and running costs switching between discrete…
The paper is devoted to the optimal control of a system with two time-scales, in a regime when the limit equation is not of averaging type but, in the spirit of Wong-Zakai principle, it is a stochastic differential equation for the slow…
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the…
We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem…
This paper gives an introduction to \textit{Cognidynamics}, that is to the dynamics of cognitive systems driven by optimal objectives imposed over time when they interact either with a defined virtual or with a real-world environment. The…
We study the problem of generating control laws for systems with unknown dynamics. Our approach is to represent the controller and the value function with neural networks, and to train them using loss functions adapted from the…
This paper is concerned with a linear-quadratic (LQ, for short) optimal control problem for backward stochastic differential equations (BSDEs, for short), where the coefficients of the backward control system and the weighting matrices in…
This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…
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…
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in…
Optimal control problems can be solved via a one-shot (single) optimization or a sequence of optimization using dynamic programming (DP). However, the computation of their global optima often faces NP-hardness, and thus only locally optimal…
Moment optimization techniques have been recently proposed to solve globally various classes of optimal control problems. As those methods return truncated moment sequences of occupation measures, this paper explores a numeric method for…
Optimization of deep neural networks (DNNs) has been a driving force in the advancement of modern machine learning and artificial intelligence. With DNNs characterized by a prolonged sequence of nonlinear propagation, determining their…
This paper addresses the inverse optimal control problem of finding the state weighting function that leads to a quadratic value function when the cost on the input is fixed to be quadratic. The paper focuses on a class of infinite horizon…
This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed…
This paper presents a provably optimal, real-time capable energy management policy for race cars that provides simple human-driver-implementable control cues. Specifically, we first formulate the energy-constrained minimum-lap-time control…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
We develop a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time. We describe a discrete analogue of Jacobi's solution and…
In this paper, we consider the stochastic optimal control problem for a generalized Volterra control system. The corresponding state process is a kind of a generalized stochastic Volterra integral differential equations. We prove the…
We study the quadratic regulator problem on a finite time horizon for the wave equation with high internal damping controlled on the boundary by square integrable controls. The approach in this paper transforms the wave equation with high…