Related papers: Pontryagin Maximum Principle - a generalization
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory is applied to these systems and a hybrid version of Pontryagin's maximum principle is presented. This…
This work advances the maximum hands-off sparse control framework by developing a robust counterpart for constrained linear systems with parametric uncertainties. The resulting optimal control problem minimizes an $L^{0}$ objective subject…
Optimal control is ubiquitous in many fields of engineering. A common technique to find candidate solutions is via Pontryagin's maximum principle. An unfortunate aspect of this method is that the dimension of system doubles. When the system…
The paper addresses an optimal ensemble control problem for nonlocal continuity equations on the space of probability measures. We admit the general nonlinear cost functional, and an option to directly control the nonlocal terms of the…
We study an explicit mirror-descent method for finite-horizon deterministic optimal control problems. The method is motivated by Pontryagin's maximum principle: at each iteration, one solves the state and adjoint equations and updates the…
The paper presents new sufficient conditions for the property of strong bi-metric regularity of the optimality map associated with an optimal control problem which is affine with respect to the control variable ({\em affine problem}). The…
We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals,…
This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain…
This paper is dedicated to the elementary proof of Pontryagin's maximum principle for problems with free right end point. The proof for the standard problem is taken from the monography of Ioffe and Tichomirov. We assume piecewise…
Consider, on the one part, a general nonlinear finite-dimensional optimal control problem and assume that it has a unique solution whose state is denoted by $x^*$. On the other part, consider the sampled-data control version of it. Under…
We study time-optimal state-to-state control for two- and multi-qubit operations motivated by neutral-atom quantum processors within the Rydberg blockade regime. Block-diagonalization of the Hamiltonian simplifies the dynamics and enables…
This paper is concerned with devising the nonlinear optimal guidance for intercepting a stationary target with a fixed impact time. According to Pontryagin's Maximum Principle (PMP), some optimality conditions for the solutions of the…
In this paper we consider the problem of the optimal control of an ensemble of affine-control systems. After proving the well-posedness of the minimization problem under examination, we establish a $\Gamma$-convergence result that allows us…
In this paper, a model of a pair of Dubins vehicles is considered. The vehicles move from an initial position and orientation to final position and orientation. A long the motion, the two vehicles are not allowed to collide however the two…
We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value function estimate and identifies the part of the state space…
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…
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…
The turnpike principle is a fundamental concept in optimal control theory, stating that for a wide class of long-horizon optimal control problems, the optimal trajectory spends most of its time near a steady-state solution (the…
In this study, we address a control-constrained optimal control problem pertaining to the transformation of quantum states. Our objective is to navigate a quantum system from an initial state to a desired target state while adhering to the…
The Pontryagin-type maximum principle derived in [30] for optimal control problems involving sweeping processes is generalized to the case where the sweeping set C is nonsmooth and not necessarily bounded, namely, C is the intersection of a…