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We discuss contact geometry naturally related with optimal control problems (and Pontryagin Maximum Principle). We explore and expand the observations of [Ohsawa, 2015], providing simple and elegant characterizations of normal and abnormal…
The mathematical modeling of numerous real-world applications results in hierarchical optimization problems with two decision makers where at least one of them has to solve an optimal control problem of ordinary or partial differential…
In this paper we study optimal control problems with either fractional or regional fractional $p$-Laplace equation, of order $s$ and $p\in [2,\infty)$, as constraints over a bounded open set with Lipschitz continuous boundary. The control,…
We design and compute a class of optimal control problems for reaction-diffusion systems. They form mean field control problems related to multi-density reaction-diffusion systems. To solve proposed optimal control problems numerically, we…
Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
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…
In this paper we study an optimal control problem with nonsmooth mixed state and control constraints. In most of the existing results, the necessary optimality condition for optimal control problems with mixed state and control constraints…
In this paper, we present a framework for solving continuous optimal control problems when the true system dynamics are approximated through an imperfect model. We derive a control strategy by applying Pontryagin's Minimum Principle to the…
At the core of optimal control theory is the Pontryagin maximum principle - the celebrated first order necessary optimality condition - whose solutions are called extremals and which are obtained through a function called Hamiltonian, akin…
This work studies optimal control problems of systems with uncertain, probabilistically distributed parameters to optimize average performance. Known as Riemann-Stieltjes, average, or ensemble optimal control, this kind of problem is…
This paper consists of a detailed and novel stochastic optimal control analysis of a coupled non-linear dynamical system. The state equations are modeled as additional food provided prey-predator system with Holling Type-III functional…
This paper concerns an optimal control problem $(P)$ related to a nonlinear Fokker-Planck equation. The problem is deeply related to a stochastic optimal control problem $(P_S)$ for a McKean-Vlasov equation. The existence of an optimal…
We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain…
Given a sequential learning algorithm and a target model, sequential machine teaching aims to find the shortest training sequence to drive the learning algorithm to the target model. We present the first principled way to find such shortest…
While the Pontryagin Maximum Principle can be used to calculate candidate extremals for optimal orbital transfer problems, these candidates cannot be guaranteed to be at least locally optimal unless sufficient optimality conditions are…
In this paper, we consider the optimal control problem for a class of evolution inclusions with Volterra type operators, which can be history-dependent. We establish the existence of a solution to the stated optimal control problem under…
We provide an improvement of the maximum principle of Pontryagin of the Optimal Control problems. We establish differentiability properties of the value function of problems of Optimal Control with assumptions as low as possible. Notably,…
Necessary optimality conditions in the form of the maximum principle for control problems with infinite time horizon are considered. Both finite and infinite values of objective functional are allowed since the concept of overtaking or…