Modelling, control and Pontryagin Maximum Principle for a two-body wave energy device

Pontryagin Maximum Principle for Optimal Control of

In this paper we investigate optimal control problems governed by variational inequalities. We present a method for deriving optimality conditions in the form of Pontryagin's principle. The main tools used are the Ekeland's variational principle combined with penalization and spike variation techniques. 1. Introduction. The purpose of this paper is to present a method for deriving a Pontryagin ...

The Pontryagin Maximum Principle

Theorem (PontryaginMaximum Principle). Suppose a final time T and controlstate pair (û, x̂) on [τ, T ] give the minimum in the problem above; assume that û is piecewise continuous. Then there exist a vector of Lagrange multipliers (λ0, λ) ∈ R × R with λ0 ≥ 0 and a piecewise smooth function p: [τ, T ] → R n such that the function ĥ(t) def =H(t, x̂(t), p(t), û(t)) is piecewise smooth, and one has ̇̂ ...

A Pontryagin Maximum Principle for Multi–Input Boolean Control Networks⋆

A Boolean network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean networks have been studied extensively as models for simple artificial neural networks. Recently, Boolean networks gained considerable interest as models for biological systems composed of elements that can be in one of two possible states. Examples include genetic regul...

The Maximum Principle of Pontryagin

Mean-Field Pontryagin Maximum Principle

We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as Γ-limits of optimal control problems subject to ODE constraints, modeling, for instance, external interventions on crowd dynamics. We obtain these first-order optimality conditions in the form of Hamiltonian flows in the...