In this article we consider an optimal control problem of a semi-linear elliptic equation, with bound constraints on the control. Our aim is to characterize local quadratic growth for cost function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper J"> <mml:semantics> <mml:mi>J</mml:mi> <mml:annotation encoding="application/x-tex">J</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in sense strong solutions. This...

In this paper we provide a second order analysis for strong solutions in the optimal control of parabolic equations. We consider first case box constraints on general setting and then, quadratic Hamiltonian, also impose final integral state. For problem, rather framework, prove characterization growth property sense, i.e., admissible controls whose associated states are uniformly near to state nominal control. Assuming Hamiltonian constrained case, sufficient optimality condition...

In this paper, we investigate the problem of species separation in minimal time. Droop model is considered to describe evolution two distinct populations microorganisms that are competition for same resource a photobioreactor. We focus on an optimal control (OCP) subject five-dimensional controlled system which represents dilution rate chemostat. The objective select desired minimal-time and synthesize feedback control. This very challenging issue, since dealing with ten-dimensional...

In this work, we study a minimal time control problem for perfectly mixed continuous culture with n ≥ 2 species and one limiting resource. The model that consider includes mutation factor the microorganisms. Our aim is to provide optimal feedback laws optimise selection of interest. Thanks Pontryagin's Principle, derive optimality conditions on controls introduce sub-optimal law based most rapid approach singular arc depends initial condition. Using adaptive dynamics theory, also simplified...

We consider the problem of minimizing a functional (such as area, perimeter and surface) within class convex bodies whose support functions are trigonometric polynomials. The convexity constraint is transformed via Fejér–Riesz theorem on positive polynomials into semidefinite programming problem. Several problems such minimization area in constant-width planar bodies, rotors space revolution revisited. approach seems promising to investigate more difficult optimization three-dimensional bodies.

Summary In this work, we provide a reformulation of the minimal time crisis problem associated with constraint set as free terminal control problem. The proof requires existence nonempty viability kernel that is reachable from state space. addition, suppose uniform lower bound between two consecutive crossing times set. Thanks to result, compute an optimal synthesis for governed by prey‐predator dynamics, controlled mortality on predators. Finally, compare spent in trajectories minimum reach...

We study the minimum time control problem of a series two interconnected chemostats under input constraint $u_{2}\leq u_{1}$, where $u_{i}$ are respective dilution rates in tanks. This brings controllability issues optimal strategies. overcome this difficulty by splitting state domain into subdomains, one with no lack target, and its complement any trajectory satisfies $u_{1}=u_{2}$. explicitly compute complete synthesis that depends on position target respect to semipermeable curve passes...

This paper studies a periodic optimal control problem governed by one-dimensional system, linear with respect to the $ u $, under an integral constraint on $. We give conditions for which value of cost function at steady state constant \bar can be improved considering average equal leads so-called 'over-yielding' met in several applications. With use Pontryagin Maximum Principle, we provide synthesis strategies constraint. The results are illustrated single population model order study...

This paper studies an optimal control problem related to membrane filtration processes. A simple mathematical model of fouling is used capture the dynamic behavior process which consists in attachment matter onto during period and detachment cleaning period. We consider maximization net production a system (i.e. filtrate) over finite time horizon, where variable sequence filtration/backwashing cycles operation process. Based on Pontryagin Maximum Principle, we characterize strategy show that...

In this work, we study the coupling of a culture microalgae limited by light and an anaerobic digester in two-tank bioreactor. The model for reactor combines periodic day-night classical chemostat digester. We first prove existence attraction solutions problem 1 day period. Then, optimal control optimizing production methane during certain timeframe, on system being dilution rate (the input flow digester). apply Pontryagin's Maximum Principle order to characterize controls, including...