Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements

The detection of optimal trajectories with multiple coast arcs represents a significant and challenging problem of practical relevance in space mission analysis. Two such types of optimal paths are analyzed in this study: (a) minimum-time low-thrust trajectories with eclipse intervals and (b) minimum-fuel finite-thrust paths. Modified equinoctial elements are used to describe the orbit dynamics. Problem (a) is formulated as a multiple-arc optimization problem, and additional, specific multipoint necessary conditions for optimality are derived. These yield the jump conditions for the costate variables at the transitions from light to shadow (and vice versa). A sequential solution methodology capable of enforcing all the multipoint conditions is proposed and successfully applied in an illustrative numerical example. Unlike several preceding researches, no regularization or averaging is required to make tractable and solve the problem. Moreover, this work revisits problem (b), formulated as a single-arc optimization problem, while emphasizing the substantial analytical differences between minimum-fuel paths and problem (a). This study also proves the existence and provides the derivation of the closed-form expressions for the costate variables (associated with equinoctial elements) along optimal coast arcs.

Optimal conditions for a control problem associated to an economical model

In this paper, we presents a growth model in infinite and continuous time, leads to a control optimal problem. Using the Pontryagin's principle we done necessary conditions for optimality. Also, weprove the existence, uniqueness and stability of the steady state for a differential equations system.

Maximum principle for a nonlinear size-structured model of fish and fry management

This paper investigates the maximum principle for a nonlinear size-structured model that describes the optimal management of the fish resources taking into account harvesting the fish and putting the fry. We establish the well-posedness of the state system by Banach fixed-point theorem. Necessary conditions for optimality are established via the normal cone technique and adjoint system. The existence of a unique optimal policy is proved via Ekeland's variational principle and fixed-point reasoning. Finally, some examples and numerical results demonstrate the effectiveness of the theoretical results in our paper.

Optimal open-loop strategies in a debt management problem

The paper studies optimal strategies for a borrower who needs to repay his debt, in an infinite time horizon. An instantaneous bankruptcy risk is present, which increases with the size of the debt. This induces a pool of risk-neutral lenders to charge a higher interest rate, to compensate for the possible loss of part of their investment. Solutions are interpreted as Stackelberg equilibria, where the borrower announces his repayment strategy [Formula: see text] at all future times, and lenders adjust the interest rate accordingly. This yields a highly non-standard problem of optimal control, where the instantaneous dynamics depend on the entire future evolution of the system. Our analysis shows the existence of optimal open-loop controls, deriving necessary conditions for optimality and characterizing possible asymptotic limits as [Formula: see text].

Infinite horizon optimal control of forward–backward stochastic system driven by Teugels martingales with Lévy processes

In this paper, we consider the infinite horizon nonlinear optimal control of forward–backward stochastic system governed by Teugels martingales associated with Lévy processes and one dimensional independent Brownian motion. Our aim is to establish the sufficient and necessary conditions for optimality of the above stochastic system under the convexity assumptions. Finally an application is given to illustrate the problem of optimal control of stochastic system.

A boundary control problem for the pure Cahn–Hilliard equation with dynamic boundary conditions

A boundary control problem for the pure Cahn–Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved.

Optimality, reduction and collective motion

The planar self-steering particle model of agents in a collective gives rise to dynamics on the N -fold direct product of SE (2), the rigid motion group in the plane. Assuming a connected, undirected graph of interaction between agents, we pose a family of symmetric optimal control problems with a coupling parameter capturing the strength of interactions. The Hamiltonian system associated with the necessary conditions for optimality is reducible to a Lie–Poisson dynamical system possessing interesting structure. In particular, the strong coupling limit reveals additional (hidden) symmetry, beyond the manifest one used in reduction: this enables explicit integration of the dynamics, and demonstrates the presence of a ‘master clock’ that governs all agents to steer identically. For finite coupling strength, we show that special solutions exist with steering controls proportional across the collective. These results suggest that optimality principles may provide a framework for understanding imitative behaviours observed in certain animal aggregations.