1,720,964 research outputs found
Optimal Motion of a Scallop: Some Case Studies
No full textIn this letter, we analyze two optimal control problems for the scallop: a two-link swimmer that is able to self-propel changing dynamics between two fluids regimes. We address and solve explicitly the minimum time problem and the minimum quadratic one, computing the cost needed to move the swimmer between two fixed positions using a periodic control. We focus on the case of only one switching in the dynamics and exploiting the structure of the equation of motion we are able to split the problem into simpler ones. We solve explicitly each sub-problem obtaining a discontinuous global solution. Then we approximate it through a suitable sequence of continuous functions
Multi-agent dynamic financial portfolio management: a differential game approach
No full textIn this paper we extend the classical Merton model to the case of several players and we propose a multi-agent Merton-type portfolio optimization model formulated by means of differential games. Each player is price-taker and invests on the market in order to maximize her inter-temporal utility. On the market there are p different assets, p-1 of them are risky and their price are generated by a geometric Brownian motion, while one is risk-free. We discuss the non-cooperative and cooperative case and show the existence of a closed-form solution when the class of CRRA utility functions is assumed for both infinite and finite time horizon. We perform a numerical study which illustrates that a cooperative strategy is preferable to a non-cooperative one as it allows for the adoption of optimal strategies from both players. Non-cooperation, instead, leads to sub-optimal solutions
Distributed Dynamic Pricing of Multiscale Transportation Networks
Full text linkWe study transportation networks controlled by dynamic feedback tolls. We focus on a multiscale model whereby the dynamics of the traffic flows are intertwined with those of the routing choices.The latter are influenced by the current traffic state of the network as well as by dynamic tolls controlled in feedback by the system planner. We prove that a class of decentralized monotone flow-dependent tolls allow for globally stabilizing the transportation network around a generalized Wardrop equilibrium. In particular, our results imply that using decentralized marginal cost tolls, stability of the dynamic transportation network is guaranteed around the social optimum traffic assignment.This is particularly remarkable as such dynamic feedback tolls can be computed in a fully local way without the need for any global information about the network structure, its state, or the exogenous network loads. Through numerical simulations, we also compare the performance of such decentralized dynamic feedback marginal cost tolls with constant off-line (and centrally) optimized tolls both in the asymptotic and in the transient regime and we investigate their robustness to information delays
Stability and optimality of multi-scale transportation networks with distributed dynamic tolls
Full text linkWe study transportation networks controlled by dynamical feedback tolls. We consider a multiscale transportation network model whereby the dynamics of the traffic flows are intertwined with those of the drivers' route choices. The latter are influenced by the congestion status on the whole network as well as dynamic tolls set by the system operator. Our main result shows that a broad class of decentralized congestion-dependent tolls globally stabilise the transportation network around a Wardrop equilibrium. Moreover, using dynamic marginal cost tolls, stability of the transportation network can be guaranteed around the social optimum traffic assignment. This is particularly remarkable as the considered decentralized feedback toll policies do not require any global information about the network structure or the exogenous traffic load on the network or state and can be computed in a fully local way. We also evaluate the performance of these feedback toll policies both in the asymptotic and during the transient regime, through numerical simulations
Swimming by switching
Full text linkIn this paper we investigate different strategies to overcome the scallop theorem. We will show how to obtain a net motion exploiting the fluid’s type change during a periodic deformation. We are interested in two different models: in the first one that change is linked to the magnitude of the opening and closing velocity. Instead, in the second one it is related to the sign of the above velocity. An interesting feature of the latter model is the introduction of a delay-switching rule through a thermostat. We remark that the latter is fundamental in order to get both forward and backward motion
Dangerous tangents: an application of Γ-convergence to the control of dynamical systems
Full text linkInspired by the classical riot model proposed by Granovetter in
1978, we consider a parametric stochastic dynamical system describing
the collective behavior of a large population of interacting agents.
By controlling a parameter, a policy maker aims at maximizing her
own utility which, in turn, depends on the steady state of the system.
We show that this economically sensible optimization is ill-posed and
illustrate a novel way to tackle this practical and formal issue. Our
approach is based on Gamma-convergence of a sequence of mean-regularized
instances of the original problem. The corresponding maximizers converge
towards a unique value which intuitively is the solution of the
original ill-posed problem. Notably, to the best of our knowledge, this
is one of the first applications of Gamma-convergence in economics
Transboundary Pollution Control under Evolving Social Norms: a Mean-Field Approach
No full textWe analyze a dynamic game of transboundary pollution control under endogenously evolving social norms over a finite time horizon. Each player chooses their emission level in order to minimize the social cost of mitigation, which partly depends on the lack of conformity to the social norm establishing the pollution standards at the local level. We show that social norms per se are unable to favor pollution reductions, but if combined with some public reclamation effort, they become very effective in improving environmental outcomes. Indeed, provided that some minimal public reclamation takes place, social norms promote a reduction in the average of the expected value of the local pollution stocks across locations, both in the case in which players rely on an open loop and a closed loop strategy. Moreover, by explicitly characterizing the equilibrium outcome, we formally confirm the reliability of the mean-field approximation of the finite-population dynamics, despite such an approximation introduces some distortion regarding the difference between open and closed loop strategies. We also show that our results are robust to the introduction of individual abatement efforts and heterogeneity across players
A Differential Game with Exit Costs
Full text linkWe study a differential game where two players separately control their own dynamics, pay a running cost, and moreover pay an exit cost (quitting the game) when they leave a fixed domain. In particular, each player has its own domain and the exit cost consists of three different exit costs, depending whether either the first player only leaves its domain, or the second player only leaves its domain, or they both simultaneously leave their own domain. We prove that, under suitable hypotheses, the lower and upper values are continuous and are, respectively, the unique viscosity solution of a suitable Dirichlet problem for a Hamilton-Jacobi-Isaacs equation. The continuity of the values relies on the existence of suitable non-anticipating strategies respecting the domain constraint. This problem is also treated in this work
Sustainable Management of Tourist Flow Networks: a Mean Field Model
Full text linkIn this article, we propose a mean field game approach {for modeling the flows of excursionists} within a network of tourist attractions.
We prove the existence of an equilibrium within the network using a balance ordinary differential equation together with optimality conditions in terms of the value function.
We also propose a bi-level formulation of the problem where we aim at achieving a sustainable-oriented control strategy in the upper level
and at maximizing excursionists' satisfaction in the lower level.
Our proposed model may provide an effective management tool for local authorities who deal with the challenging problem of finding an optimal control policy to the often conflicting objectives of ensuring the maximum excursionists' satisfaction while pursuing the highest sustainability benefits
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