Explore the vast range of titles available.

Overhead cranes are widely used in industrial applications for material displacing. Many linear or non-linear control schemes have been proposed for overhead cranes and implemented on electronic systems, but energy efficiency of transportation has seldom been considered in motion planning. This study aims at finding an optimal solution of motion planning in terms of energy efficiency for overhead cranes. Using the optimal control method an optimal trajectory is obtained with less energy consumption than the compared trajectories and is also satisfying physical and practical constraints such as swing, acceleration and jerk. Besides the energy optimal model, the authors also propose two other models to optimise time efficiency and safety during transportation. The results obtained have been compared with some existing motion trajectories, and have been shown to be superior to these benchmarks in terms of energy efficiency, time efficiency and safety, respectively.

We analyze a dynamic stochastic general-equilibrium (DSGE) model with an externality—through climate change—from using fossil energy. Our central result is a simple formula for the marginal externality damage of emissions (or, equivalently, for the optimal carbon tax). This formula, which holds under quite plausible assumptions, reveals that the damage is proportional to current GDP, with the proportion depending only on three factors: (i) discounting, (ii) the expected damage elasticity (how many percent of the output flow is lost from an extra unit of carbon in the atmosphere), and (iii) the structure of carbon depreciation in the atmosphere. Thus, the stochastic values of future output, consumption, and the atmospheric CO 2 concentration, as well as the paths of technology (whether endogenous or exogenous) and population, and so on, all disappear from the formula. We find that the optimal tax should be a bit higher than the median, or most well-known, estimates in the literature. We also formulate a parsimonious yet comprehensive and easily solved model allowing us to compute the optimal and market paths for the use of different sources of energy and the corresponding climate change. We find coal—rather than oil—to be the main threat to economic welfare, largely due to its abundance. We also find that the costs of inaction are particularly sensitive to the assumptions regarding the substitutability of different energy sources and technological progress.

We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body

In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric subdifferential for compactly supported probability measures, and investigate the intrinsic linearised Cauchy problems associated to non-local continuity equations. In particular, we show that when the velocity perturbations belong to the tangent cone to the convexification of the set of admissible velocities, the solutions of these linearised problems are tangent to the solution set of the corresponding continuity inclusion. We then make use of these novel concepts to provide a synthetic and geometric proof of the celebrated Pontryagin Maximum Principle for an optimal control problem with inequality final-point constraints. In addition, we propose sufficient conditions ensuring the normality of the maximum principle.

We take a new look at the relation between the optimal transport problem and the Schrödinger bridge problem from a stochastic control perspective. Our aim is to highlight new connections between the two that are richer and deeper than those previously described in the literature. We begin with an elementary derivation of the Benamou–Brenier fluid dynamic version of the optimal transport problem and provide, in parallel, a new fluid dynamic version of the Schrödinger bridge problem. We observe that the latter establishes an important connection with optimal transport without zero-noise limits and solves a question posed by Eric Carlen in 2006. Indeed, the two variational problems differ by a Fisher information functional . We motivate and consider a generalization of optimal mass transport in the form of a (fluid dynamic) problem of optimal transport with prior . This can be seen as the zero-noise limit of Schrödinger bridges when the prior is any Markovian evolution. We finally specialize to the Gaussian case and derive an explicit computational theory based on matrix Riccati differential equations. A numerical example involving Brownian particles is also provided.

This paper focuses on the role of a government of a large population of interacting agents as a meanfield optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a Partial Differential Equation of continuity-type without diffusion, governing the dynamics of the probability distribution of the agent population. We derive existence of optimal controls in a measure-theoretical setting as natural limits of finite agent optimal controls without any assumption on the regularity of control competitors. In particular, we prove the consistency of mean-field optimal controls with corresponding underlying finite agent ones. The results follow from a Γ -convergence argument constructed over the mean-field limit, which stems from leveraging the superposition principle.

We analyze a class of nonlinear partial differential equations (PDEs) defined on

We study the incidence of nonlinear labor income taxes in an economy with a continuum of endogenous wages. We derive in closed form the effects of reforming nonlinearly an arbitrary tax system, by showing that this problem can be formalized as an integral equation. Our tax incidence formulas are valid both when the underlying assignment of skills to tasks is fixed or endogenous. We show qualitatively and quantitatively that contrary to conventional wisdom, if the tax system is initially suboptimal and progressive, the general-equilibrium “trickle-down” forces may raise the benefits of increasing the marginal tax rates on high incomes. We finally derive a parsimonious characterization of optimal taxes.

We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean-field games (MFGs). Our algorithm is geared toward high-dimensional instances of MFGs that are not approachable with existing solution methods. We achieve this in two steps. First, we take advantage of the underlying variational primal-dual structure that MFGs exhibit and phrase it as a convex–concave saddle-point problem. Second, we parameterize the value and density functions by two neural networks, respectively. By phrasing the problem in this manner, solving the MFG can be interpreted as a special case of training a generative adversarial network (GAN). We show the potential of our method on up to 100-dimensional MFG problems.

We design new navigation strategies for travel time optimization of microscopic self-propelled particles in complex and noisy environments. In contrast to strategies relying on the results of optimal control theory or machine learning approaches, implementation of these protocols can be done in a semi-autonomous fashion, as it does not require control over the microswimmer motion via external feedback loops. Although the strategies we propose rely on simple principles, they show arrival time statistics strikingly close to optimality, as well as performances that are robust to environmental changes and strong fluctuations. These features, as well as their applicability to more general optimization problems, make these strategies promising candidates for the realization of optimized semi-autonomous navigation.