1,720,978 research outputs found
Optimal Contact Points for an Octopus Arm
No full textWe investigate the optimality of the configurations of a tentacle-like soft manipulator ensuring a planar force-closure condition. In particular, the optimization is performed with respect to both to the control strategies and to the set of contact points ensuring a planar, frictionless, first-order force-closure of the target. The case of an elliptic target object is discussed in detail, and numerical simulation are presented
A dynamic programming approach for controlled fractional SIS models
No full textWe investigate a susceptible-infected-susceptible (SIS) epidemic
model based on the Caputo–Fabrizio operator. After performing an
asymptotic analysis of the system, we study a related finite horizon optimal control problem with state constraints. We prove that the corresponding value function satisfies in the viscosity sense a dynamic programming
equation. We then turn to the asymptotic behavior of the value function,
proving its convergence to the solution of a stationary problem, as the
planning horizon tends to infinity. Finally, we present some numerical
simulations providing a qualitative description of the optimal dynamics
and the value functions involved
Reliable optimal controls for SEIR models in epidemiology
Full text linkWe present and compare two different optimal control approaches applied to
SEIR models in epidemiology, which allow us to obtain some policies for
controlling the spread of an epidemic. The first approach uses Dynamic
Programming to characterise the value function of the problem as the solution
of a partial differential equation, the Hamilton-Jacobi-Bellman equation, and
derive the optimal policy in feedback form. The second is based on Pontryagin's
maximum principle and directly gives open-loop controls, via the solution of an
optimality system of ordinary differential equations. This method, however, may
not converge to the optimal solution. We propose a combination of the two
methods in order to obtain high-quality and reliable solutions. Several
simulations are presented and discussed, also checking first and second order
necessary optimality conditions for the corresponding numerical solutions
Approximation of the value function for optimal control problems on stratified domains
Full text linkIn optimal control problems defined on stratified domains, the dynamics and
the running cost may have discontinuities on a finite union of submanifolds of
RN. In [8, 5], the corresponding value function is characterized as the unique
viscosity solution of a discontinuous Hamilton-Jacobi equation satisfying
additional viscosity conditions on the submanifolds. In this paper, we consider
a semi-Lagrangian approximation scheme for the previous problem. Relying on a
classical stability argument in viscosity solution theory, we prove the
convergence of the scheme to the value function. We also present HJSD, a free
software we developed for the numerical solution of control problems on
stratified domains in two and three dimensions, showing, in various examples,
the particular phenomena that can arise with respect to the classical
continuous framework
Computation of optimal trajectories for delay systems: An optimize-then-discretize strategy for general-purpose NLP solvers
No full textWe propose an “optimize-then-discretize” approach for the numerical solution of optimal control problems for systems with delays in both state and control. We first derive the optimality conditions and an explicit representation of the gradient of the cost functional. Then, we use explicit discretizations of the state/costate equations and employ general-purpose Non-Linear Programming (NLP) solvers, in particular Conjugate Gradient or Quasi-Newton schemes, to easily implement a descent method. Finally, we prove convergence of the algorithm to stationary points of the cost, and present some numerical simulations on model problems, including performance evaluation
A dynamic domain decomposition for the eikonal-diffusion equation
No full textWe propose a parallel algorithm for the numerical solution of the eikonal-diffusion equation, by means of a dynamic domain decomposition technique. The new method is an extension of the patchy domain decomposition method presented in [5] for first order Hamilton-Jacobi-Bellman equations. Using the connection with stochastic
optimal control theory, the semi-Lagrangian scheme underlying the original method is modified in order to deal with (possibly degenerate) diffusion. We show that under suitable relations between the discretization parameters and the diffusion coefficient, the parallel computation on the proposed dynamic decomposition can be faster than that on a static decomposition. Some numerical tests in dimension two are presented, in order to show the features of the proposed method
A mean field games model for finite mixtures of Bernoulli and categorical distributions
No full textFinite mixture models are an important tool in the statistical analysis of data, for example in data clustering. The optimal parameters of a mixture model are usually computed by maximizing the log-likelihood functional via the Expectation-Maximization algorithm. We propose an alternative approach based on the theory of Mean Field Games, a class of differential games with an infinite number of agents. We show that the solution of a finite state space multi-population Mean Field Games system characterizes the critical points of the log-likelihood functional for a Bernoulli mixture. The approach is then generalized to mixture models of categorical distributions. Hence, the Mean Field Games approach provides a method to compute the parameters of the mixture model, and we show its application to some standard examples in cluster analysis
A multi-phase transition model for dislocations with interfacial microstructure
No full textWe study, by means Gamma-convergence, the asymptotic behavior of a variational model for dislocations moving on a slip plane. The variational functional is a two-dimensional multi-phase transition-type energy given by a nonlocal term and a nonlinear potential which penalizes noninteger values for the components of the phase. In the limit we obtain an anisotropic sharp interfaces model. The relevant feature of this problem is that optimal sequences in general are not given by a one-dimensional profile, but they can create microstructure
A generalized Newton method for homogenization of hamilton-jacobi equations
Full text linkWe propose a new approach to the numerical solution of cell problems arising in the homogenization of Hamilton-Jacobi equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming from the discretization of the corresponding cell problems. We show that our method is able to solve efficiently cell problems in very general contexts, e.g., for first and second order scalar convex and nonconvex Hamiltonians, weakly coupled systems, dislocation dynamics, and mean field games, also in the case of more competing populations. A large collection of numerical tests in dimensions one and two shows the performance of the proposed method, both in terms of accuracy and computational time. © 2016 Society for Industrial and Applied Mathematics
- …
