We show the existence of a local solution to a Hamilton–Jacobi–Bellman (HJB) PDE around a critical point where the corresponding Hamiltonian ODE is not hyperbolic, i.e., it has eigenvalues on the imaginary axis. Such problems arise in nonlinear regulation, disturbance rejection, gain scheduling, and linear parameter varying control. The proof is based on an extension of the center manifold theo...

When dealing with dynamic optimization problems, time consistency is a desirable property as it allows one to solve the problem efficiently through backward recursion. The mean-risk known be inconsistent when considered in its scalarized form. However, left original bi-objective form, turns out satisfy more general that seems better suited vector problem. In “Time Consistency of Mean-Risk Probl...

This paper deals with an endogenous growth model with vintage capital and, more precisely, with the AK model proposed in [R. Boucekkine, O. Licandro, L.A. Puch, F. del Rio, Vintage capital and the dynamics of the AK model, J. Econ. Theory 120 (1) (2005) 39–72]. In endogenous growth models the introduction of vintage capital allows to explain some growth facts but strongly increases the mathemat...

We consider the exploration/exploitation problem in reinforcement learning. For exploitation, it is well known that the Bellman equation connects the value at any time-step to the expected value at subsequent time-steps. In this paper we consider a similar uncertainty Bellman equation (UBE), which connects the uncertainty at any time-step to the expected uncertainties at subsequent time-steps, ...

In this paper, the dynamic-programming algorithm for continuous-speech recognition is modified in orderto obtain a top-N sentence-hypotheses Iist instead of the usual one sentence only. The theoretical basis of this extension is a generalization of Bellman's principle of optimality. Due to the computational complexity of the new algorithm, a sub-optimal variant is proposed, and experimental res...