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...

This paper presents a convergent scheme for Hamilton-Jacobi (HJ) equations posed on a junction. The general aim of the approach is to develop a framework using similar tools to the variational principle in traffic theory to model intersections taking in account many incoming and outgoing roads. Then a time-explicit numerical scheme is proposed. It is based on the very classical Godunov scheme. ...

In this paper the application of the comparison principle for Hamilton-Jacobi equations to a particular nonlinear control system is discussed. Two classes of approximations of the reachability sets for this system are constructed. Numerical examples of the reachability set approximations and the solutions to control synthesis problem are given to illustrate the proposed approach.

Sufficient and necessary global optimality conditions for nonlinear impulsive dynamic optimization problems with endpoint constraints are obtained. Proofs of these results are based on Hamilton-Jacobi canonical optimality theory. As consequence, a Maximum Principle reverse into sufficient optimality conditions is proposed.

We establish uniqueness for a class of first-order Hamilton–Jacobi equations with Hamiltonians that arise from the large deviations empirical measure and flux pair weakly interacting Markov jump processes. As corollary, we obtain such deviation principle in context processes time-periodic rates which period-length converges to 0.

We extend to incremental thermoelectroelasticity with biasing fields certain classical theorems, that have been stated and proved in linear thermopiezoelectricity referred to a natural configuration. A uniqueness theorem for the solutions to the initial boundary value problem, the generalized Hamilton principle and a theorem of reciprocity of work are deduced for incremental fields superposed o...

Abstract An established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential can be derived. However, there exist a variety models also need to take into account non-local effects capture microstructure evolution. In this case, the described partial equation. contribution, we present how Hamilton’s principle provid...