Related papers: A Bellman approach for regional optimal control pr…
We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study…
We consider the problem of computing safety regions, modeled as nonconvex backward reachable sets, for a nonlinear car collision avoidance model with time-dependent obstacles. The Hamilton-Jacobi-Bellman framework is used. A new formulation…
We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…
In this paper, we study a time-inconsistent stochastic optimal control problem with a recursive cost functional by a multi-person hierarchical differential game approach. An equilibrium strategy of this problem is constructed and a…
This work proposes an optimal safe controller minimizing an infinite horizon cost functional subject to control barrier functions (CBFs) safety conditions. The constrained optimal control problem is reformulated as a minimization problem of…
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
We consider a deterministic optimal control problem with a maximum running cost functional, in a finite horizon context, and propose deep neural network approximations for Bellman's dynamic programming principle, corresponding also to some…
This paper presents an inverse optimality method to solve the Hamilton-Jacobi-Bellman equation for a class of nonlinear problems for which the cost is quadratic and the dynamics are affine in the input. The method is inverse optimal because…
We introduce a modification to the patchy method of Navasca and Krener for solving the stationary Hamilton Jacobi Bellman equation. The numerical solution that we generate is a set of polynomials that approximate the optimal cost and…
This manuscript studies the Minkowski-Bellman equation, which is the Bellman equation arising from finite or infinite horizon optimal control of unconstrained linear discrete time systems with stage and terminal cost functions specified as…
This paper investigates the convergence properties of the upwind difference scheme for the Hamilton--Jacobi--Bellman (HJB) equation, a central partial differential equation in optimal control theory. First, assuming the existence of a…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
We consider an optimal control problem with ergodic (long term average) reward for a McKean-Vlasov dynamics, where the coefficients of a controlled stochastic differential equation depend on the marginal law of the solution. Starting from…
In this paper we consider the numerical approximation of infinite horizon problems via the dynamic programming approach. The value function of the problem solves a Hamilton-Jacobi-Bellman (HJB) equation that is approximated by a fully…
The minimization of energy-like cost functionals is addressed in the context of optimal control problems. For a general class of dynamical systems, with possibly unstable and nonlinear free dynamics, it is shown that a sequence of solutions…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
This work considers infinite-horizon optimal control of positive linear systems applied to the case of network routing problems. We demonstrate the equivalence between Stochastic Shortest Path (SSP) problems and optimal control of a certain…