Optimal control with state-space constraint I
SIAM Journal on Control and Optimization
Optimal control with state-space constraint II
SIAM Journal on Control and Optimization
The Bellman equation for minimizing the maximum cost
Non-Linear Analysis
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
Pursuit-evasion problems and viscosity solutions of Isaacs equations
SIAM Journal on Control and Optimization
Level sets of viscosity solutions: some applications to fronts and rendez-vous problems
SIAM Journal on Applied Mathematics
On Nonlinear Optimal Control Problems with State Constraints
SIAM Journal on Control and Optimization
A New Formulation of State Constraint Problems for First-Order PDEs
SIAM Journal on Control and Optimization
Pursuit Differential Games with State Constraints
SIAM Journal on Control and Optimization
Convergence of a first order scheme for a non-local Eikonal equation
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Ellipsoidal Techniques for Reachability Under State Constraints
SIAM Journal on Control and Optimization
Controllers for reachability specifications for hybrid systems
Automatica (Journal of IFAC)
On reachability and minimum cost optimal control
Automatica (Journal of IFAC)
A Discontinuous Galerkin Solver for Front Propagation
SIAM Journal on Scientific Computing
HJB approach for motion planning and reachabilty analysis
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Optimal Trajectories of Curvature Constrained Motion in the Hamilton---Jacobi Formulation
Journal of Scientific Computing
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We consider a target problem for a nonlinear system under state constraints. We give a new continuous level-set approach for characterizing the optimal times and the backward-reachability sets. This approach leads to a characterization via a Hamilton-Jacobi equation, without assuming any controllability assumption. We also treat the case of time-dependent state constraints, as well as a target problem for a two-player game with state constraints. Our method gives a good framework for numerical approximations, and some numerical illustrations are included in the paper.