Optimal Control: Novel Directions and Applications

1.Optimality conditions (in Pontryagin form).- 1.1 Introduction.- 1.2.- On first order necessary conditions under pure state constraints.- 1.3 Optimality conditions and local regularity of the value function for the optimal exit time problem.- 1.4 Relaxation in Optimal Control.- 1.5 An Introduction to Optimal Control Problems with Time Delays.- 1.6 Variational Integrators for the Optimal Control of Mechanical Systems.- 1.7 Pointwise necessary second order conditions.- 1.8 On the shooting method for control-affine problems.- 1.9 On second order conditions in the optimal control of Partial Differential Equations.- 2.Hamilton-Jacobi-Bellman equations.- 2.1 Introduction .- 2.2 Hamilton-Jacobi-Bellman approach for State-Constrained Optimal Control Problems, by Cristopher Hermosilla and Athena Picarelli.- 2.3 Hamilton-Jacobi-Bellman approach for State-Constrained Optimal Control Problems.- 2.4 High-order schemes for Hamilton-Jacobi-Bellman equations.- 2.5 Conclusion.- 2.6 Some Recent Applications of Hamilton-Jacobi-Bellman equations.- 2.7 A Brief Survey on Semi-Lagrangian Schemes for Mean Field Games, by Roberto Guglielmi and Francisco Silva.- 3. Direct Optimal Control and Model Predictive Control.- 3.1 Introduction.- 3.2 MPC Stability.- 3.3 Numerical Methods for MPC.- 3.4 Applications.