Second order conditions for bang-bang control problems
Second order conditions for periodic optimal control problems
Second order conditions in optimal control problems with mixed equality-type constraints on a variable time interval
Second order optimality conditions in the smooth case and applications in optimal control
The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions...
Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints
Second-order sufficient conditions for strong solutions to optimal control problems
In this article, given a reference feasible trajectory of an optimal control problem, we say that the quadratic growth property for bounded strong solutions holds if the cost function of the problem has a quadratic growth over the set of feasible trajectories with a bounded control and with a state variable sufficiently close to the reference state variable. Our sufficient second-order optimality conditions in Pontryagin form ensure this property and ensure a fortiori that the reference trajectory...
Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints
Second-order sufficient conditions of a bounded strong minimum are derived for optimal control problems of ordinary differential equations with initial-final state constraints of equality and inequality type and control constraints of inequality type. The conditions are stated in terms of quadratic forms associated with certain tuples of Lagrange multipliers. Under the assumption of linear independence of gradients of active control constraints they guarantee the bounded strong quadratic growth...
Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints
Second-order sufficient conditions of a bounded strong minimum are derived for optimal control problems of ordinary differential equations with initial-final state constraints of equality and inequality type and control constraints of inequality type. The conditions are stated in terms of quadratic forms associated with certain tuples of Lagrange multipliers. Under the assumption of linear independence of gradients of active control constraints they...
Singular controls and chattering arcs in optimal control problems arising in biomedicine
Singular extremals in multi-input time-optimal problems: a sufficient condition
Singular quadratic functionals and transformation of linear Hamiltonian systems
Solution for a classical problem in the calculus of variations via rationalized Haar functions
A numerical technique for solving the classical brachistochrone problem in the calculus of variations is presented. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Application of this method results in the transformation of differential and integral expressions into some algebraic equations to which Newton-type methods can be applied. The method is general, and yields accurate results.
Stability and sensitivity analysis for optimal control problems with control-state constraints [Book]
Sufficient optimality conditions for a bang--singular extremal in the minimum time problem
Switchings of optimal controls and the equation ,
Symmetries and integrals of motion in optimal control