This paper is concerned with an optimal control problem governed by a semilinear, nonsmooth operator differential equation. The nonlinearity is locally Lipschitz-continuous and directionally differentiable, but not Gâteaux-differentiable. Two types of necessary optimality conditions are derived, the first one by means of regularization, the second one by using the directional differentiability ...

A class of nonlinear elliptic optimal control problems with mixed control-state constraints arising, e.g., in Lavrentiev-type regularized state constrained optimal control is considered. Based on its first order necessary optimality conditions, a semismooth Newton method is proposed and its fast local convergence in function space as well as a mesh-independence principle for appropriate discret...

The strengthened discrete-time optimal projection equations (SDOPE) are presented in a form based on the delta operator. This form unifies discrete-time and continuous-time results. Based on this unification, recently established results and algorithms for finite and infinite-horizon fixed-order LQG compensation of discrete-time systems are carried over to the continuous-time case. The results ...

We investigate local convergence of an SQP method for non-linear optimal control of weakly singular Hammerstein integral equations. Suucient conditions for local quadratic convergence of the method based are discussed.

A nonlinear feedback control law that achieves global asymptotic stabilization of a 2D thermal convection loop (widely known for its `Lorenz systema approximation) is presented. The loop consists of viscous Newtonian #uid contained in between two concentric cylinders standing in a vertical plane. The lower half of the loop is heated while the upper half is cooled, which makes the no-motion stea...

This paper studies optimal control problems for dynamical systems governed by neutral functional-differential inclusions that linearly depend on delayed velocity variables. Developing the method of discrete approximations, we derive new necessary optimality conditions for such problems in both EulerLagrange and Hamiltonian forms. The results obtained are expressed in terms of advanced generaliz...

The discrete-time optimal projection equations for systems with white parameters are strengthened. For the class of minimal ms (mean square) stabilizing compensators the strengthened discrete-time optimal projection equations are proved to be equivalent to first-order necessary optimality conditions for optimal reduced-order dynamic compensation of systems with white parameters. The conventiona...