This paper shows how to construct and implement explicit MPC feedback laws for systems with a large number of states. Specifically, the construction of critical regions of the explicit MPC solution is replaced by a two-step procedure. First, all optimal active sets are enumerated off-line and corresponding KKT matrices are pre-factored. Then, in the on-line step, the optimal control inputs are ...

For some optimal control problems with pathwise state constraints the standard versions of the necessary conditions of optimality are unable to provide useful information to select minimizers. There exist some literature on stronger forms of the maximum principle, the so-called nondegenerate necessary conditions, that can be informative for those problems. These conditions can be applied when c...

A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, suucient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L 1-norm. It is shown that these conditions are also necessary, provided that the ...

An optimal control problem is studied for a predator-prey reaction-diffusion system. A hunter population is introduced in the ecosystem and it is interpreted as a control variable. One finds necessary optimality conditions in order that, in the end of a given time interval, the total density of the two populations is maximal.

In this paper we consider a elastic vector-valued Allen-Cahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.

The paper revisits the issue of necessary optimality conditions for infinite-horizon optimal control problems. It is proved that the normal form maximum principle holds with an explicitly specified adjoint variable if an appropriate relation between the discount rate, the growth rate of the solution and the growth rate of the objective function is satisfied. The main novelty is that the result ...

We present a general method, based on conjugate duality, for solving a convex minimization problem without assuming unnecessary topological restrictions on the constraint set. It leads to dual equalities and characterizations of the minimizers without constraint qualification. As an example of application, the Monge-Kantorovich optimal transport problem is solved in great detail. In particular,...

We prove a continuous version of a relaxation theorem for the nonconvex Darboux problem x,T e F(t, z, x, x,,xz). This result allows us to use Warga's open mapping theorem for deriving necessary conditions in the form of a maximum principle for optimization problems with endpoint constraints. Neither constraint qualification nor regularity assumption is supposed.

Lagrange multiplier rules for abstract optimization problems with mixed smooth and convex terms in the cost, with smooth equality constrained and convex inequality constraints are presented. The typical case for the equality constraints that the theory is meant for is given by differential equations. Applications are given to L-minimum norm control problems, L∞norm minimization, and a class of ...

In this work, we continue our investigations of optimal control problems for the bidomain system. After the study of the monodomain approximation of the equations and a thorough stability and regularity analysis of weak solutions for the full bidomain equations, as contained in the previous papers [ Kunisch/Wagner 12 ] and [ Kunisch/Wagner 11 ] , we are now in position to analyze the related co...