Primal-dual interior point methods for PDE-constrained optimization

This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in $L^p$. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier $L^\infty$-setting is analyzed, but also a more involved $L^q$-analysis, $q

Efficient Robust Optimization for Robust Control with Constraints

This paper proposes an efficient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed polytopic constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques … Read more

Optimal Nodal Control of Networked Hyperbolic Systems: Evaluation of Derivatives

We consider a networked system defined on a graph where each edge corresponds to a quasilinear hyperbolic system with space dimension one. At the nodes, the system is governed by algebraic node conditions. The system is controlled at the nodes of the graph. Optimal control problems for systems of this type arise in the operation … Read more

A Remarkable Property of the Dynamic Optimization Extremals

A dynamic optimization continuous problem poses the question of what is the optimal magnitude of a choice variable, at each point of time, in a given interval. To tackle such problems, three major approaches are available: dynamic programming; the calculus of variations; and the powerful optimal control approach. At the core of optimal control theory … Read more

Sufficient Optimality in a Parabolic Control Problem

We define a class of parabolic problems with control and state constraints and identify a problem within this class which possesses a locally unique critical point satisfying the second order sufficient optimality conditions. In this solution inequality constraints on the control are strongly active. The second derivative of the Lagrangian is not globally coercive. This … Read more

Fast iterative solution of saddle point problems in optimal control based on wavelets

In this paper, wavelet techniques are employed for the fast numerical solution of a control problem governed by an elliptic boundary value problem with boundary control. A quadratic cost functional involving natural norms of the state and the control is to be minimized. Firstly the constraint, the elliptic boundary value problem, is formulated in an … Read more

Multiscale Concepts for Moving Horizon Optimization

In chemical engineering complex dynamic optimization problems formulated on moving horizons have to be solved on-line. In this work, we present a multiscale approach based on wavelets where a hierarchy of successively, adaptively refined problems are constructed.They are solved in the framework of nested iteration as long as the real-time restrictions are fulfilled. To avoid … Read more

Optimal Control of Distributed Proceses using Reduced Order Models

The open loop optimal control (dynamic optimization) of distributed parameter systems is considered here. These problems are usually solved by the Control Vector Parameterization (CVP) approach, which transforms the original dynamic optimization method into an outer nonlinear programming problem, which requires the solution of an inner initial value problem (IVP). The solution of this IVP … Read more