External optimal control of fractional parabolic PDEs

Numerical Optimal Control of Parabolic Pdes Using Dasopt

This paper gives a preliminary description of DASOPT, a software system for the optimal control of processes described by time-dependent partial differential equations (PDEs). DASOPT combines the use of efficient numerical methods for solving differential-algebraic equations (DAEs) with a package for large-scale optimization based on sequential quadratic programming (SQP). DASOPT is intended fo...

State Trajectory Compression for Optimal Control with Parabolic PDEs

In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and Newton type methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. T...

Introduction to the Optimal Control of Systems with Distributed Parameters Iv. Optimality Condition in Optimal Control of Parabolic Pdes

Introduction to Optimal Control for Systems with Distributed Parameters. I. Frechet Differentiability in Optimal Control of Parabolic Pdes – Part 1

Today I start a series of lectures on the optimal control of systems with distributed parameters, that is to say, optimal control of systems described by partial differential equations. Optimal Control theory is the generalization of the classical calculus of variations where minimization of the functional is pursued in the class of non-smooth functions. In XX century optimal control theory mad...

Numerical Solution of Differential Riccati Equations Arising in Optimal Control for Parabolic PDEs

The numerical treatment of linear-quadratic regulator problems on finite time horizons for parabolic partial differential equations requires the solution of large-scale differential Riccati equations (DREs). Typically the coefficient matrices of the resulting DRE have a given structure (e.g. sparse, symmetric or low rank). Here we discuss numerical methods for solving DREs capable of exploiting...