Error estimates for linear-quadratic elliptic control problems

The discretization of control functions by piecewise constant and piecewise linear functions is considered for linear-quadratic elliptic optimal control problems. Error estimates are derived for the optimal controls. Special emphasis is laid on the case of boundary control and convex polygonal domains

Error estimates for linear-quadratic control problems with control constraints

An abstract linear-quadratic optimal control problem is investigated with pointwise control constraints. This paper is concerned in discretization of the control by piecewise linear functions. Under the assumption that the optimal control and the optimal adjoint state is Lipschitz continuous and piecewise of class $C^2$ an approximation of order $h^{3/2}$ is proved for the solution of the control discretized problem with respect to the solution of the continuous one. Numerical tests are presented after the theoretical part

A computational method for simultaneous LQ optimal control design via piecewise constant output feedback

This paper is concerned with simultaneous linear-quadratic (LQ) optimal control design for a set of LTI systems via piecewise constant output feedback. First, the discrete-time simultaneous LQ optimal control design problem is reduced to solving a set of coupled matrix inequalities and an iterative LMI algorithm is presented to compute the feedback gain. Then, simultaneous stabilization and simultaneous LQ optimal control design of a set of LTI continuous-time systems are considered via periodic piecewise constant feedback gain. It is shown that the design of a periodic piecewise constant feedback gain simultaneously minimizing a set of given continuous-time performance indexes can be reduced to that of a constant feedback gain minimizing a set of equivalent discrete-time performance indexes. Explicit formulas for computing the equivalent discrete-time systems and performance indexes are derived. Examples are used to demonstrate the effectiveness of the proposed method.published_or_final_versio