Singular Linear-quadratic Control Problem Research Articles

A separation theorem for stochastic singular linear quadratic control problem with partial information

In this paper, we provide a separation theorem for the singular linear quadratic (LQ) control problem of Ito-type linear systems in the case of the state being partially observable. Above all, the Kalman-Bucy filtering of the dynamics is given by means of Girsanov transformation, by which the suboptimal feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent to the solvability of a generalized differential Riccati equation (GDRE).

All optimal controls for the singular linear-quadratic problem without stability; a new interpretation of the optimal cost

The singular linear-quadratic control problem without stability is solved by means of a generalized dual structure algorithm in order to generate all optimal inputs. Furthermore it is shown that the optimal cost can be interpreted as the smallest nonnegative rank-minimizing solution of a certain matrix inequality, the so-called dissipation inequality.

Transformational solution of singular linear-quadratic control problems

General linear-quadratic singular variational problems with free end-point are studied. An algorithm is presented, involving the execution of a sequence of coordinate basis transformations in the state and control space; the algorithm establishes whether a prescribed problem has a solution, determining the optimal control and performance index in case the solution exists.

Partially singular linear-quadratic control problems

Necessary and sufficient conditions are given for the nonnegativity of a partially singular quadratic functional associated with a linear system. The conditions parallel known conditions for the totally singular problem, and a known sufficiency condition for the partially singular problem can be derived from them.