Platzman, L. K. | Search NASA

NASA NTRS1976

A linear-quadratic-Gaussian control problem with innovations-feedthrough solution

The structure of the separation-theorem solution to the standard linear-quadratic-Gaussian (LQG) control problem does not involve direct output feedback as a consequence of the form of the performance index. It is shown that the performance index may be generalized in a natural fashion so that the optimal control law involves output feedback or, equivalently, innovations feedthrough (IF). Applications where this formulation may be advantageous are indicated through an examination of properties of the IF control law.

Platzman, L. K.↗

NASA NTRS1972

Computation of optimal output-feedback compensators for linear time-invariant systems

The control of linear time-invariant systems with respect to a quadratic performance criterion was considered, subject to the constraint that the control vector be a constant linear transformation of the output vector. The optimal feedback matrix, f*, was selected to optimize the expected performance, given the covariance of the initial state. It is first shown that the expected performance criterion can be expressed as the ratio of two multinomials in the element of f. This expression provides the basis for a feasible method of determining f* in the case of single-input single-output systems. A number of iterative algorithms are then proposed for the calculation of f* for multiple input-output systems. For two of these, monotone convergence is proved, but they involve the solution of nonlinear matrix equations at each iteration. Another is proposed involving the solution of Lyapunov equations at each iteration, and the gradual increase of the magnitude of a penalty function. Experience with this algorithm will be needed to determine whether or not it does, indeed, possess desirable convergence properties, and whether it can be used to determine the globally optimal f*.

Platzman, L. K.↗