BRIAN D . 0 . ANDEBSON JOHN B . XOORE Linear Optimal Control

Frequency Shaped Linear Optimal Control Wxth Transfer Function Riccati Equations*

Standard linear optimal control theory is generalized using a spectral factorization approach to elucidate some effects of frequency shaped performance indices. The theory discusses robustness results which parallel those of standard optimal control design. Matrix transfer function Riccati equations emerge as a conceptual tool associated with the frequency shaped optimal designs.

Optimal State Estimation in High Noise

The problem is examined of estimating the state of a linear dy namical system in the presence of high measurement noise. It is coneluded that optimal filter design maybe simplified to the extent that it need not depend on the solution of a matrix Riccati differential equation )butonly onthesolutionof amatrix linear differential equation. For a related problem, that of estimating a signal s(t) g...

Optimal Filtering INFORMATION AND SYSTEM SCIENCES SERIES

Linear-quadratic Optimal Control with Integral Quadratic Constraints

We derive closed-form solutions for the linear-quadratic (LQ) optimal control problem subject to integral quadratic constraints. The optimal control is a non-linear function of the current state and the initial state. Furthermore, the optimal control is easily calculated by solving an unconstrained LQ control problem together with an optimal parameter selection problem. Gradient formulae for th...

Chapter 4 Optimal Control Problems in Infinite Dimensional Function

In this chapter, we will consider optimal control problems in function space where we will restrict ourselves to state equations that are both linear in the state and linear in the control: We assume that E is a reflexive, separable Banach space with norm ‖ · ‖E and dual space E∗ and X is another separable Banach space with norm ‖ · ‖X and separable dual space X∗. We further suppose A : D(A) ⊆ ...