State-Space Systems Open-loop Estimators Closed-loop Estimators Observer Theory (no noise)-Luenberger IEEE TAC Vol 16, No. 6, pp. 596-602, December 1971 Estimation Theory(with noise)-Kalman Copyright [2001 by JOnathan dHow

State-Space Systems e Ful-state feedback Control How do we change the poles of the state-space system? Or, even if we can change the pole locations Where do we change the pole locations to? How well does this approach work?

This is a bit strange, because previously our figure of merit when comparing one state-space model to another(page 8-8)was whether they reproduced the same same transfer function Now we have two very different models that result in the same transfer function

MIMO Systems Singular Value Decomposition Multivariable Frequency Response Plots Copyright 2001 by Jonathan How

Reference input -II 16. 3117-23 On page 17-5, compensator implemented with a reference command y changing to feedback on e(t=r(t-y(t) rather than -y(t)

Weighting Matrix Selection a good rule of thumb when selecting the weighting matrices Rxx (or Ru and R uu is to normalize

Deterministic lOR Optimal control and the riccati equation · Lagrange multipliers The Hamiltonian matrix and the symmetric root locus Factoids: for symmtric R

Bounded gain There exist very easy ways of testing(analytically) whether S Gu)< SISO Bounded Gain Theorem: Gain of generic stable system

tate-Space Systems Closed-loop control using estimators and regulators Dynamics output feedback “ Back to reality' Copyright[2001by JOnathan dHow

Network Development of Network First measurements made in July 1992; just after start of International GPS Serviceigs). Since then measurements each year and often multiple campaigns per year. -The current network has over 1000 sites, many of them being recovery marks for the main