L5-2_observability

# L5-2_observability - CDS 110b: Lecture 1-2 Observability...

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CDS 110b: Lecture 1-2 Observability and State Estimation Richard M. Murray 5 January 2007 Goals: Define observability and give conditions for checking observability for linear control systems Introduce the state estimation problem and Luenberger observers Provide examples of state estimation in the context of closed loop design Reading: Åström and Murray, Feedback Systems, Sections 7.1-7.3 (available online) Friedland, Chapters 7 and 8

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5 Jan 07 R. M. Murray, Caltech 2 Modern Control System Design CDS 110a - Control using state feedback: u = -K x + k r r Weeks 1-4: State Estimation Given process measurements, how do we determine the state for use in state feedback and/or receding horizon control? Theory is also useful for pure estimation problems (eg, sensor fusion) Requires that we start talking about noise in a more fundamental way Process ! Controller ! ! Estimator Trajectory Generation
5 Jan 07 R. M. Murray, Caltech 3 The State Estimation Problem Problem Setup Given a dynamical system with noise and uncertainty, estimate the state is called the estimate of x Remarks Several sources of uncertainty: noise, disturbances, process, initial condition Uncertainties are unknown, except through their effect on measured output First question: when is this even possible? Process ! Controller Estimator ! ! disturbances noise estimator expected value

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5 Jan 07 R. M. Murray, Caltech 4 Observability Defn A dynamical system of the form is observable if for any T > 0 it is possible to determine the state of the system x ( T
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## This note was uploaded on 09/09/2009 for the course EE 4233 taught by Professor Georgio during the Spring '09 term at Minnesota Colleges.

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L5-2_observability - CDS 110b: Lecture 1-2 Observability...

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