Stochastic models, estimation and control. Volume 3 by Peter S. Maybeck PDF

By Peter S. Maybeck

ISBN-10: 0080960030

ISBN-13: 9780080960036

ISBN-10: 0124807038

ISBN-13: 9780124807037

This quantity builds upon the rules set in Volumes 1 and a couple of. bankruptcy thirteen introduces the elemental suggestions of stochastic keep an eye on and dynamic programming because the basic technique of synthesizing optimum stochastic regulate legislation.

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Sample text

Moreover, one would probably be less inclined to allow as much overall control activity as when the aircraft is very low, so the U(rJentries might be increased at this time too. 3 could be used for each sample period on states and controls. However, a “tuning” procedure on X ( r i ) and U ( t j )for all ti and on X, is usually required, in analogy to tuning of Q d ( t i and ) R(t,) for all ij and of Po in a Kalman filter. This “duality” relationship will be discussed to a greater degree in Chapter 14.

The estimate %(ti') from a Kalman filter that has processed the measurement history Z i , as seen in Eq. (13-22). The same feedback gains G,*(ti) are valid for all three cases, and these gains are independent of the stochastic nature of any problem. (ti'). We have achieved a linear memoryless feedback control law that does not vary from case to case. That the optimal stochastic controller in this case is equivalent to the associated optimal deterministic controller function, but with the state replaced by the conditional mean of the state given the observed measurements, is often described by saying the LQG optimal controller has the certainty equivalence property.

Vertical component of lift 4 I Lift vector of lift FIG. 5 37 OPTIMAL STOCHASTIC CONTROL Threshold Landing site FIG. 13 Single-switch trajectory for deterministic problem One can envision a deterministic control problem of rolling to the right, and then determining when to roll left to reach the landing site exactly with a single switch. This is portrayed in Fig. 13, as seen from above. One might also consider using multiple switch points, but rolling the vehicle consumes attitude control rocket propellant, so a minimum number of rollovers (one for the deterministic case) is desirable.

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Stochastic models, estimation and control. Volume 3 by Peter S. Maybeck

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