Abstract
The time evolution of a system with nondeterministic behavior can be described by a differential equation with “random” inputs, such as
If the values of the disturbances u i at different times are arbitrarily large and essentially uncorrelated, then one can model them as white noise and write (1.1) as a stochastic equation:
where the w i are components of an m-dimensional standard Brownian motion [4]. On the other hand, if some constraints on the u i are a-priori known, say
then (1.2) is no longer appropriate. In this case, one can still define some probability distribution on the set of inputs u which satisfy (1.3); however, no simple or canonical way for doing so is available. The choice of any particular probability distribution thus requires considerable additional information about the system to be modelled.
Keywords
- Maximum Likelihood Estimator
- Differential Inclusion
- Admissible Control
- Stochastic Equation
- Constant Rank
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
J.P.Aubin and A.Cellina, “Differential Inclusions”, Springer-Verlag, Berlin, 1984.
A. Bressan, The most likely path of a differential inclusion, J.Differential Equations, to appear.
L.Cesari, “Optimization -Theory and Applications”, Springer-Verlag, New York, 1983.
W.H.Fleming and R.W.Rishel, “Deterministic and Stochastic Optimal Control”, Springer-Verlag, Berlin, 1975.
H.J.Kushner, Nonlinear filtering: the exact dynamical equations satisfied by the conditional mode, IEEE Trans. Automatic Control Vol. AC-12, 1967.
R.E.Mortensen, Maximum-likelihood recursive nonlinear filtering, J. Optim. Theory and Appl. 2, (1968), 386–394.
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© 1991 Springer Science+Business Media New York
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Bressan, A. (1991). Nonprobabilistic Filtering. In: New Trends in Systems Theory. Progress in Systems and Control Theory, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0439-8_19
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DOI: https://doi.org/10.1007/978-1-4612-0439-8_19
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6760-7
Online ISBN: 978-1-4612-0439-8
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