Authors:
Yu-Chi Ho,
Jonathan T. Lee,
Volume: 1, Page 103 Paper number 1700
Abstract:
Finding a function that minimizes a functional is a common problem,
e.g., determining the feedback control law for a system. However, it
remains to be a challenge due to the large and structureless search
space. In this paper, we present a search algorithm, granular optimization,
to deal with this type of problems under some mild constraints. The
algorithm is tested on two different problems. One of them is the well-known
Witsenhausen counterexample. On the counterexample, the result from
our automated algorithm comes close to the currently known best solution,
which involves much human intervention. This shows the potential usefulness
of the algorithm in more general problems.
Authors:
Andrew R. Teel,
Volume: 1, Page 112 Paper number 1556
Abstract:
A recent converse Lyapunov theorem for differential inclusions is used
to generate a large class of algorithms for nonsmooth optimization.
Particular attention is given to quasi-Newton algorithms for the minimization
of locally Lipschitz, regular functions. The main contribution is
to show that when such functions have compact sublevel sets, they generically
admit smooth functions that decrease along every direction in the generalized
gradient at every point that is not a stationary point. This generalizes
a well-known result for convex functions which states that the Euclidean
distance to the minimizer is a smooth descent function. We also show
that linear transformations on the generalized gradient also admit
smooth descent functions. This fact enables a large class of quasi-Newton
algorithms for nonsmooth optimization.
Authors:
Andrew R. Teel,
Volume: 1, Page 118 Paper number 1987
Abstract:
A recent converse Lyapunov theorem for differential inclusions is used
to generate a class of finite difference algorithms for nonsmooth optimization.
The algorithms rely on a proof of asymptotic stability for differential
inclusions that contain persistently exciting signals and the ability
to approximate these differential inclusions with finite differences.
The notion of persistency of excitation that is used here generalizes
that which is typically used in the identification and adaptive control
literature.
Authors:
Peter L. Bartlett,
Jonathan Baxter,
Volume: 1, Page 124 Paper number 1788
Abstract:
We introduce an on-line algorithm for finding local maxima of the average
reward in a Partially Observable Markov Decision Process (POMDP) controlled
by a parameterized policy. Optimization is over the parameters of the
policy. The algorithm's chief advantages are that it requires only
a single sample path of the POMDP, it uses only one free parameter
(beta), which has a natural interpretation in terms of a bias-variance
trade-off, and it requires no knowledge of the underlying state. In
addition, the algorithm can be applied to infinite state, control and
observation spaces. We prove almost-sure convergence of our algorithm,
and show how the correct setting of (beta) is related to the mixing
time of the Markov chain induced by the POMDP.
Authors:
Stefan M. Jakubek,
Hanns P. Jörgl,
Volume: 1, Page 130 Paper number 1647
Abstract:
In this work the principle of observer-based sensor fault detection
and isolation is improved by the use of genetic optimization algorithms.
Residual signals are generated by taking linear combinations of the
observation errors such that asymptotic decoupling can be achieved.
While the residual-generator itself is easy to implement its design
in view of fault-isolation turns out to be a complex problem. It
is demonstrated how the observer-eigenstructure can be optimized for
transient decoupling of the residuals using genetic optimization algorithms.
In order to illustrate its applicability, the method is applied to
an industrial turbo-charged combustion engine power plant.
Authors:
Urszula A. Ledzewicz,
Heinz M. Schättler,
Volume: 1, Page 136 Paper number 17
Abstract:
We illustrate a generalized local Maximum Principle published earlier
which gives necessary conditions for optimality of abnormal trajectories
in optimal control problems. In this theorem the multiplier associated
with the objective is non-zero.
Authors:
Jason L. Speyer,
Ravi N. Banavar,
David F. Chichka,
Ihnseok Rhee,
Volume: 1, Page 142 Paper number 2088
Abstract:
Extremum seeking (also peak-seeking) controllers are designed to operate
at an unknown set-point that extremizes the value of a performance
function. This performance function is approximated by an assumed function
with a finite number of parameters. These parameters, which are estimated
on-line, are assumed to change slowly compared to the plant and compensator
dynamics. Philosophically, the approach of assuming a function is in
contrast with traditional approaches that use time scale separation
between gradient computation and function minimization and the system
dynamics. To analyze our current scheme, quadratic functions or exponentials
of quadratic functions are assumed as approximations to the performance
function. This allows the peak-seeking control loop to be reduced
to a linear system. For this loop, compensators can be designed and
robust performance and stability analysis of the loop due to parameter
uncertainty in the assumed performance functions can be obtained.
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