Abstract
Chapter 6 deals with the cost function shaping concept. Cost function shaping is the name that we have given to a set of procedures and maneuvers that change the cost function so that it is more amenable to optimization, yet maintaining its original design objective. Cost function shaping involves mainly choosing the input signal in the experiments (aka input design) and changing stepwise the reference model (aka cautious control). Proper data windowing can also be very helpful in shaping the cost function so that it becomes “well-behaved” as desired. Each one of these procedures and maneuvers is presented, and theoretically justified, in this chapter. It is shown that it is always possible to reshape the cost function so that there are no local minima in the whole parameter space. This implies that convergence to the global minimum is “easily” obtained starting from any stabilizing controller. Several simulation examples are given along this chapter to illustrate the concepts and to show how to perform cost function shaping in real control design.
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Notes
- 1.
We will see that under Assumption B y this is not even necessary.
- 2.
Granted, this is a rather artificial control objective, but the purpose of this example is not to illustrate practical applications but rather to explain the ideas. Accordingly, the choice of this particular example was based on obtaining easily understandable equations and pictures rather than on its practical meaning. Real life examples are given elsewhere, particularly in Chap. 8.
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Sanfelice Bazanella, A., Campestrini, L., Eckhard, D. (2012). Cost Function Shaping. In: Data-Driven Controller Design. Communications and Control Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2300-9_6
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DOI: https://doi.org/10.1007/978-94-007-2300-9_6
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