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Mayer Form


The Mayer form of a variational or optimal control problem has a cost depending only on the endpoint times and states. The Mayer term is the part of the cost that depends on these quantities. In Mayer form it is the entire cost. A Bolza problem with integrand L(t,y(t),y^'(t)) and endpoint cost Phi on [t_0,t_1] can be put in Mayer form by adding a state z(t) with z(t_0)=0 and

 z^'(t)=L(t,y(t),y^'(t)),

where primes denote derivatives with respect to time t. The new endpoint cost is Phi+z(t_1), which includes the accumulated integral of L (Liberzon 2012).


See also

Bolza Problem, Calculus of Variations

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References

Liberzon, D. Calculus of Variations and Optimal Control Theory: A Concise Introduction. Princeton, NJ: Princeton University Press, 2012. https://liberzon.csl.illinois.edu/teaching/cvoc.pdf.

Cite this as:

Weisstein, Eric W. "Mayer Form." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MayerForm.html

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