192
11 Optimal Control Theory
5. Consider the the dynamical system, defined by ˙
x = αx
β
+ u with α, β > 0, and
the performance measure given by (11.61). Derive the Hamiltonian from (11.40)
and the equations of motion, given by (11.41), for this system. Assuming boundary
conditions x = x 0 at t = 0 and x = 0 at t = t f , explore whether you can use
methods, similar to those from Sect. 11.5, to solve this problem.
References
1. G. McCandless, The ABCs of RBCs (Harvard University Press, Cambridge, Ma, 2008)
2. R. Dorfman, An economic interpretation of optimal control theory. Am. Econ. Rev. 59, 817
(1969)
3. D. Kirk, Optimal Control Theory (Dover Publications, New York, 2004)
4. L. Landau, E. Lifschitz, Lehrbuch der theoretischen Physik, Band I: Mechanik (Akademie
Verlag, Berlin, 1979)
5. H. Goldstein, J. Safko, C. Poole, Classical Mechanics (Pearson, Harlow, 2014)
11 Optimal Control Theory
5. Consider the the dynamical system, defined by ˙
x = αx
β
+ u with α, β > 0, and
the performance measure given by (11.61). Derive the Hamiltonian from (11.40)
and the equations of motion, given by (11.41), for this system. Assuming boundary
conditions x = x 0 at t = 0 and x = 0 at t = t f , explore whether you can use
methods, similar to those from Sect. 11.5, to solve this problem.
References
1. G. McCandless, The ABCs of RBCs (Harvard University Press, Cambridge, Ma, 2008)
2. R. Dorfman, An economic interpretation of optimal control theory. Am. Econ. Rev. 59, 817
(1969)
3. D. Kirk, Optimal Control Theory (Dover Publications, New York, 2004)
4. L. Landau, E. Lifschitz, Lehrbuch der theoretischen Physik, Band I: Mechanik (Akademie
Verlag, Berlin, 1979)
5. H. Goldstein, J. Safko, C. Poole, Classical Mechanics (Pearson, Harlow, 2014)