Minimal-power control of hydrogen evolution reactions

VICENTE COSTANZA; PABLO S. RIVADENEIRA

OPTIMAL CONTROL APPLICATIONS & METHODS

Wiley

Lugar: Chichester, UK; Año: 2010 vol. 31 p. 105 - 115

0143-2087

An integral approach to solve .nite-horizon optimal control problems posed by set-point changes in electrochemical hydrogen reactions is developed. The methodology extends to nonlinear problems with regular, convex Hamiltonians that cannot be explicitly minimized, i.e., where the functional dependence of the H-minimal control on the state and costate variables is not known. The Lagrangian functions determining trajectory costs will not have special restrictions other than positiveness, but for simplicity the .nal penalty will be assumed quadratic. The answer to the problem is constructed through the solution to a coupled system of three first-order quasilinear PDEs for the missing boundary conditions x(T); lambda(0) of the Hamiltonian equations, and for the .nal value of the control variable u(T). The independent variables of these PDEs are the time-duration T of the process and the characteristic parameter S of the .nal penalty. The solution provides information on the whole (T; S)-family of control problems, which can be used not only to construct the individual optimal control strategies on-line, but also for global design purposes.  H-minimal control on the state and costate variables is not known. The Lagrangian functions determining trajectory costs will not have special restrictions other than positiveness, but for simplicity the .nal penalty will be assumed quadratic. The answer to the problem is constructed through the solution to a coupled system of three first-order quasilinear PDEs for the missing boundary conditions x(T); lambda(0) of the Hamiltonian equations, and for the .nal value of the control variable u(T). The independent variables of these PDEs are the time-duration T of the process and the characteristic parameter S of the .nal penalty. The solution provides information on the whole (T; S)-family of control problems, which can be used not only to construct the individual optimal control strategies on-line, but also for global design purposes. H-minimal control on the state and costate variables is not known. The Lagrangian functions determining trajectory costs will not have special restrictions other than positiveness, but for simplicity the .nal penalty will be assumed quadratic. The answer to the problem is constructed through the solution to a coupled system of three first-order quasilinear PDEs for the missing boundary conditions x(T); lambda(0) of the Hamiltonian equations, and for the .nal value of the control variable u(T). The independent variables of these PDEs are the time-duration T of the process and the characteristic parameter S of the .nal penalty. The solution provides information on the whole (T; S)-family of control problems, which can be used not only to construct the individual optimal control strategies on-line, but also for global design purposes.