Regular Hamiltonian Problems with Implicit H-Optimal Controls

V. COSTANZA, P. S. RIVADENEIRA

Río Gallegos, Santa Cruz, Argentina

Congreso; XII Reunión de Trabajo en Procesamiento de la Información y Control, RPIC 2007; 2007

U.N.P.A. - RPIC

A new approach to solve nitehorizon optimal control problems for certain nonlinear systems is developed. The methodology applies to one-dimensional problems with regular, convex Hamiltonians that can not 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 under the sequel, but for simplicity the nal penalty will be assumed quadratic. The answer to the problem is constructed through the solution of a coupled system of three rst-order quasilinear PDEs for the missing boundary conditions x(T); (0) of the Hamiltonian equations and the nal value of the control variableH- minimal control on the state and costate variables is not known. The Lagrangian functions determining trajectory costs will not have special restrictions under the sequel, but for simplicity the nal penalty will be assumed quadratic. The answer to the problem is constructed through the solution of a coupled system of three rst-order quasilinear PDEs for the missing boundary conditions x(T); (0) of the Hamiltonian equations and the nal value of the control variablex(T); (0) of the Hamiltonian equations and 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 (on-line) the individual optimal control strategies, but also for global design purposes.(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 (on-line) the individual optimal control strategies, but also for global design purposes.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 (on-line) the individual optimal control strategies, but also for global design purposes.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 (on-line) the individual optimal control strategies, but also for global design purposes.(T; S)-family of control problems, which can be used not only to construct (on-line) the individual optimal control strategies, but also for global design purposes.