Solving LQR Problems with Free Endpoints and Restricted Controls

VICENTE COSTANZA; PABLO S. RIVADENEIRA

Oro Verde, Entre Rios

Congreso; XIV RPIC; 2011

Facultad de Bioingeniería, UNER

Optimal control strategies are substantiate for LQR problems with free but penalized endpoints, when constraints on control values are present. The missing boundary values of the Hamiltonian equations are obtained by (off-line) solving two uncoupled, first-order, linear partial differential equations for two auxiliary n×n matrices, whose independent variables are the time-horizon duration T and the eigenvalues of the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole (T,S,x₀)-family of control problems. The optimal strategy for a given (T,S,x₀)-problem with restricted control is shown to coincide with the `saturated´ version of the solution to some (T,S,y₀)-problem with unbounded controls, where y₀ can be calculated from the existing information. Illustrations of numerical results are provided and checked against analytical solutions of a classical case-study.