Minimizing control-energy in bounded-control LQR problems

COSTANZA, VICENTE; RIVADENEIRA, SANTIAGO; GONZÁLEZ, ALEJANDRO HERNÁN

OPTIMAL CONTROL APPLICATIONS & METHODS

JOHN WILEY & SONS LTD

Lugar: Londres; Año: 2013 vol. 35 p. 361 - 382

0143-2087

Minimal-control-energy strategies are substantiated and illustrated for linear-quadratic problems with penalizedendpoints and no state-trajectory cost, when bounds in control values are imposed. The optimal solutionfor a given process with restricted controls, starting at a known initial state, is shown to coincide with thesaturated solution to the unrestricted problem that has the same coefficients but starts at a generally differentinitial state. This result reduces the searching span for the solution: from the infinite-dimensional set ofadmissible control trajectories to the finite-dimensional Euclidean space of initial conditions. An efficientreal-time scheme is proposed here to approximate (eventually to find) the optimal control strategy, basedon the detection of the appropriate initial state while avoiding as much as possible the generation andevaluation of state and control trajectories. Numerical (including model predictive control) simulations areprovided, compared, and checked against the analytical solution to ?the cheapest stop of a train? problem inits pure-upper-bounded brake, flexible-endpoint setting.