Premium
Minimizing control energy in a class of bounded‐control linear‐quadratic regulator problems
Author(s) -
Costanza V.,
Rivadeneira P. S.,
González A. H.
Publication year - 2013
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2072
Subject(s) - bounded function , linear quadratic regulator , mathematics , control theory (sociology) , state (computer science) , optimal control , quadratic equation , euclidean space , mathematical optimization , model predictive control , trajectory , control (management) , computer science , mathematical analysis , algorithm , geometry , physics , astronomy , artificial intelligence
SUMMARY Minimal‐control‐energy strategies are substantiated and illustrated for linear‐quadratic problems with penalized endpoints and no state‐trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite‐dimensional set of admissible control trajectories to the finite‐dimensional Euclidean space of initial conditions. An efficient real‐time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure‐upper‐bounded brake, flexible‐endpoint setting. Copyright © 2013 John Wiley & Sons, Ltd.