Title :
An Efficient Method to Estimate the Suboptimality of Affine Controllers
Author :
Hadjiyiannis, Michael J. ; Goulart, Paul J. ; Kuhn, Daniel
Author_Institution :
Dept. of Comput., Imperial Coll. London, London, UK
Abstract :
We consider robust feedback control of time-varying, linear discrete-time systems operating over a finite horizon. For such systems, we consider the problem of designing robust causal controllers that minimize the expected value of a convex quadratic cost function, subject to mixed linear state and input constraints. Determination of an optimal control policy for such problems is generally computationally intractable, but suboptimal policies can be computed by restricting the class of admissible policies to be affine on the observation. By using a suitable re-parameterization and robust optimization techniques, these approximations can be solved efficiently as convex optimization problems. We investigate the loss of optimality due to the use of such affine policies. Using duality arguments and by imposing an affine structure on the dual variables, we provide an efficient method to estimate a lower bound on the value of the optimal cost function for any causal policy, by solving a cone program whose size is a polynomial function of the problem data. This lower bound can then be used to quantify the loss of optimality incurred by the affine policy.
Keywords :
control system synthesis; convex programming; cost optimal control; discrete time systems; duality (mathematics); feedback; linear programming; linear systems; minimisation; polynomials; quadratic programming; robust control; time-varying systems; affine controllers; convex optimization problems; convex quadratic cost function; cost optimal control; discrete-time systems; duality; feedback; finite horizon; linear systems; lower bound; minimization; mixed linear state; polynomial function; robust controller design; suboptimality estimation; time-varying systems; Approximation methods; Cost function; Discrete time systems; Feedback control; Optimization; Robustness; Affine control policies; stochastic optimal control;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2011.2139390