@article{Goulart:2007:10.1007/s10107-007-0096-6,
author = {Goulart, PJ and Kerrigan, EC and Ralph, D},
doi = {10.1007/s10107-007-0096-6},
journal = {Mathematical Programming},
pages = {115--147},
title = {Efficient Robust Optimization for Robust Control with Constraints.},
url = {http://dx.doi.org/10.1007/s10107-007-0096-6},
volume = {114},
year = {2007}
}

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TY  - JOUR
AB  - This paper proposes an efficient computational technique for theoptimal control of linear discrete-time systems subject to bounded disturbanceswith mixed linear constraints on the states and inputs. The problem of computingan optimal state feedback control policy, given the current state, is non-convex.A recent breakthrough has been the application of robust optimizationtechniques to reparameterize this problem as a convex program. While thereparameterized problem is theoretically tractable, the number of variables isquadratic in the number of stages or horizon length N and has no apparentexploitable structure, leading to computational time of O(N6) per iteration ofan interior-point method. We focus on the case when the disturbance set is ∞-norm bounded or the linear map of a hypercube, and the cost function involvesthe minimization of a quadratic cost. Here we make use of state variables toregain a sparse problem structure that is related to the structure of the originalproblem, that is, the policy optimization problem may be decomposed into aset of coupled finite horizon control problems. This decomposition can then be formulated as a highly structured quadratic program, solvable by primaldualinterior-point methods in which each iteration requires O(N3) time. Thiscubic iteration time can be guaranteed using a Riccati-based block factorizationtechnique, which is standard in discrete-time optimal control. Numerical resultsare presented, using a standard sparse primal-dual interior point solver, thatillustrate the efficiency of this approach.
AU  - Goulart,PJ
AU  - Kerrigan,EC
AU  - Ralph,D
DO  - 10.1007/s10107-007-0096-6
EP  - 147
PY  - 2007///
SN  - 1436-4646
SP  - 115
TI  - Efficient Robust Optimization for Robust Control with Constraints.
T2  - Mathematical Programming
UR  - http://dx.doi.org/10.1007/s10107-007-0096-6
UR  - http://hdl.handle.net/10044/1/26461
VL  - 114
ER  - 

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