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PJ Goulart (pgoulartalum.mit.edu) Abstract: This paper proposes an efficient computational technique for the optimal control of linear discretetime systems subject to bounded disturbances with mixed polytopic constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is nonconvex. A recent breakthrough has been the application of robust optimization techniques to reparameterise this problem as a convex program. While the reparameterised problem is theoretically tractable, the number of variables is quadratic in the number of stages or horizon length N and has no apparent exploitable structure, leading to computational time of O(N^6) per iteration of an interiorpoint method. We focus on the case when the disturbance set is infinitynorm bounded or the linear map of a hypercube, and the cost function involves the minimization of a quadratic cost. Here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem, that is, the policy optimization problem may be decomposed into a set of coupled finite horizon control problems. This decomposition can then be formulated as a highly structured quadratic program, solvable by primaldual interiorpoint methods in which each iteration requires O(N^3) time. This cubic iteration time can be guaranteed using a Riccatibased block factorization technique, which is standard in discretetime optimal control. Numerical results are presented, using a standard sparse primaldual interior point solver, which illustrate the efficiency of this approach. Keywords: Constrained control, robust optimization, optimal control, robust control, receding horizon control, predictive control. Category 1: Applications  Science and Engineering (Control Applications ) Category 2: Robust Optimization Citation: CUED/FINFENG/TR.495 May, 2005. Department of Engineering University of Cambridge Cambridge CB2 1PZ United Kingdom Download: [PDF] Entry Submitted: 10/03/2005 Modify/Update this entry  
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