Efficient optimization for robust optimal control with constraints

Dr. Eric Kerrigan, Imperial College London, UK

This talk will present an efficient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with linear constraints on the states and inputs. The problem of computing a finite-horizon state feedback control policy, which guarantees robust constraint satisfaction, is known to be non- convex. However, a recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program. While the reparameterized 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 a computational time of O(N^6) per iteration of an interior-point method. We focus on the case when the disturbance set is infinity-norm bounded or the linear map of a hypercube. 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 optimization problem, solvable by primal-dual interior-point methods in which each iteration requires O(N^3) time. This cubic iteration time can be guaranteed using a Riccati-based block factorization technique, which is standard in discrete-time optimal control. Numerical results are presented, using a standard sparse primal-dual interior point solver, that illustrate the efficiency of this approach.

Biography
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Eric Kerrigan is a Lecturer and Royal Academy of Engineering Research Fellow in the Department of Aeronautics and the Department of Electrical and Electronic Engineering at Imperial College London. He received a BSc(Eng) in Electrical Engineering from the University of Cape Town in 1996, and a PhD in Control Engineering from the University of Cambridge in 2001. During 1997 he was with the Council for Scientific and Industrial Research (CSIR), South Africa and from 2001 to 2005 he was a Research Fellow at the Department of Engineering, University of Cambridge. His research interests include optimal and robust control of systems with constraints and applications of control in aerodynamics.