Efficient robust optimization for robust control with constraints

This paper proposes an efficient computational technique for the optimal control of linear discrete-time 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 non-convex. 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(N6 ) per iteration of an 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 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 origina...

• Type: Journal
• Year: 2008
• Where: MP
• Authors: Paul J. Goulart, Eric C. Kerrigan, Daniel Ralph
• Keywords: Efficient Computational Technique, Linear Discrete-time Systems, MP 2008, Optimal Control