Brief paper: Using hash tables to manage the time-storage complexity in a point location problem: Application to explicit model predictive control

Authors:
Farhad Bayat;Tor Arne Johansen;Ali Akbar Jalali
Affiliations:
Department of Electrical Engineering, Iran University of Science and Technology, Narmak, 1684613114 Tehran, Iran;Department of Engineering Cybernetics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway;Department of Electrical Engineering, Iran University of Science and Technology, Narmak, 1684613114 Tehran, Iran
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

The online computational burden of linear model predictive control (MPC) can be moved offline by using multi-parametric programming, so-called explicit MPC. The solution to the explicit MPC problem is a piecewise affine (PWA) state feedback function defined over a polyhedral subdivision of the set of feasible states. The online evaluation of such a control law needs to determine the polyhedral region in which the current state lies. This procedure is called point location; its computational complexity is challenging, and determines the minimum possible sampling time of the system. A new flexible algorithm is proposed which enables the designer to trade off between time and storage complexities. Utilizing the concept of hash tables and the associated hash functions, the proposed method solves an aggregated point location problem that overcomes prohibitive complexity growth with the number of polyhedral regions, while the storage-processing trade-off can be optimized via scaling parameters. The flexibility and power of this approach is supported by several numerical examples.