Summers, S.
Jones, Colin
Lygeros, J.
Morari, M.
A multiresolution approximation method for fast explicit model predictive control
IEEE Transactions on Automatic Control
IEEE Transactions on Automatic Control
IEEE Transactions on Automatic Control
IEEE Transactions on Automatic Control
56
11
2011
2011
A model predictive control law is given by the solution to a parametric optimization problem that can be pre- computed offline and provides an explicit map from state to control input. In this paper, an algorithm is introduced based on wavelet multiresolution analysis that returns a low complexity explicit model predictive control law built on a hierarchy of second order interpolets. The resulting interpolation is shown to be everywhere feasible and continuous. Further, tests to confirm stability and to compute a bound on the performance loss are introduced. Since the controller approximation is built on a grid hierarchy, convergence to a stabilizing control law is guaranteed and the evaluation of the control law in real-time systems is naturally fast and runs in a bounded logarithmic time. Two examples are provided; A two-dimensional example with an evaluation speed of 31 ns and a four-dimensional example with an evaluation speed of 119 ns.
Institute of Electrical and Electronics Engineers
0018-9286
IEEE Transactions on Automatic Control
Journal Articles
10.1109/TAC.2011.2146990