"Fast explicit model
predictive control"
M. Mönnigmann
Automatic Control and Systems Theory,
Ruhr-Universität Bochum, Germany
Model predictive control (MPC) is an established method for the control of constrained multivariable systems. New
theoretical insights, improved and tailored optimization algorithms, and the
ever growing performance of hardware have helped MPC advance to higher and
higher sampling frequencies. For linear systems and sampling times below a
millisecond, explicit MPC (EMPC) methods are an interesting alternative. In
EMPC it is no longer necessary to solve a receding horizon optimal control
problem online. Instead, an analytical expression for the MPC control law can
be found by solving a parametric optimization problem offline. EMPC can,
however, still only be applied to very simple problems with short horizons for
two reasons: The parametric optimization problem is more complex than its
non-parametric receding horizon counterpart. Secondly, the expression for the
explicit control law u(x) may grow so large that a naive online evaluation of
u(x) takes as much time as solving the receding horizon optimal control problem
online. The talk summarizes recent progress with respect to both obstacles, the
offline calculation of explicit control laws, and their fast online evaluation.
Specifically, a simple new approaches to the fast evaluation of EMPC control
laws results in online evaluation times on the order of 10ns. This approach
does not require a CPU, but it can be implemented on low-cost, compact hardware
with low power consumption such as programmable gate arrays. Progress in the
fast evaluation of EMPC control laws has triggered the development of new
approaches to solving the offline optimization problem. To this end, a new
approach is suggested that avoids the state space exploration common to most
existing methods.
