Fast Evaluation of Quadratic Control-Lyapunov Policy
IEEE Transactions on Control Systems Technology, 19(4):939–946, July 2011.
The evaluation of a control-Lyapunov policy, with quadratic Lyapunov
function, requires the solution of a quadratic program (QP) at each time
step. For small problems this QP can be solved explicitly; for larger
problems an on-line optimization method can be used. For this reason the
control-Lyapunov control policy is considered a computationally intensive
control law, as opposed to an ‘analytical’ control law, such as
conventional linear state feedback, LQG, or 
, too complex or slow
to be used in high speed control applications. In this note we show that
by pre-computing certain quantities, the control-Lyapunov policy can be
evaluated extremely efficiently. We will show that when the number of
inputs is on the order of the square-root of the state dimension, the cost
of evaluating a control-Lyapunov policy is on the same order as the cost of
evaluating a simple linear state feedback policy, and less (in order) than
the cost of updating a Kalman filter state estimate. To give an idea of
the speeds involved, for a problem with 100 states and 10 inputs, the
control-Lyapunov policy can be evaluated in around 67
s, on a 2GHz AMD
processor; the same processor requires 44s to carry out a Kalman
filter update.