Parallelizing LQR Computation Through Endpoint-Explicit Riccati Recursion

Forrest Laine, Claire J. Tomlin

Abstract: A method is presented for parallelizing the computation of solutions to discrete-time, linear dynamic, quadratic objective, finite-horizon optimal control problems, which we refer to as LQR problems. For many applications, the size of these problems can be large enough that computing the solution is prohibitively slow when using a single processor. In this work, we present a novel method for parallelizing the computation of solutions across multiple processors. As a byproduct of the computation, the method presented generates feedback control policies that are useful when computing solutions to nonlinear optimal control problems and in the control of autonomous systems. The feedback policies generated by this method differ from those generated in existing methods, and the implications and benefits of this difference are discussed through the use of an example.