High-Speed Integer Optimal Control using Approximate Dynamic Programming

We introduce a novel method to deal with hybrid MPC problems with fast linear dynamics and integer inputs. In contrast to common formulations where the input effort is reduced indirectly via the penalization of the input switchings over the controller horizon, in this work the system dynamics are augmented to directly estimate the switching frequency. To address the computational issues of long prediction horizons, we cast the optimization problem in the framework of approximate dynamic programming (ADP). The infinite horizon value function is approximated by solving a semidefinite program offline. This enables us to shorten the controller horizon by applying the estimated tail cost to the last stage while maintaining good control performance. Our approach is applied to a variable-speed drive system consisting of a voltage source inverter connected to a medium-voltage induction machine. The plant is modeled as a linear system with a switched three-phase input with equal switching steps for all phases. We implemented our algorithm on a small size Xilinx Zynq FPGA (xc7z020) in fixed-point arithmetic. Hardware in the loop (HIL) experiments showed that our method even with very short prediction horizons outperforms state of the art approaches with much longer planning horizons while achieving extremely low computation times under 25 us.