Fixed-Point Dual Gradient Projection for Embedded Model Predictive Control

Although linear Model Predictive Control has gained increasing popularity for controlling dynamical systems subject to constraints, the main barrier that prevents its widespread use in embedded applications is the need to solve a Quadratic Program (QP) in real-time. This paper proposes a dual gradient projection (DGP) algorithm specifically tailored for implementation on fixed-point hardware. A detailed convergence rate analysis is presented in the presence of round-off errors due to fixed-point arithmetic. Based on these results, concrete guidelines are provided for selecting the minimum number of fractional and integer bits that guarantee convergence to a suboptimal solution within a prespecified tolerance, therefore reducing the cost and power consumption of the hardware device.