Embedded model predictive control: finite precision arithmetic and aerospace applications

Model Predictive Control (MPC) is a multivariable advanced control technique widely popular inmany industrial applications due to its ability to explicitly optimize performance, straightforwardly handling constraints on system variables. However, MPC requires solving a Quadratic Programming (QP) optimization problem at each sampling step. This has slowed down its diffusion in embedded applications, in which fast sampling rates are paired with scarce computational capabilities, as in the automotive and aerospace industries. This thesis proposes optimization techniques and controller formulations specifically tailored to embedded applications. First, fixed-point implementations of Dual Gradient Projection (DGP) and Proximal Newton methods are introduced. Detailed convergence analysis in the presence of round-off errors and algorithm optimizations are presented, and concrete guidelines for selecting the minimum number of fractional and integer bits that guarantee convergence are provided. Moreover, extensive simulations and experimental tests on embedded devices, supported by general-purpose processing units and FPGAs, are reported to demonstrate the feasibility of the proposed solvers, and to expose the benefits of fixed-point arithmetic in terms of computation speeds and memory requirements. Finally, an embedded MPC application to spacecraft attitude control with reaction wheels actuators is presented. A lightweight controller with specific optimizations is developed, and its good performance evaluated in simulations. Moreover, special MPC formulations that address the problem of reaction wheel desaturation are discussed, where the constraint handling property of MPC is exploited to achieve desaturation without the need of fuel-consuming devices such as thrusters.