Bounded-variable least-squares methods for linear and nonlinear model predictive control

This dissertation presents an alternative approach to formulateand solve optimization problems arising in real-time modelpredictive control (MPC). First it has been shown that byusing a quadratic penalty function, the linear MPC optimizationproblem can be formulated as a least-squares problemsubject to bounded variables while directly employingmodels in their input/output form. A theoretical analysison stability and optimality is included with a comparisonagainst the conventional condensed approach based on linearstate-space models. These concepts are straightforwardlyextended for fast nonlinear MPC with bounded variables.An active-set algorithm based on a novel application of linearalgebra methods is proposed for efficiently solving theresulting box-constrained (nonlinear) least-squares problemswith global convergence, numerical robustness, and easy deployabilityon industrial embedded hardware platforms. Finally,new methods and tools are devised for maximizingefficiency of the solution algorithm considering the numericallysparse structure of the non-condensed MPC problem.Based on these methods, the problem construction phase inMPC design is systematically eliminated by parameterizingthe optimization algorithm such that it can adapt to real-timechanges in the model and tuning parameters while significantlyreducing memory and computational complexity witha potentially self-contained matrix-free implementation. Numericalsimulation results included in this thesis testify thepotential, applicability, numerical robustness and efficiencyof the proposed methods for practical real-time embeddedMPC.