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

This dissertation presents an alternative approach to formulate and solve optimization problems arising in real-time model predictive control (MPC). First it has been shown that by using a quadratic penalty function, the linear MPC optimization problem can be formulated as a least-squares problem subject to bounded variables while directly employing models in their input/output form. A theoretical analysis on stability and optimality is included with a comparison against the conventional condensed approach based on linear state-space models. These concepts are straightforwardly extended for fast nonlinear MPC with bounded variables. An active-set algorithm based on a novel application of linear algebra methods is proposed for efficiently solving the resulting box-constrained (nonlinear) least-squares problems with global convergence, numerical robustness, and easy deployability on industrial embedded hardware platforms. Finally, new methods and tools are devised for maximizing efficiency of the solution algorithm considering the numerically sparse structure of the non-condensed MPC problem. Based on these methods, the problem construction phase in MPC design is systematically eliminated by parameterizing the optimization algorithm such that it can adapt to real-time changes in the model and tuning parameters while significantly reducing memory and computational complexity with a potentially self-contained matrix-free implementation. Numerical simulation results included in this thesis testify the potential, applicability, numerical robustness and efficiency of the proposed methods for practical real-time embedded MPC.