Tensor Networks for Model Predictive Control

Abstract

Model predictive control (MPC) computes optimal control actions while enforcing the physical and safety limits of a system, a combination that has led to its wide adoption. Yet each action requires solving an optimisation problem within one sampling interval, a computational burden that restricts where it can be deployed. To reduce this burden, semi-explicit MPC precomputes state-independent operators. At scale, however, storage becomes the dominant cost, as the largest operator grows quadratically with the number of constraints stacked over the horizon. Because the same dynamics repeat at every step, these operators carry a regular block structure well suited to tensor train compression. This thesis presents the first tensor train formulation of semi-explicit MPC. Rewriting the semi-explicit pipeline to separate the horizon from the per-step dynamics makes it tractable to construct the operators directly in this format and to evaluate the online active-set law without ever decompressing the operators. On a benchmark that is scaled in system size and horizon, the compressed controller remains closed-loop admissible while reducing storage by up to a factor of 36. These gains come at a price. Construction in compressed format is orders of magnitude slower than its matrix counterpart. Online evaluation is 2 to 54 times slower, since every entry used by the active-set loop must be computed on demand rather than read from memory. The approach is therefore advantageous where storage, rather than computation, is the limiting resource. At long horizons the matrix-form controller no longer fits in fast memory, whereas the compressed controller, once built, does. The reported experiments stop short of that regime because, although the final controller is small, the intermediate rank growth during construction exhausts memory. Closing this gap rests on a single open problem: evaluating the inverse action that arises during operator construction while containing rank growth. Solving it would extend semi-explicit MPC to horizons beyond the reach of current methods.