ℓasso MPC: Smart regulation of over-actuated systems

In this paper, a novel MPC strategy is proposed, and referred to as “ℓ_asso MPC”. The new paradigm features an ℓ₁-regularised least squares loss function, in which the control error variance competes with the sum of input channels magnitude (or slew rate) over the whole horizon length. This cost choice is motivated by the successful development of LASSO theory in signal processing and machine learning. In the latter fields, “sum-of-norms regularisation” have shown a strong capability to provide robust and sparse solutions for system identification and feature selection. In this paper, a discrete-time dual-mode ℓ_asso MPC is formulated, and its stability is proven by application of standard MPC arguments. The controller is then tested for the problem of ship course keeping and roll reduction with rudder and fins, in a directional stochastic sea. Simulations show the ℓ_asso MPC to inherit positive features from its corresponding regressor: extreme reduction of decision variables´ magnitude, namely, actuators´ magnitude (or variations), with a finite energy error, being particularly promising for over-actuated systems.