Nonlinear adaptive trajectory control of multi-input multi-output submarines with input constraints

The paper presents a new nonlinear adaptive control system for the dive-plane control of multi-input multi-output submarine models with input constraints, in the presence of external disturbances. It is assumed that all the system parameters, except the signs of the principal minors of the input matrix, are unknown. The objective is to design an adaptive control law for the tracking of reference depth and pitch angle trajectories, despite constraints on the rotation angles of the bow and stern hydroplanes. For the derivation of a singularity-free adaptation law, the decomposition of the input matrix as a product of a positive-definite symmetric matrix, a diagonal matrix, and an upper triangular matrix (termed SDU decomposition) is obtained. Then an adaptive control system is designed which accomplishes uniform ultimate boundedness of the closed-loop system trajectories. The control system includes an auxiliary dynamic system to counter the effect of control input saturation. Simulation results show that the designed adaptive law accomplishes precise depth and pitch angle trajectory control, despite symmetric and non-symmetric input constraints, parametric uncertainties and external disturbance inputs. These results also show that the designed saturating adaptive controller can accomplish certain dive-plane maneuvers using either of the hydroplanes; but the bow hydroplane can execute larger maneuvers than the stern hydroplane. The robust performance of the controller, despite non-symmetric input constraints, is useful in situations in which partial failure of actuators causes rotation of the hydroplanes in unequal ranges.