Nonlinear optimal control of autonomous submarines’ diving

The article presents a nonlinear H-infinity (optimal) control approach for the problem of the control of the depth and heading angle of an autonomous submarine. This is a multivariable nonlinear control problem and its solution allows for precise underwater navigation of the submarine. The submarine’s dynamic model undergoes approximate linearization around a temporary equilibrium that is recomputed at each iteration of the control algorithm. The linearization procedure is based on Taylor series expansion and on the computation of the submarine’s model Jacobian matrices. For the approximately linearized model, the optimal control problem is solved through the design of an H-infinity feedback controller. The computation of the controller’s gain requires the solution of an algebraic Riccati equation, which is performed at each time-step of the control method. The global stability of the control scheme is proven through Lyapunov analysis. First, it is demonstrated that for the submarine’s control loop, the H-infinity tracking performance criterion holds. Moreover, under moderate conditions, it is shown that the control scheme is globally asymptotically stable.