State-dependent Riccati equation-based robust dive plane control of AUV with control constraints

The paper treats the question of suboptimal dive plane control of autonomous underwater vehicles (AUVs) using the state-dependent Riccati equation (SDRE) technique. The SDRE method provides an effective mean of designing nonlinear control systems for minimum as well as nonminimum phase AUV models. It is assumed that the hydrodynamic parameters of the nonlinear vehicle model are imprecisely known, and in order to obtain a practical design, a hard constraint on control fin deflection is imposed. The problem of depth control is treated as a robust nonlinear output (depth) regulation problem with constant disturbance and reference exogenous signals. As such an internal model of first-order fed by the tracking error is constructed. A quadratic performance index is chosen for optimization and the algebraic Riccati equation is solved to obtain a suboptimal control law for the model with unconstrained input. For the design of model with fin angle constraints, a slack variable is introduced to transform the constrained control input problem into an unconstrained problem, and a suboptimal control law is designed for the augmented system using a modified performance index. Using the center manifold theorem, it is shown that in the closed-loop system, the system trajectories are regulated to a manifold (called output zeroing manifold) on which the depth tracking error is zero and the equilibrium state is asymptotically stable. Simulation results are presented which show that effective depth control is accomplished in spite of the uncertainties in the system parameters and control fin deflection constraints.