Software toolbox for analysis and design of nonlinear control systems and its application to multi-AUV path-following control

In the paper, we present a software toolbox for rigorous analysis and design of nonlinear continuous and discrete-continuous (digital) control systems based on the reduction method and sublinear vector Lyapunov functions. For these systems, the toolbox provides solution of the following problems: verification of dynamic properties of dissipativity, asymptotic and practical stability; computation of estimates of basic direct indicators of dynamic quality (accuracy, domains of attraction and dissipativity, settling time and others); synthesis of parameters that ensure desirable or optimal quality of the system. In addition, we show how the toolbox could be applied to solve the path-following control problem for a single autonomous underwater vehicle (AUV) as well as for multi-AUV formations. In our statements of the path-following control problem, we take into account together uncertainties of AUVs model, inaccuracy of measurements, and constraints on control actions.