Fuzzy Logic System-Based Robust Adaptive Control of AUV with Target Tracking

Abstract

This article investigates the robust adaptive control for the longitudinal dynamics of autonomous underwater vehicle with target tracking based on fuzzy logic system. Through dynamic transformation, the target tracking command is converted to the pitch angle command. The tracking controller using switching mechanism is designed where the fuzzy logic system (FLS) cooperates with the robust design to deal with dynamics uncertainty. Considering the approximation ability of FLS, the modeling error is constructed and employed to design the fuzzy update law. The parameter adaptation law is further introduced for the unknown control gain function. The uniformly ultimate boundedness stability is proved through Lyapunov analysis. Simulation tests on the task of moving target tracking present higher tracking and learning performance.

Appendix

According to [29], the coefficients in Eqs. (1)–(6) are given as follows

$$\begin{aligned} {a_{11}}= & {} - {A_x}/m,{a_{14}} = - P/m,{a_{18}} = T/m\nonumber \\ {a_{21}}= & {} [{\lambda _{26}}A_{{m_z}}^\alpha - ({J_{z1}} + {\lambda _{66}})A_y^\alpha ]/{D_{26}}\nonumber \\&- {a_{11}}[({J_{z1}} + {\lambda _{66}}){\lambda _{22}} - \lambda _{26}^2]/{D_{26}}\nonumber \\ {a_{22}}= & {} [({J_{z1}} + {\lambda _{66}})(m - A_y^\omega ) - {\lambda _{26}}A_{{m_{z1}}}^\omega ]/{D_{26}}\nonumber \\ {a_{23}}= & {} [\lambda _{26}^2 - ({J_{z1}} + {\lambda _{66}})(m + {\lambda _{22}})]/(m{D_{26}})\nonumber \\ {a_{24}}= & {} P[ - \lambda _{26}^2 + ({J_{z1}} + {\lambda _{66}}){\lambda _{22}}]/(m{D_{26}})\nonumber \\ {a_{25}}= & {} P({J_{z1}} + {\lambda _{66}})/{D_{26}},{a_{26}} = - {\lambda _{26}}B{x_c}/{D_{26}}\nonumber \\ {a_{27}}= & {} {\lambda _{26}}Bh/{D_{26}},{a_{28}} = - {\lambda _{26}}Th/{D_{26}}\nonumber \\ {a_{29}}= & {} A_y^\delta [ - ({J_{z1}} + {\lambda _{66}}) - {\lambda _{26}}{x_e}]/{D_{26}}\nonumber \\ {a_{31}}= & {} [A_{{m_z}}^\alpha (m + {\lambda _{22}}) - {\lambda _{26}}({A_x} + A_y^\alpha )]/{D_{26}}\nonumber \\ {a_{32}}= & {} [{\lambda _{26}}(m - A_y^\omega ) - A_{{m_{z1}}}^\omega (m + {\lambda _{22}})]/{D_{26}}\nonumber \\ {a_{34}}= & {} - {\lambda _{26}}P/{D_{26}},{a_{35}} = {\lambda _{26}}P/{D_{26}}\nonumber \\ {a_{36}}= & {} - (m + {\lambda _{22}})B{x_c}/{D_{26}}\nonumber \\ {a_{37}}= & {} (m + {\lambda _{22}})Bh/{D_{26}},{a_{38}} = - (m + {\lambda _{22}})Th/{D_{26}}\nonumber \\ {a_{39}}= & {} A_y^\delta [ - {\lambda _{26}} - {x_e}(m\mathrm{{ + }}{\lambda _{22}})]/{D_{26}}\nonumber \\ {D_{26}}= & {} ({J_{z1}} + {\lambda _{66}})(m+{\lambda _{22}}) - \lambda _{26}^2\nonumber \\ {A_x}= & {} (1/2)\rho S{C_{xS}},A_y^\alpha = (1/2)\rho SC_y^\alpha \nonumber \\ A_y^\delta= & {} (1/2)\rho SC_y^{{\delta _e}},A_y^\omega = (1/2)\rho SC_y^{\bar{\omega }}\nonumber \\ A_{{m_z}}^\alpha= & {} (1/2)\rho Sm_z^\alpha ,A_{{m_{z1}}}^\omega = (1/2)\rho SC_z^{{{\bar{\omega }}_y}}\nonumber \\ {\lambda _{22}}= & {} {K_{22}}\rho V,{\lambda _{26}} = {K_{26}}\rho {V^{4/3}},{\lambda _{66}} = {K_{66}}\rho {V^{5/3}} \end{aligned}$$