The generalized super‐twisting algorithm with adaptive gains

Abstract

In this paper a novel adaptive generalized supertwisting algorithm is proposed for a class of systems whose perturbations and uncertain control coefficients are time-and statedependent. The proposed approach uses dynamically adapted control gains, and it is proven that this ensures global finitetime convergence. A non-smooth strict Lyapunov function is used to obtain the conditions for the global finite-time stability. As a case study, it is also shown that the tracking errors of an articulated intervention AUV converge asymptotically to zero when the proposed adaptive generalized super-twisting algorithm is applied. A simulation study is performed that shows the effectiveness of the proposed algorithm.

Adaptive Generalized Super-Twisting Tracking Control of an Underwater Vehicle

“…2) The adaptive generalized super-twisting algorithm: An alternative to the fixed-gain GSTA ( 14)-( 15) is to allow for the gain matrices K 1 , K 2 to be updated through the use of an adaptive law. In accordance with the proposed adaptive laws in [13], K 1 , K 2 are diagonal matrices whose i-th elements are updated according to…”

“…Underwater vehicles are affected by such uncertainties through, e.g., the inertia moment due to added mass effects [12], and through control coefficients due to vortex effects stemming from the thrusters. In [13], an adaptive GSTA control law is proposed that combines the state-and time-dependent robustness property of GSTA with adaptive STA's robustness to perturbations of unknown bounds. The GSTA control law has successfully been applied for underwater vehicles such as AUV [14] and underwater snake robots [13], [15], in addition to other types of vehicles (e.g., spacecraft [16] and quad-copters [17]).…”

“…In [13], an adaptive GSTA control law is proposed that combines the state-and time-dependent robustness property of GSTA with adaptive STA's robustness to perturbations of unknown bounds. The GSTA control law has successfully been applied for underwater vehicles such as AUV [14] and underwater snake robots [13], [15], in addition to other types of vehicles (e.g., spacecraft [16] and quad-copters [17]). In [14], GSTA was successfully applied in sea trials for an AUV to control depth and yaw.…”

Experimental validation of fuzzy type‐2 against type‐1 scheme applied in DC/DC converter integrated to a PEM fuel cell system

“…26 This tool is a dynamic extension that generates a continuous control integrated signal that shadows the discontinuity of the SMC. 27 A disadvantage of this structure is the slow convergence and settling time caused by the tuning gains. 28 However, to speed up the convergence, authors of Rakhtala and Casavola 29 have proposed a cascade structure for the STA.…”

“…Several solutions had appeared during the recent decades and probably the most efficient one is the super‐twisting algorithm (STA) 26 . This tool is a dynamic extension that generates a continuous control integrated signal that shadows the discontinuity of the SMC 27 . A disadvantage of this structure is the slow convergence and settling time caused by the tuning gains 28 .…”