This article involves the adaptive inverse control of 1 a coupled vessel-riser system with input backlash and system 2 uncertainties. By introducing an adaptive inverse dynamics of 3 backlash, the backlash control input is divided into a mis-4 match error and an expected control command, and then a 5 novel adaptive inverse control strategy is established to elim-6 inate vibration, tackle backlash, and compensate for system 7 uncertainties. The bounded stability of the controlled system 8 is analyzed and demonstrated by exploiting the Lyapunov's 9 criterion. The simulation comparison experiments are finally 10 presented to verify the feasibility and effectiveness of the control 11 algorithm. 12 Index Terms-Adaptive inverse control, boundary control, 13 flexible risers, input backlash, vibration control. 14 I. INTRODUCTION 15 A DAPTIVE control as a common method for handling 16 parametric uncertainty, provides techniques and algo-17 rithms for parameter estimation and is introduced in many 18 literatures [1]-[6]. In recent decades, significant advance-19 ments in adaptive control for the nonlinear systems have 20 been documented. To list some, in [7] and [8], switched 21 nonlinear systems were stabilized by developing an adap-22 tive neural tracking control and the semiglobal boundedness 23 was ensured. In [9]-[11], an adaptive finite-time convergence 24 Manuscript o f o f d d e. for flexible riser systems with nonsmooth input nonlinear 71 constraints. 72 In recent years, significant attention has focused on con-73 trol of nonlinear systems subject to input nonlinearities, such 74 as backlash, deadzone, saturation, and hysteresis [47]-[53], 75 which are common and tough issues in mechanical 76 connections, piezoelectric translators, and hydraulic servo 77 valves [54]-[56]. Recently, boundary control has achieved 78 rapid development on handling the input constraints in flex-79 ible riser systems [57]-[59]. In [60], an input-restricted riser 80 system was significantly stabilized by using anti-saturation 81 vibration control strategies. In [57], backstepping technique 82 was employed to construct an adaptive control for riser 83 systems to resolve the oscillation elimination, input saturation, 84 and output constraint. Further, anti-saturation control strate-85 gies were presented to restrain the oscillation of flexible risers 86 with input constraint by introducing the Nussbaum function 87 in [58]. Note that the chattering phenomenon caused by the 88 discontinuous sign function in [57] was removed. In [59], 89 hybrid input deadzone and saturation constraint issue in the 90 riser system was addressed by exploiting the auxiliary function 91 to propose a boundary control law. However, in the aforemen-92 tioned research, the design was confined to eliminate vibration, 93 tackle input saturation, or eliminate mixed input deadzone and 94 saturation in the riser system. 95 However, the effect of the input backlash nonlinearity char-96 acteristic was not considered in these mentioned literatures. 97 Backlash, which describ...
