Control of nonlinear systems with time-varying output constraints

Tracking error constrained adaptive dynamic surface control for a class of uncertain nonlinear systems

“…Lemma 1 (See [12], [11]) The following inequality holds for all £ in the interval |£| < 1 log < l-£ 2 l-£ :…”

“…Inspired by this, Tee, Ge, and Tay proposed novel asymmet ric BLFs and addressed the output constraints problem in [9]. Subsequently, in [10], [11], the results in [9] were ex tended to the time-varying output constraints case, by using a time-varying symmetric BLF and a time-varying asymmet ric BLF, respectively.…”

“…However, these widely adopted artincialintelligence-based techniques inherently introduce certain issues affecting closed loop stability and robustness and also increase the complexity of the proposed control schemes in the sense that extra adaptive parameters have to be updated, and thus making implementation difficult [7]. Besides these, the work of [11] considered uncertain bounded disturbances and designed an adaptive controller to handle them. In this paper, we investigate the BLF-based symmetric performance constraints problems for tracking control of a class of uncertain nonlinear systems.…”

“…In this paper, we investigate the BLF-based symmetric performance constraints problems for tracking control of a class of uncertain nonlinear systems. The uncertainties we consider here consist of both linearly parameterized uncer tainties and nonlinear function uncertainties, which are dif ferent from those in [9], where the uncertainties only con sists of the linearly parameterized ones, and the results in [11] can be included as a special case, for the unknown non linear function could be measurement noise, modeling er rors, external disturbances, modeling simplifications, and so on. The performance constraints are firstly characterized as a prescribed time-varying error bounding function.…”

Backstepping funnel control for prescribed performance of robotic manipulators with unknown dead zone

“…Recently, robust adaptive neural network control schemes have been investigated without constructing a dead-zone inverse and knowing some parameter bounds of dead-zones [9]- [12]. For dealing with the output constraints, a barrier Lyapunov function (BLF) is constructed by using the logarithmic function in the Lyapunov function design, where a symmetric or asymmetric constraint is utilized to constrain the state variable of the control system so that the tracking errors can be indirectly constrained [13]- [15]. On the other hand, the expression of BLF is complex, and it needs extra efforts to ensure the continuity and differentiability of BLF.…”