The regularization of the Green's function removes its singularity by introducing a regularization radius which is related to the discretization length and hence imposes a minimum resolved scale.
By introducing a modified Lyapunov function, a smooth and singularity-free adaptive controller is firstly designed for a first-order plant.
By introducing a double iterative technique, in the case of the nonlinearity with singularity at time and space variables, the unique positive solution to the problem is established.
By introducing a domain transformation in the z-direction, we solve the corresponding complex difference equations containing an interface singularity over a computational space for great simplicity and efficiency.
The problem of matrix singularity for this class of systems is solved by using the property of the regularized inverse and by introducing a compensator term in the proposed control law.
A recent paper by these authors introduced a singularity avoidance algorithm for the 3-RRR mechanism using kinematic redundancy.
The problem was reduced to a three-material wedge singularity type by introducing several curvilinear coordinate systems and systematic expansions in power series of the distance from the contour of the stress singularity.
For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent funciton.
In addition, the number of the online adaptive parameters is not more than the order of the considered system and the possible controller singularity problem is removed by introducing the modified integral Lyapunov functions.
In this paper, the above singularity problem has been solved by introducing side conditions without sacrifice of convergence.
