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The resulting nonlinear feedback control law yields convergence of the path following error trajectories to zero.
The closed-loop system is analyzed showing uniformly ultimately boundedness of the error trajectories.
Figure 5 Synchronization error trajectories (pmb{e_{i1}(t)}), (pmb{i=1,ldots,8}).
A novel parameter mapping is proposed to obtain a simple relationship between the design parameter and the ultimate bounds of error trajectories.
Also, it is shown that the asymptotic convergence of the estimation error trajectories is shaped by the landmark geometry and observer design parameters.
This phenomenon is better investigated in Figure 15b and 15c where different error trajectories for the initial 4 s are shown for MMSES and BJ, respectively.
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Error trajectory controllers offer the advantage of being index one differential-algebraic problems with no associated initialization difficulties.
This formulation, which uses the concept of a tracking error trajectory in a differential geometric setting, provides a framework for direct comparison of a number of recently proposed nonlinear process controllers.
The algorithm repeatedly identifies the currently worst resolved parameter (a), orthogonalizes the corresponding full trajectory with the current reduced space (b), computes a POD of the error trajectory (c), and inserts the dominant mode into the basis (d).
In this situation any suitable controller can only provide the boundedness of the tracking-error trajectories within a bounded zone with probability one.
In this paper we suggest designing of both the control and observer "optimal" gain-matrices minimizing the "size" of the attractive ellipsoid containing all tracking-error trajectories in the vicinity of the origin.
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