Sentence examples for trajectory of error from inspiring English sources

The time derivative of V along the trajectory of error system (5) is V ˙ = e T e ˙ + e θ T e ˙ θ + e β T e ˙ β = e T e ˙ + e θ T ( − θ ˙ r ) + e β T ( − β ˙ r ).

In addition, based on the same finite-time stability theory and the same sliding mode control, we ensure that the trajectory of error system converges to a chosen sliding surface within finite time and remains on it forever.

For example, Wiersema and colleagues [ 6] examined the developmental trajectory of error processing in children (aged 7-8), young adolescent 13-144), adultsults (age 23-24).

Figure 5 The trajectories of error signals (pmb{e_{i1}}), (pmb{e_{i2}}), (pmb{e_{i3}}) ( (pmb{i=1,2,3,4}) ) for system in Example 4.3 with pinning impulsive control.

Figure 2 The trajectories of error signals (pmb{e_{11}}), (pmb{e_{12}}), (pmb{e_{21}}), (pmb{e_{22}}) for system in Example 4.1 with pinning impulsive control.

Figure 3 The trajectories of error signals (pmb{e_{i1}}), (pmb{e_{i2}}) ( (pmb{i=1,2,3,4}) ) for system in Example 4.2 with pinning impulsive control.

In addition, an appropriate sliding mode controller is designed to drive the state trajectories of error system to the prescribed sliding surface in finite time and remain on it evermore.

Under the action of adaptive controller (4), taking the initial conditions as x ( 0 ) = ( 1.2, − 0.8 ) T and y ( 0 ) = ( − 12, 8 ) T, α = β = 0.1, we show the state trajectories of error system (2) and updated laws in adaptive controller (4) in Figures 2-4, respectively.

Figure 5 State trajectories of errors (pmb{e_{1} k)}).

In other words, an integral sliding mode controller is designed such that the sliding motion is globally asymptotically stable, and the state trajectory of the error system (4) is globally driven onto the specified sliding surface and maintained there for all subsequent time.

Table 2 shows average and standard deviation of trajectory tracking error of each method.