### Table . Solutions of nonlinear systems (8)

Cited by 1

### Table 6.3 Asymptotic complexity for nonlinear systems.

2003

Cited by 9

### Table 5.2. The total costs for the real nonlinear system

### Table 5.2. The total costs for the real nonlinear system

### Table 4. Fuzzy systems of nonlinear plant.

"... In PAGE 9: ... The interpretability-driven simplification methods and the multi-objective genetic algorithm are used to optimize the initial fuzzy system. The performance of the obtained four Pareto-optimal fuzzy systems is described in Table4 . The decision-marker can choose an appropriate fuzzy system according to a specific situation, either the one with higher interpretability (less number of fuzzy rules or/and fuzzy sets) or the one with less error.... In PAGE 9: ... The decision-marker can choose an appropriate fuzzy system according to a specific situation, either the one with higher interpretability (less number of fuzzy rules or/and fuzzy sets) or the one with less error. Table4 also shows the comparison with other published results, which indicates that the proposed -2 -1.5 -1 -0.... ..."

### Table 2. Fuzzy systems of nonlinear plant.

### Table 4.2: Comparison of computation time to integrating original nonlinear system and its quadratic and linear reduced systems

1999

Cited by 7

### Table 2. Reduced-order transfer function and standard deviation matrices for the nonlinear system of (18)~(19)

"... In PAGE 7: ... A reduced model here is required to be of the third-order in the application of a controller design. The transfer functions and RMS errors of a reduced model obtained by Gong and Murray-Smith (1993) are shown in the first row of Table2 . To compare with the complex curve-fitting technique, the hybrid EA has been applied to the original model to evolve reduced models for 10 minutes on a 100 MHz Pentium PC.... In PAGE 7: ... To compare with the complex curve-fitting technique, the hybrid EA has been applied to the original model to evolve reduced models for 10 minutes on a 100 MHz Pentium PC. The results are shown in the middle row of Table2 . It can be derived that the evolved model provides an improved reduction quality by 7.... In PAGE 8: ... For this variable-order reduction task, the evolution revealed that a first- order reduced model should be used because of the penalty on the order number. This model is shown in the last row of Table2 . It can be seen that it offers a reduction quality almost as high as the fixed third-order model, and better than that obtained by Gong and Murray-Smith (1993).... ..."

### Table 3. Reduced-order transfer function and standard deviation matrices for the nonlinear system of (20)

"... In PAGE 9: ... Giving the order trade-off in the form of (13) and (14), the EA tends to suggest a first-order reduced model as the overall choice. At the end of the evolution, the best model and its corresponding RMS errors are shown in the first row of Table3 . For a fixed-order linearisation problem, Tan et al.... In PAGE 9: ... For a fixed-order linearisation problem, Tan et al. (1995) reported a second-order linearised model and the results are as shown in the last row of Table3 . Note that the first-order model obtained by the joint order optimisation approach here offers an even smaller overall RMS error than the second-order model.... ..."

### Table 2: The first six differential invariants for nonlinear systems in the plane V = K2 with quadratic coefficients. All sums are from 1 to 2.

in The Symbolic Computation of Differential Invariants of Polynomial Vector Field Systems Using Trees ∗

1995

"... In PAGE 2: ...easily computed in terms of a few basic operations on the space of trees. Our main result is expressed in Theorem 5 and illustrated in Figure 2 and Table2 . It provides a simple and direct combinatorial means of computing dif- ferential invariants.... In PAGE 4: ... Differential invariants are naturally expressed and easily computed in terms of a few basic operations on the space of trees. Our main result is expressed in Theorem 5 and illustrated in Figure 2 and Table2 . It provides a simple and direct combinatorial means of computing dif- ferential invariants.... In PAGE 8: ... This can be done either by hand or using DIFF-INV. See [11], for example and Table2 . Given the differential polynomials, one can then compute a basis using standard symbolic packages.... In PAGE 10: ...for planar systems with quadratic coefficients listed in Table2 . Except for I2, this is the same invariant basis as in Sibursky [11].... ..."