Universal Fuzzy Controllers for Non-affine Nonlinear Systems by Qing Gao

By Qing Gao

This thesis presents a scientific and crucial solution to an open challenge about the universality of dynamic fuzzy controllers. It offers a few novel principles and methods to numerous concerns together with common functionality approximation, common fuzzy versions, common fuzzy stabilization controllers, and common fuzzy fundamental sliding mode controllers. The proposed keep an eye on layout standards may be very easily demonstrated utilizing the MATLAB toolbox. furthermore, the thesis presents a brand new, easy-to-use type of fuzzy variable constitution regulate. Emphasis is given to the purpose that, within the context of deterministic/stochastic platforms generally, the authors are in reality discussing non-affine nonlinear structures utilizing a category of generalized T-S fuzzy types, which supply huge capability in a variety of applications.

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By Qing Gao

This thesis presents a scientific and crucial solution to an open challenge about the universality of dynamic fuzzy controllers. It offers a few novel principles and methods to numerous concerns together with common functionality approximation, common fuzzy versions, common fuzzy stabilization controllers, and common fuzzy fundamental sliding mode controllers. The proposed keep an eye on layout standards may be very easily demonstrated utilizing the MATLAB toolbox. furthermore, the thesis presents a brand new, easy-to-use type of fuzzy variable constitution regulate. Emphasis is given to the purpose that, within the context of deterministic/stochastic platforms generally, the authors are in reality discussing non-affine nonlinear structures utilizing a category of generalized T-S fuzzy types, which supply huge capability in a variety of applications.

Show description

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Extra info for Universal Fuzzy Controllers for Non-affine Nonlinear Systems

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Sontag, E. , & Wang, Y. (1996). A smooth converse Lyapunov theorem for robust stability. SIAM Journal on Control and Optimization, 34(1), 124–160. 43. , Cao, C. , & Lavretsky, E. (2006). Control of a nonaffine doublependulum system via dynamic inversion and time-scale separation. Proceedings of the 2006 American Control Conference (pp. 1820–1825), Minneapolis, Minnesota, USA. 44. Cao, S. , Rees, N. , & Feng, G. (1999). Analysis and design of fuzzy control systems using dynamic fuzzy-state space models.

Thus the proof is completed. 1 provides a constructive procedure to obtain the generalized T–S model with the aid of the following fact. 1 The matrix function Q(x) = [Q i j (x)] ∈ ij ij ij μl (x)ql , μl (x) ≥ 0 and Q l˜ where Q l˜ ∈ m×n r0 l=1 m×n where Q i j (x) = ij μl (x) = 1, can be rewritten as Q(x) = , νl˜(x) ≥ 0 and r0m×n ˜ l=1 r0m×n ˜ l=1 r0 l=1 νl˜(x) νl˜(x) = 1. Proof We first define L0 = {1, . . , r0 }, I = {1, . . , m}, J = {1, . . , n} and ij L˜0 = {1, . . , r0m×n }. Let Q l˜ = [qk ˜(i, j) ], where i ∈ I , j ∈ J , l˜ ∈ L˜0 and l kl˜(i, j) : I × J → L0 .

1993). Variable structure control of nonlinear systems: a new approach. IEEE Transactions on Industrial Electronics, 40(1), 45–55. 136. , & Wu, B. (1998). “Design of fuzzy sliding-mode control systems,”. Fuzzy Sets and Systems, 95(3), 295–306. 137. , & Xia, Y. (2010). Robust adaptive sliding-mode control for fuzzy systems with mismatched uncertainties. IEEE Transactions on Fuzzy Systems, 18(4), 700–711. 138. , & Lee, T. H. (2005). Stabilization of uncertain fuzzy time-delay systems via variable structure control approach.

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