By Jeffrey T. Spooner, Manfredi Maggiore, Raúl Ordóñez, Kevin M. Passino
Contains a answer handbook for problems.Provides MATLAB code for examples and solutions.Deals with powerful platforms in either concept and perform.
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Extra resources for Stable Adaptive Control and Estimation for Nonlinear Systems: Neural and Fuzzy Approximator Techniques
Note that f&74 = 4 -ax + bu) = -ax2 + bxu. 83) Choose $(lul) = 1~1. N ow we must show that when (xl > $([u() we can . find an appropriate 73. 82) is input-to-state stable. Sec. 7 Special Classes 41 of Systems As another simple example, for the interconnected the two-dimensional ordinary differential equation ,j II -dy system case, consider + cx, where a > 0 and d > 0. We can think of the x-subsystem as generating trajectories to input to the y-subsystem. Choose VR: = yzl = yz. = $x2, and S;, = yYl = yy2 = $y”.
Uniformly asymptotically stable: If V(t, x) is continuously differentia,ble, positive definite, and decrescent, with negative definite lii(&x), then xe = 0 is uniformly asymptotically stable (uniformly Sec. 5 Lyapunov’s Direct Method a#symptotically ally). 55) -Y3(/4) for all t 2 0 and 12;E Bh for some h > 0, then 2, = 0 is uniformly asymptotically stable. 55) hold for all it: E R” and 73 E La t > 0, then 2, = 0 is uniformly asymptotically stable in the large. 43) are uniformly bounded and lim W(X@)) = 0.
Notice that each of these is a global property of a system in the sensethat they apply to trajectories (solutions) of the system that can be defined over all of the state space. 52) I~k~o,~o>l < P for all t > to > 0. A system is said to possessLagrange stability each to > 0 and x0 E R”, the solution z(t, to, x0) is bounded. if for Notice that if an equilibrium is asymptotically stable in the large or exponentially stable in the large then the system for which the equilibrium is defined is also Lagrange stable (but not necessarily vice versa).
Stable Adaptive Control and Estimation for Nonlinear Systems: Neural and Fuzzy Approximator Techniques by Jeffrey T. Spooner, Manfredi Maggiore, Raúl Ordóñez, Kevin M. Passino