Download Advanced Topics in Nonlinear Control Systems by T P Leung, Hua Shu Qin PDF

By T P Leung, Hua Shu Qin

During the last 50 years or so, a few textbooks, monographs or even renowned books were released on nonlinear keep watch over conception and layout equipment. within the zone of classical regulate, for instance, there exist books interested by phase-plane research, describing functionality method, absolute balance and so forth. within the region of recent keep watch over there are these regarding optimum keep watch over, utilizing differential geometry and the differential algebra procedure, variable structural keep watch over, H-infinite keep an eye on etc. those books were helpful in selling the improvement of computerized regulate technological know-how and know-how. for the reason that 1990 there were many new effects and contributions within the region of nonlinear regulate. This booklet introduces these themes to readers. it may additionally profit automation engineers, researchers and students in comparable fields.

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Example text

Precisely, let F, G, H be three smooth functions. 6 Integrability We consider the integrability of the distribution generated by the generalized Hamiltonian vector fields. 7), it is obvious that AM is a well defined distribution. Similarly, the unique decomposition of Massures that AJ,AR,AS,AJ_R,AS_R:=AP, spanned by the columns of the corresponding matrices, are all well defined distributions. Note that each column of them can not be considered as a vector field because it is coordinate-depending.

8) in a coordinate frame friend to A. • Finally, we consider a local version of pseudo-Hamiltonian vector fields. The following result for standard Hamiltonian vector fields remains true. 8 X is a local pseudo-Hamiltonian vector field iff ix is closed. When N is simply connected the conclusion is globally true. Prccf. Using Poincare's Lemma there exists a function H such that ixQ = XTW = dH it follows that X = W ~TVH = XH . 8 Structure group and its algebra The symplectic group and its symplectic algebra play an important role in the theory of Hamiltonian systems.

Let N =J = -I 0 We have symplectic group denoted by Sp(2n,R) with its Lie algebra, called symplectic algebra denoted by sp(2n, R). 3. Let N be a diagonal matrix as N = diag(-1,1,1,1). We have Lorentz group, which are useful in relativity etc. (Clarke 1979). D Through the dimension of g the dimension of G^ can be determined easily. 4 Suppose an nxn matrix N is non-singular. 1. Let N = H be symmetric. Thendim(Gfj) = «(w -1) / 2;Particularly, dim(SO(n,R)) = n(n -1)/2. 2. Let N = K be skew-symmetric.

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