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Based on the solution of the linear state equation, the mean square envelope matrix can be obtained for a linear approximation to the controlled nonlinear system, and the transfer rule of mean square envelope matrix for the nonlinear system is discussed. By making of the Taylor expansion, the nonlinear state equation of controlled systems under ideal state is transformed to a set of ordinary differential...
To controlled systems under deterministic and random trade-off state, it is presented by general Langevin gradient equation while dynamic variational rule of the systems is described. The nonlinear differential equation is equivalent to its nonlinear Volterra's integral equation of the second kind, and any order approximate solution of the equation is also obtained, by successive approximation method...
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