Demonstration of a Stochastic Analysis Technique for Nonlinear Dynamical Systems.
Final rept. Sep 78-Sep 79,
STEVENS INST OF TECH HOBOKEN N J DAVIDSON LAB
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In order to demonstrate a promising technique, the control gain for a nonlinear, first order system with limited control and with random input, required to obtain a limited range of state with given likelihood is evaluated. The proposed technique is based on a series approximation for the solution of the partial differential equation for the joint probability density function of the state variable, i.e., the Fokker-Planck Equation. For the simple illustrative example, the exact stationary density function is found to give control gains in good agreement with the proposed series approximation technique. The exact and approximate variances of state are also found in good agreement, but the fourth order moments begin to show some discrepancy and the detailed density functions do not show good agreement. However, for many control problems and for system performance analysis, accurate prediction of means and second order moments is sufficient, as was found for the illustrate example. The series solution technique is further demonstrated by calculating the transient state density function with given initial condition for the same nonlinear, first order system. The results are discussed and elaborated in order to indicate the significance of this promising technique. Author
- Statistics and Probability