Question

Consider the nonlinear system i = a f(x) + a2f2(x) +6181(x)u +6282(x)u, where u, x E R; figi are known nonlinear functions of x; and a, b, are unknown constant parameters and i = 1, 2. The system is such that u € Lo implies x € Lo. Assuming that x, u can be measured at each time 1, design an estimation scheme for estimating the unknown parameters online.Use the series-parallel model to design the estimator, derive the adaptive parameter estimation algorithm, and analyze the stability and convergence properties of the method.

Answer 1

To estimate unknown parameters in a nonlinear system, one must derive an adaptive parameter estimation algorithm, measure variables, and analyze the estimator's stability and convergence.

Step-by-step explanation:

The student is tasked with designing an online estimation scheme for unknown parameters in a nonlinear system using a series-parallel model. The scheme involves measuring variables at each time to update the estimation of parameters a and b. Here is a step-by-step approach:

1. Set up the regressor vector with measurable signals and the unknown parameters.
2. Choose a suitable algorithm for updating parameter estimates online.
3. Analyze the properties of the estimator, ensuring stability and convergence.

To successfully estimate the unknown parameters a and b, one must derive an adaptive algorithm based on the regressive form of the system and the measurable variables. The stability and convergence analysis involves looking at the behavior of the error between the actual parameters and the estimates over time.