HOMEWORK SET NO. 2
Problem 1:
(a) For the project topic that you have selected, formulate a meaningful parameter estimation problem based on recursive least squares. The parameter estimation could be intended for purposes of adaptive control or simply for system identification. Show your equations in regression form, and indicate reasonable initial values for the parameter estimates and for the estimation gain (covariance) matrix.
(b) Utilize the formulation in part (a) to carry out the following parameter estimation studies: (i) unknown but constant parameters, (ii) a step change in the parameters from -50% of their nominal values to +50% of their nominal values. Utilize any appropriate simulation software (e.g., Matlab, MatrixX) or write your own program as desired.
Problem 2:
Consider the following discrete-time system:
y(t+1) = q1[y(t)3 + q2y(t)u(t) + exp(q3)u(t)]
Rearrange the equation into regression form, so that the parameters can be estimated using the recursive least squares (RLS) algorithm. Define clearly the parameter and measurement vectors for use in the RLS. Can the algorithm be applied even though the system is nonlinear? Why?
Problem 3:
Problem 2.2 from your textbook.
Problem 4:
The RLS with exponential forgetting is given in Equation (2.21) of your textbook. Derive this algorithm following the derivation of the basic RLS algorithm that we went over in class.
Problem 5:
Problem 2.8 from your textbook.