12.2.1  Solution to the Finite-Horizon Discrete-Time Mixed H2/H Nonlinear Filtering Problem

We similarly consider the following class of estimators:

daf:{ x^k+1=f(xk)+L(x^k,k)[ ykh2(xk) ],x^(k0)=x^0z^=h1(x^k)


where x^kX is the estimated state, L(.,.)n×m(X×Z) is the error-gain matrix which is smooth and has to be determined, and z^s is the estimated output of the filter. We can now define the estimation error or penalty variable, z, which has to be controlled as:


Then, we combine the plant (12.42) and estimator (12.46) dynamics to obtain the following augmented system:





Get Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.