Variational Method and Computation for H_∞ Control

The variational approach is further applied to the measurement feedback H_∞ control problems.Based on the induced norm description of the system Г,the variational functionals J_c and J_p of state feedback H_∞ control for the future time interval(t,t_f],and of H_∞ filter for the past time interval[0,t),respectively,are combined together to generate the variational functional of the measurement feedback for the whole time interval[0,t_f].The connection condition at the present time t is that the estimated state vector x(t) must be continuously extended to be the initial condition of the future state vector estimation.Another connection condition for the dual vector K(t)can be naturally derived from the variational principle.The equations thus derived show that the third condition for the optimal parameter γ_cr^-2 is again a bound of the smallest Rayleigh quotient.Therefore,the precise integration method developed formerly to determine the optimal parameter γ_cr^-2 of H_∞ control and of H_∞ filter respectively can be further applied to the determination of the optimal parameter.