The variational approach is further applied to the measurement feedback H ∞ control problems. Based on the induced norm description of the system Γ,the variational functionals J c and J p of state feedback H ...The variational approach is further applied to the measurement feedback H ∞ control problems. Based on the induced norm description of the system Γ,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 (t) must be continuously extended to be the initial condition of the future state vector estimation. Another connection condition for the dual vector λ(t) can be naturally derived from the variational principle. The equations thus derived show that the third condition for the optimal parameter γ -2 cr is again a bound of the smallest Rayleigh quotient. Therefore, the precise integration method developed formerly to determine the optimal parameter γ -2 cr of H ∞ control and of H ∞ filter respectively can be further applied to the determination of the optimal parameter.展开更多
文摘The variational approach is further applied to the measurement feedback H ∞ control problems. Based on the induced norm description of the system Γ,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 (t) must be continuously extended to be the initial condition of the future state vector estimation. Another connection condition for the dual vector λ(t) can be naturally derived from the variational principle. The equations thus derived show that the third condition for the optimal parameter γ -2 cr is again a bound of the smallest Rayleigh quotient. Therefore, the precise integration method developed formerly to determine the optimal parameter γ -2 cr of H ∞ control and of H ∞ filter respectively can be further applied to the determination of the optimal parameter.
