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This paper considers the optimal control problem for time-delay bilinear systems affected by sinusoidal disturbances with known frequency and measurable amplitude and phase. Firstly, using the differential homeomorphism, a time-delay bilinear system affected by sinusoidal disturbances is changed to a time-delay pseudo linear system through the coordinate transformation. Then the system with time-delay in control variable is transformed to a linear controllable system without delay using model transformation. At last based on the theory of linear quadratic optimal control, an optimal control law which is used to eliminate the influence of the disturbances is derived from a Riccati equation and Matrix equations. The simulation results show the effectiveness of the method.
Objective: To compare efficacy of therapy scheme as Transhepatic Artery Chemoembolization (TACE) + Radiofrequency Ablation (RFA) + Introportal Vein Chemotherapy (PVC) + Percutaneous Ethanol Injection (PEI) therapy (quadruplet group) with TACE + RFA combinational therapy (diad group) in treating hepatocellular carcinoma (HCC). Methods: 25 cases in quadruplet group were treated by TACE for 3 weeks, then by RFA, after 2 months, by PVC + PEI; 23 cases in diad group were treated by TACE for 3 weeks and then by PEI. After completion of each treatment course in both groups, Alphafetoprotein (AFP) was tested 2 months later; abdomen colorful doppler, CT and AFP were retested 6 months later. Results: AFP was significantly decreased in 23 cases of quadruplet group and 20 cases of diad group among those with AFP positive results. 6 months later, examinations of CT, colorful Doppler and AFP in two groups showed: quadruplet group has significantly decreased (X2 = 6.81, P < 0.01) blood supply of cancer tissue and significantly diminished (X2 = 8.29, P < 0.01) tumor size, few cases with AFP elevation (X2 = 5.06, P < 0.05); lower 1 year relapse rate and two years mortality than that in diad group (X2 = 5.30, P < 0.05). Conclusion: TACE +