ROBUST CONTROL DESIGN FOR BILINEAR SYSTEMS USING SUCCESSIVE METHOD

• Main Author: KESUMA ARUM (NIM: 20116026), ANITA
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/25639
• Institution: Institut Teknologi Bandung

Bilinear systems is the simplest class of nonlinear systems that represent many real physical processes. In the control bilinear system problems, it has the characteristic where the state of the system is multiplied by the control input. Disturbances is a factor that can interfere the work process of the system, so it is possible for the output of the system to be not in accordance with the desired output. Thus a robust controller must be found to make the system produce the desired output. This controller requires a solution to the state dependent algebraic Riccati equation (SDARE). However it is difficult to solve the SDARE. Successive method is one of the methods that can be used to solve this issue. The idea of this method is converting the bilinear systems into time-varying linear system. This method has the following steps : first, we need to obtain the robust control for the linear system by ignoring the multiplicative term of bilinear system. Second, convert the bilinear systems into the time-varying linear systems using the previous result, and then solve the SDARE by the new performance index and the associated Hamilton-Jacobi-Isaacs equation. Last, iterate the steps until the convergence of state satisfied. In this study, successive method were applied in virotherapy control problems. The virotherapy model has been widely developed, one of which is the cell cycle-specific model. This model is a bilinear systems. There are four compartment in this model: quiescent cells (Q), cancer cells (S), viruses (V), and infected cells (I). Viruses are injected into the human body as the control input to control the amount of the cancer cells. In this case viruses can only infect the cancer cells, and the infected cells will die when the lysis process occurs. Viruses, as a control, is given with the aim of minimizing the energy used in the system. In this model we consider the body’s immune response as an additive disturbances to the model. With the successive method, the problems in this model can be solved. Therefore we can always find the perfect strategy to control the cancer cells.