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Bilinear Robust Control Design for Virotherapy Model
Arum A.K.a, Saragih R.a, Handayani D.a
a Bandung Institute of Technology, Department of Mathematics, Bandung, 40132, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2019 Institute of Control, Robotics and Systems – ICROS.In this paper we concerned with the application bilinear robust control for virotherapy model. In designing the controller, it 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 step: firstly, 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. The virotherapy model has been widely developed and can be considered as a model in bilinear system. There are four groups in this model: quiescent cells (Q), cancer cells (S), virus (V), and infected cells (I). Virus are injected into the human body as the control input to control the amount of the cancer cells. In this case, virus can only infect the cancer cells, and the infected cells will die when the lysis process occurs. Virus, 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 disturbance to the model. From the simulation results, it is shown that virotherapy can reduce the number of cancer cells in the body on day 50th, so the number of cancer cells in the body is only 16.6%. Based on the simulation, the next virototherapy can be done after the day 50th.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Additive disturbance,Bilinear robust control,Bilinear system,Hamilton-Jacobi-Isaacs equations,State-dependent algebraic riccati equations,successive method,Time varying linear systems,Virotherapy[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]bilinear system,Robust control,successive method,virotherapy model[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.23919/ICCAS47443.2019.8971508[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]