Model-based Angiogenic Inhibition of Tumor Growth using Modern Robust Control Method

Cancer is one of the most destructive and lethal illnesses of the modern civilization. In the last decades, clinical cancer research shifted towards molecular targeted therapies which have limited side e�ects in comparison to conventional chemotherapy and radiation therapy. Anti-angiogenic therapy is one of the most promising cancer treatment methods. The dynamical model for tumor growth under angiogenic stimulator/inhibitor control was posed by Hahnfeldt et al. (1999), and it was investigated and partly modi�ed many times. In this paper, a modi�ed version of the originally published model is used in order to describe a continuous infusion therapy. To generalize individualized therapies a robust control method is proposed using H 1 methodology. Uncertainty weighting functions are determined based on the real pathophysiological case and simulations are performed on di�erent tumor volumes to demonstrate the robustness of the proposed method

Comparison of Path Tracking Flat Control and Working Point Linearization Based Set Point Control of Tumor Growth with Angiogenic Inhibition

Targeted molecular therapies (TMT) represent new perspectives in cancer treatment, fighting against the specific characteristic of the investigated tumor. Antiangiogenic therapy represents a specific TMT and its role is to stop the angiogenesis of the tumor, the process of forming new blood vessels; hence, to stop tumor growth. Proper control algorithms for tumor growth control with angiogenic inhibition are analyzed in the current article in order to find optimal therapeutic protocols. Two slightly different approaches are compared: nonlinear control by exact linearization with path tracking control, and linear control by working point linearization with set point control. The control strategies are compared in terms of the characteristics of the input signal (the inhibitor, drug intake) that is crucial if the therapy will be put into practice

A NEW TYPE OF DISCRETE EULER-LAGRANGE EQUATION WITH APPLICATIONS IN OPTIMAL CONTROL

A new type of discrete Euler-Lagrange equation, suitable for generalization, is presented in this paper. Several forms of this equation can be found in references. They have different differential operators as well as combinations of them. The equation given in this paper uses only one differential operator providing easy generalizations of Euler-Lagrange equation. In the paper, generalizations for the case of more variables and more ordered differences in the functional which is optimized, are derived. The application in determining optimal control of a discrete system is also given

Lorenz System Stabilization Using Fuzzy Controllers

The paper suggests a Takagi Sugeno (TS) fuzzy logic controller (FLC) designed to stabilize the Lorentz chaotic systems. The stability analysis of the fuzzy control system is performed using Barbashin-Krasovskii theorem. This paper proves that if the derivative of Lyapunov function is negative semi-definite for each fuzzy rule then the controlled Lorentz system is asymptotically stable in the sense of Lyapunov. The stability theorem suggested here offers sufficient conditions for the stability of the Lorenz system controlled by TS FLCs. An illustrative example describes the application of the new stability analysis method

An Approach to Fuzzy Modeling of Electromagnetic Actuated Clutch Systems

This paper proposes an approach to fuzzy modeling of a nonlinear servo system application represented by an electromagnetic actuated clutch system. The nonlinear model of the process is simplified and linearized around several operating points of the input-output static map of the process. Discrete-time Takagi-Sugeno (T-S) fuzzy models of the processes are derived on the basis of the modal equivalence principle; the rule consequents of these T-S fuzzy models contain the state-space models of the process. Three discrete-time T-S fuzzy models are suggested and compared. The simulation results validate the new fuzzy models of the electromagnetic actuated clutch system