Nonlinear Adaptive Control of Bipolar Mood Disorder: A New Approach for Quenching the Mood Swing.

Background/Objectives: Mood disorders are described by marked disruptions in emotions. Generally speaking, mood disorders are classified into two main categories: unipolar mood disorder, also known as unipolar depression, and bipolar mood disorder, also called manic-depressive illness. It is estimated that 40 million people live with bipolar disorder worldwide. Mathematical modeling of the dynamics of bipolar disorder may help to both better understand and treat the illness. This is especially important for bipolar disorder since, unlike unipolar disorder, there is an oscillation to be quenched between hypomanic and depressive episodes. Methods: By using a nonlinear dynamical model of bipolar disorder, this study offers two different control (treatment) approaches for the disorder. The first one is a nonlinear exact model knowledge controller assuming that all the parameters of the patient model are known. The second one is a nonlinear adaptive controller assuming that all the parameters are unknown. Results: Both controllers aim to drive both emotional mood and the change rate to a stable state. The Backstepping Technique is utilized as a nonlinear controller design tool. For both controllers, Lyapunov-type arguments are used to design the controller and to prove the stability of the designed controllers. Numerical simulation results are also provided to show the performance and feasibility of the proposed controllers. Conclusions: It has been shown that a nonlinear controller is capable of driving the emotional mood to its equilibrium point, zero, by quenching the mood swing.