Feedback linearization and optimal control-based approach for steering steady-states of nonlinear biochemical networks

Biochemical networks normally operate in the neighbourhood of its steady-state which may be of multiple in number. It may reach from one steady-state to other within a finite time. In this paper, it is shown how the biochemical network reaches to a desired steady-state within optimal time and energy, with positive control input. Control signals i.e., the independent state variables in the network, are found in two steps. The first step is designed for steering biochemical network to a desired state within a finite time and then, in the second step, the steered state is preserved as a steady-state of the network. In the first step, the synergism and saturation system, commonly known as S-system, is transformed to the linear controllable Brunovsky Canonical form using feedback linearization and then the optimal control theory is used to find optimal control input. In second step, the control inputs are found from steady-state equations for the new steady-state. In this article, it is shown how to select control inputs so that, biochemical network will reach to a desired steady-state applying a feasible control input profile instead of designing a complex feedback path.