Subspace identification of stable nonnegative and compartmental dynamical systems via constrained optimization

Nonnegative and compartmental dynamical system models are widespread in biological, physiological, and ecological sciences and play a key role in understanding these processes. In the specific field of pharmacokinetics involving the study of drug concentrations (in various tissue groups) as a function of time and dose, nonnegative and compartmental models are vital in understanding system wide effects of pharmacological agents. These systems are stable with nonnegative system matrices. In this paper, we present a constrained optimization framework for nonnegative and compartmental system identification that guarantees asymptotic stability of the plant system dynamics as well as the nonnegativity of the system matrices. Our approach is based on a subspace identification method wherein the resulting constrained optimization problem is cast as a convex linear programming problem with mixed equality, inequality, quadratic, and nonnegative-definite constraints. Finally, several examples are presented to illustrate the utility of the proposed approach.