Optimal Control of R & D Investment in a Techno-Metabolic System

The nonlinear model of economic growth involving production, technology stock and their rates is considered. Two trends - growth and decline, in interaction between production and R&D investment are examined in the balance dynamics. The optimal control problem of R&D investment is studied for the balance dynamics and discounted utility function of consumption index. Pontryagin's optimality principle is applied for designing optimal nonlinear dynamics. The existence and uniqueness result is proved for the saddle type equilibrium and the convergence property of optimal trajectories is shown. Quasioptimal feedbacks of the rational type for balancing the dynamical system are proposed. Growth properties of production rate, R&D intensity and technology intensity are examined on generated trajectories. In the test example explicit formulas for the optimal feedback and the value function are obtained