The Optimal Control Problem with Fixed-End Trajectories for a Three-Sector Economic Model of a Cluster

Problems of Optimal Control for a Class of Linear and Nonlinear Systems of the Economic Model of a Cluster

“…In practice, there is a large number of optimal control tasks for economic systems that are nonlinear systems with coe±cients that depend on the state of the control object. In this paper, in contrast to the paper by Murzabekov et al, 17 Sec. 3 is supplemented.…”

“…it is required to ensure the optimal path through speci¯ed start and end points. This part is considered in the works of Murzabekov et al 17…”

Stabilization of one nonlinear system with coefficients depending on the condition of the control object

“…The equilibrium position in a closed system is asymptotically stable according to Lyapunov. Controlling parameters (19)- (21) are chosen in such a way that constraints on controls and balance relations (3)- (5) are satisfied. For the considered example, the optimal distribution of labor and investment resources has been determined, which satisfy the balance ratios.…”

“…Orlov [15] consider a class of nonlinear systems for which there exists a coordinate representation (diffeomorphism) that transforms the original system into a system with a linear part and nonlinear feedback. In works [20,21], optimal control problems with using of Lagrange multipliers for technical systems and a linearized system of the economic cluster were considered.…”

“…and matrix R, Q 1 , K, have a form: Using formulas (19)- (21), the optimal distribution of labor (θ 1 (t), θ 2 (t), θ 3 (t)) and investment resources (s 1 (t), s 2 (t), s 3 (t)) was determined. Figure 2 shows the changes resources that satisfy the balance relations (3)- (5).…”