Application of the Hamiltonian System in Deriving Solution to Dynamic System of the Sectoral Labour Market

  • Mary Mukuhi Mwangi University of Nairobi
  • Davis Bundi Ntwiga, PhD University of Nairobi
  • Moses Mwangi Manene, PhD University of Nairobi
  • Pokhariyal Ganesh Prasad, PhD University of Nairobi
Keywords: Hamiltonian System, Sectoral Labour Market, Labour Market Efforts, Optimal Control, Pontryagin’s Maximum Principle
Share Article:


The paper describes the application of the Hamiltonian System in deriving a solution to the dynamic system of the sectoral labour market. The aim is to determine the best control that would allow maximum sector participation in a three-sector labour market. The three sectors of the labour market are the goods-producing sector, the service-providing sector, and the agriculture sector. The sectoral labour market is formulated as an optimal control problem whose solution is sought using the Hamiltonian system by following the necessary conditions for optimality in the Hamiltonian System of Pontryagin’s Maximum Principle. The paper considered that the optimal control would be the measure of labour market efforts to produce the general worker’s population, and any split would mean there is production of active sector productive workers. The sector with the highest optimal allocation of effort, defined as the control within a fixed time, is identified as the best-performing sector. Service-providing sector, in this case, presented the best control. The obtained optimal control parameter is later applied to the experimental data to check on the effect of the control on the sectoral labour market participation rate. The results of the problem indicated that the application of the control had a significant effect on the sectoral labour market participation rate as compared to when there was no control. The sector with the highest annual growth rate measured as the sectoral participation rate was identified as the goods-producing sector


Download data is not yet available.


Aseev, S. M., and Kryazhimskiy, A. V (2005). The Pontryagin Maximum Principle and Transversality Condotions for a Class of Optimal Control Problems with Infinite Time Horizons. SIAM Journal on Control and Optimization, 43(3), 1094-1119.

Balseiro, O., Stichi, T., J., Cabrera, A., and Koller, J. (2017). About Simple Variational Splines. The Hamiltonian Viewpoint. Journal of Geometric Mechanics, 9 (3), 257290.

Chen, Z., Zhang, J., Arjovsky, M., and Bottou, L. (2020). Symplectic Recurrent Neutral Networks. 8th International Conference on Learning Representations (ICLR 2020).

Naz, R. (2022). A Current-Value Hamiltonian approach to discrete-time optimal control problems in economic growth theory. Journal of Difference Equations and Publication, 28(1) 109- 119.

Oruh, B. I., and Agwu, E. U. (2015). Application of Pontryagin’s Maximum Principles and Runge-Kutta Methods in Optimal Control Problems. IOSR Journal of Mathematics (IOSR-JM), 11 (5), 43-63.

Soumia, A., Kamel, K., and Noureddine, M. (2018). Application of Hamilton Equations to Dynamic System.

Tarasyev, A. M, Usova, A. A., and Tarasyev, A. A. (2022). Phase portraits of stabilised Hamiltonian systems in growth models. AIP Conference Proceedings 2425,110011(2022).

Tedrake, R. (2023). Under actuated Robotics: Algorithms for Walking, Running, Swimming, Flying, and Manipulation (Course Notes for MIT 6.832). Downloaded on 18/04/2023 from

25 August, 2023
How to Cite
Mwangi, M., Ntwiga, D., Manene, M., & Prasad, P. (2023). Application of the Hamiltonian System in Deriving Solution to Dynamic System of the Sectoral Labour Market. International Journal of Advanced Research, 6(1), 102-113.