Full Text: PDF
DOI: 10.23952/cot.2022.18
Received October 20, 2021; Accepted September 2, 2022; Published October 24, 2022
Abstract. In the paper, the problem of dynamic reconstruction of controls and trajectories for deterministic control-affine systems is considered. The reconstruction is performed in real time using known discrete inaccurate measurements of the observed trajectory of the system. This trajectory is generated by an unknown measurable control that satisfies known geometrical restrictions. In this paper, the case of non-convex restrictions is considered. In the previous works, the authors of this paper considered only convex restrictions. To describe the motion of the system with non-convex control restrictions, generalized dynamics and controls are introduced. A well-posed statement of the dynamic reconstruction problem is given. An algorithm for construction of approximations of the solution is proposed and justified. It is based on the variational approach developed by the authors. This approach uses auxiliary variational problems with regularized integral residual functionals. The key feature of the approach is that the integrants of the functionals in the auxiliary variational problems are d.c. functions. The suggested algorithm reduces the dynamic reconstruction problem to integration of Hamiltonian systems of ordinary linear differential equations. The results of numerical simulation are demonstrated.
How to Cite this Article:
N. Subbotina, E. Krupennikov, To the dynamic reconstruction problem with non-convex geometrical restrictions on the controls, Commun. Optim. Theory 2022 (2022) 18.