An Algorithm for Finding Feedback in a Problem with Constraints for One Class of Nonlinear Control Systems

We consider the construction of a feedback according to Kalman algorithm for continuous nonlinear control system on finite time interval with constraints where right-hand side dynamics equations is linear in and linearizable vicinity zero equilibrium position. The solution an auxiliary optimal problem quadratic functional used this task by analogy SDRE approach. Because approach literature find suboptimal synthesis problems formally systems all coefficient matrices differential criteria can contain state variables, it becomes necessary solve complicated matrix Riccati state-dependent matrices. Due nonlinearity issue significantly increases number calculations obtaining coefficients gain given accuracy comparison linear-quadratic problems. proposed constructed using extension principle V.F. Krotov developed V.I. Gurman allows one not only expand scope form closed inequalities, but also propose more efficient computational finding gains interval. This article establishes correctness application introducing analogs Lagrange multipliers, which depend time, derives formula value quality criterion. presented theoretical results are illustrated calculating feedbacks managing three-sector economic systems.