Full Text: PDF
DOI: 10.23952/cot.2025.29
Received April 18, 2024; Accepted June 2, 2024; Published online March 27, 2025
Abstract. This paper presents an exact explicit in the closed-form solution of the quadratic optimal state tracking of nonlinear system problems. The solution is motivated by the deterministic approach to estimation that derived the optimal Recursive Nonlinear Least Squares estimator of nonlinear systems. The closed-loop solution is the product of a time-varying gain matrix and the state error. The time-varying gain matrix is the solution of a respective State-Dependent Riccati Equation that depends on a precomputed open-loop optimal solution. As for linear systems, the solution for nonlinear systems is not causal and thus cannot be solved in real-time. For scalar nonlinear systems, it is the optimal solution. The solution uses the State-Dependent Coefficient form representation of a nonlinear affine system and thus it is not unique to high-order systems. This new representation shows that the existing State-Dependent Riccati Equation-based approach to tracking nonlinear systems is far from the optimum. The numerical algorithm is updated for the tracking problem and an alternate new algorithm is presented.
How to Cite this Article:
I. Rusnak, Optimal quadratic full state feedback tracking of nonlinear dynamic systems, Commun. Optim. Theory 2025 (2025) 29.