2023/04/01 by Mohamed Naveed Gul Mohamed, Raman Goyal, Mohamed, Mohamed Naveed Gul +3 · 2 citations
Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Spacecraft Dynamics and Control #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2304.00375
openalex publication_date 2023/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the infinite horizon optimal control problem for nonlinear systems. Under the conditions of controllability of the linearized system around the origin, and nonlinear controllability of the system to a terminal set containing the origin, we establish an approximate regularized solution approach consisting of a ``finite free final time" optimal transfer problem to the terminal set, and an infinite horizon linear regulation problem within the terminal set, that is shown to render the origin globally asymptotically stable. Further, we show that the approximations converge to the true optimal cost function as the size of the terminal set decreases to zero. The approach is empirically evaluated on the pendulum and cart-pole swing-up problems to show that the finite time transfer is far shorter than the effective horizon required to solve the infinite horizon problem without the proposed regularization.