Inducing Optimality in Prescribed Performance Control for Uncertain Euler–Lagrange Systems

The goal of this paper is to find a stabilizing and optimal control policy for a class of systems dictated by Euler–Lagrange dynamics, that also satisfies predetermined response criteria. The proposed methodology builds upon two stages. Initially, a neural network is trained online via an iterative process to capture the system dynamics, which are assumed to be unknown. Subsequently, a successive approximation algorithm is applied, employing the acquired dynamics from the previous step, to find a near-optimal control law that takes into consideration prescribed performance specifications, such as convergence speed and steady-state error. In addition, we concurrently guarantee that the system evolves exclusively within the compact set for which sufficient approximation capabilities have been acquired. Finally, we validate our claims through various simulated studies that confirm the success of both the identification process and the minimization of the cost function.