Data-Enabled Neighboring Extremal Optimal Control: A Computationally Efficient DeePC

Model-based optimal control strategies typically rely on accurate parametric representations of the underlying systems, which can be challenging to obtain, especially for nonlinear and complex systems. Therefore, data-driven optimal controllers have become increasingly attractive to both academics and industry practitioners. As a data-driven optimal control approach that can explicitly handle constraints, data-enabled predictive control (DeePC) makes a transition from the model-based optimal control strategies (e.g. model predictive control (MPC)) to a data-driven one such that it seeks an optimal control policy from raw input/output (I/O) data without requiring system identification prior to control deployment, achieving remarkable successes in various applications. However, this approach involves high computational cost due to the dimension of the decision variable, which is generally significantly higher than its MPC counterpart. Several approaches have been proposed to reduce the computational cost of the DeePC for linear time-invariant (LTI) systems. However, finding a computationally efficient method to implement the DeePC for the nonlinear systems is still an open challenge. In this paper, we propose a data-enabled neighboring extremal (DeeNE) to approximate the DeePC policy and reduce its computational cost for the constrained nonlinear systems. The DeeNE adapts a pre-computed nominal DeePC solution to the perturbations of the initial I/O trajectory and the reference trajectory from the nominal ones. We also develop a scheme to handle nominal non-optimal solutions so that we can use the DeeNE solution as the nominal solution during the control process. Promising simulation results on the cart inverted pendulum problem demonstrate the efficacy of the DeeNE framework.