An optimal control algorithm toward unknown constrained nonlinear systems based on the sequential sampling and updating of surrogate model

The application of optimal control theory in practical engineering is often limited by the modeling cost and complexity of the mathematical model of the controlled plant, and various constraints. To bridge the gap between the theory and practice, this paper proposes a model-free direct method based on the sequential sampling and updating of surrogate model, and extends the ability of direct method to solve model-free optimal control problems with general constraints. The algorithm selects sample points from the current actual trajectory data to update the surrogate model of controlled plant, and solve the optimal control problem of the constantly refined surrogate model until the result converges. The presented initial and subsequent sampling strategies eliminate the dependence on the model. Furthermore, the new stopping criteria ensure the overlap of final actual and planned trajectories. The several examples illustrate that the presented algorithm can obtain constrained solutions with greater accuracy and require fewer sample data.