Optimal Control for Continuous-Time Scalar Nonlinear Systems With Known Dynamics

An optimal controller for affine in the inputs scalar continuous-time nonlinear systems with the known dynamics is presented. The controller is described by an algebraic equation with variable structure. The control is derived in analytical way. A functional block-diagram of the controller is presented. The controller does not require any training procedure and is of moderate complexity. It is shown that the state-variable trajectories of the controlled system are globally asymptotically stable and globally asymptotically convergent to steady states. Computer simulations confirming theoretical derivations and illustrating the controller performance are provided.