Neighbouring-extremal control for singular dynamic optimisation problems. Part I: single-input systems

A powerful approach for dynamic optimisation in the presence of uncertainty is to incorporate measurements into the optimisation framework so as to track the optimum. For non-singular control problems, this can be done by tracking active constraints along boundary arcs and using neighbouring-extremal (NE) control along interior arcs. Essentially, NE control forces the first-order variation of the necessary conditions of optimality (NCO) to …