An algebraic approach to dynamic optimisation of nonlinear systems: a survey and some new results

Abstract

Dynamic optimisation, with a particular focus on optimal control and nonzero-sum differential games, is considered. For nonlinear systems solutions sought via the dynamic programming strategy are inevitably characterised by partial differential equations (PDEs) which are often difficult to solve. A detailed overview of a control design framework which enables the systematic construction of approximate solutions for optimal control problems and differential games without requiring the explicit solution of any PDE is provided along with a novel design of a nonlinear control gain aimed at improving the ‘level of approximation’ achieved. Multi-agent systems are considered as a possible application of the theory.