Asymptotically optimal stabilising quadratic control of an inverted pendulum

A method for the design and synthesis of near-optimal, nonlinear control laws is examined, based on a generalisation of linear quadratic optimal control theory and which effectively provides a near-optimal gain schedule. The method is simple to apply and affords greater design flexibility (via state-dependent weighting) than conventional approaches. The resulting regulator can, in principle, be implemented in real time owing to the causal nature of the required computations. However, the need to solve an algebraic Riccati equation at every time point is burdensome, and a number of algorithms that would permit parallel computation are discussed. The problem of stabilising an inverted pendulum is used to illustrate the method and proves an exacting task that highlights a number of issues.