Asymptotically Optimal Stabilizing Quadratic Control of an Inverted Pendulum

A new method for the design and synthesis of near-optimal, non linear control law is examined, based on a generalisation of LQ 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 casual 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 is discussed. The problem of stabilizing an inverted pendulum is used to illustrate the method and proves an exacting task that highlights a number of issues.