Towards Real-Time, Non-Linear Quadratic Optimal Regulation

A novel non-linear design method based on linear quadratic optimal control theory is presented that applies to a wife class of non-linear systems. The method is easy to apply and results in a globally optimal solution that can be implemented in real-time. The key feature of the "design" method is the introduction of state-dependence in the weight matrices of the usual linear quadratic cost function, leading to a "non-linear" control policy, even for linear dynamics. To demonstrate the method, a simple vehicle suspension model with a cubic damping force is used, in conjunction with non-linear state penalties that better reflect the "engineering" objectives of active vehicle vibration suppression. A number of simulations is conducted and compared with a passively mounted vehicle.