Leap-Ahead Control Theoretic Applications

The real-time implementation of controls in nonlinear systems remains one of the great challenges in applying advanced control technology. Often, linearization around a set point is the only practical approach, and many controllers implemented in hardware systems are simple PID feedback mechanisms. To apply Pontryagin’s principle or Bellman’s equation for high dimensional nonlinear systems requires more computing power than is realistic. The success of linear control theory, especially certainty equivalence and LQG approaches, leads us to hope for additional gains from fully nonlinear controls. We propose an innovation in computational nonlinear control that offers ground breaking potential for real-time control applications, making fully nonlinear problems solvable with the computational efficiency of linear problems.