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 using conventional hardware and algorithms 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. The Phase II effort builds on our proof-of-concept Phase I demonstration of an integrated hardware-software solution implementing max-plus arithmetic for efficient solution of nonlinear control problems. The small-scale problems considered in Phase I will be expanded to include flight control and guidance applications in which nonlinearities present major challenges to system performance. The prototype system we propose to develop will provide users with a complete solution for developing and implementing real-time nonlinear controls.