SBIR-STTR Award

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. Our Phase I effort will provide a proof-of-concept integrated hardware-software solution implementing max-plus arithmetic for efficient solution of nonlinear stochastic control problems. We have had success in implementing nonlinear deterministic controls in field programmable gate arrays, and we propose to extend those efforts to stochastic control in this effort. We will conduct research into the feasibility of applying max-plus arithmetic methods in the stochastic setting, coupling algorithms with innovative hardware for efficient solutions.

Benefit:
If this effort proves successful, it will revolutionize the field of control theory. The computational efficiency improvements we expect to see will permit fully nonlinear control techniques to be applied in crucial tracking and guidance systems and flight controls. Performance enhancements for unmanned systems will provide warfighters with greatly improved tools for surveillance and combat.

Keywords:
Hamilton-Jacobi, Dynamic Programming, Fpga Implementation

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. Our Phase II effort will focus on a prototype hardware-software solution implementing max-plus arithmetic for efficient solution of nonlinear control and optimization problems. The success of our two-pronged Phase I effort in devising efficient algorithms based on max-plus structure and in studying and simulating reconfigurable computing hardware solutions for efficient max-plus implementation suggests significant potential for this approach. The result of Phase II work will be a prototype solution, including a software development kit and an optimization co-processor, for solving nonlinear optimization and control problems efficiently.

Benefit:
If the feasibility studies of Phase I can be extended to a functional prototype in Phase II, the result will revolutionize the field of control theory. The computational efficiency improvements we expect to see will permit fully nonlinear control techniques to be applied in crucial tracking and guidance systems and flight controls. Performance enhancements for unmanned systems will provide warfighters with greatly improved tools for surveillance and combat.

Keywords:
Idempotent Arithmetic, Dynamic Programming, Feedback Control