Optimal Inverse Functions Created via Population-Based Optimization

Finding optimal inputs for a multiple-input, single-output system is taxing for a system operator. Population-based optimization is used to create sets of functions that produce a locally optimal input based on a desired output. An operator or higher level planner could use one of the functions in real time. For the optimization, each agent in the population uses the cost and output gradients to take steps lowering the cost while maintaining their current output. When an agent reaches an optimal input for its current output, additional agents are generated in the output gradient directions. The new agents then settle to the local optima for the new output values. The set of associated optimal points forms an inverse function, via spline interpolation, from a desired output to an optimal input. In this manner, multiple locally optimal functions can be created. These functions are naturally clustered in input and output spaces allowing for a continuous inverse function. The operator selects the best cluster over the anticipated range of desired outputs and adjusts the set point (desired output) while maintaining optimality. This reduces the demand from controlling multiple inputs, to controlling a single set point with no loss in performance. Results are demonstrated on a sample set of functions and on a robot control problem.