Automatic design of interpretable control laws through parametrized Genetic Programming with adjoint state method gradient evaluation

This work investigates the application of a Local Search (LS) enhanced Genetic Programming (GP) algorithm to the control scheme’s design task. The combination of LS and GP aims to produce an interpretable control law as similar as possible to the optimal control scheme reference. Inclusive Genetic Programming (IGP), a GP heuristic capable of promoting and maintaining the population diversity, is chosen as the GP algorithm since it proved successful on the considered task. IGP is enhanced with the Operators Gradient Descent (OPGD) approach, which consists of embedding learnable parameters into the GP individuals. These parameters are optimized during and after the evolutionary process. Moreover, the OPGD approach is combined with the adjoint state method to evaluate the gradient of the objective function. The original OPGD was formulated by relying on the backpropagation technique for the gradient’s evaluation, which is impractical in an optimization problem involving a dynamical system because of scalability and numerical errors. On the other hand, the adjoint method allows for overcoming this issue. Two experiments are formulated to test the proposed approach, named Operator Gradient Descent - Inclusive Genetic Programming (OPGD-IGP): the design of a Proportional–Derivative (PD) control law for a harmonic oscillator and the design of a Linear Quadratic Regulator (LQR) control law for an inverted pendulum on a cart. OPGD-IGP proved successful in both experiments, being capable of autonomously designing an interpretable control law similar to the optimal ones, both in terms of shape and control gains.