Stability for feedback loops containing complex algorithms

Abstract

With the advent of neural networks, fuzzy logic, genetic algorithms, and other soft computing methodologies, many researchers have demonstrated successful designs for intelligent control strategies that appear to outperform traditional linear feedback controls; however, industry has mostly ignored the new technology due to the lack of stability guarantees (required in most formal engineering risk-management processes). In this paper, we offer a Lyapunov-stability framework where one can place any arbitrary computational algorithm and still get guarantees of uniformly ultimately bounded (UUB) signals. We would expect an intelligent algorithm to be well-designed such that the proposed framework would not come into play unless unanticipated disturbances affect the system. But even if the intelligent algorithm was poorly designed, the resulting performance (inside our framework) would just look similar to that of a typical nonlinear neural-adaptive control. In our strategy, the intelligent algorithm trains a cerebellar model articulation controller (CMAC) neural network with arbitrarily bounded weights in order to achieve good performance, while a second CMAC trains in parallel using direct-adaptive-control laws in order to provide stability (even in the case of the first CMAC weights reaching their imposed bound). We test the strategy using a previously proposed ad hoc CMAC weight smoothing strategy, serving as the intelligent algorithm, with simulations and experiment controlling a two-link flexible-joint robot.