Intelligent bounds on modeling uncertainty: applications to sliding mode control

Robust control techniques such as sliding mode control (SMC) require a dynamic model of the plant and bounds on modeling uncertainty to formulate control laws with guaranteed stability. Although techniques for modeling dynamic systems and estimating model parameters are well established, very few procedures exist for estimating uncertainty bounds. In the case of SMC design, a conservative global bound is usually chosen to ensure closed-loop stability over the entire operating space. The primary drawbacks of this conservative, "hard computing" approach are excessive control activity and reduced performance, particularly in regions of the operating space where the model is accurate. In this paper, a novel approach to estimating uncertainty bounds for dynamic systems is introduced. This "soft computing" approach uses a unique artificial neural network, the 2-Sigma network, to bound modeling uncertainty adaptively. This fusion of intelligent uncertainty bound estimation with traditional SMC results in a control algorithm that is both robust and adaptive. Simulations and experimental demonstrations conducted on a magnetic levitation system confirm these capabilities and reveal excellent tracking performance without excessive control activity.