Spatiotemporal LS-SVM inverse control for nonlinear distributed parameter systems with application to heating process

In actual industrial systems, numerous processes are characterized as distributed parameter systems (DPSs) that exhibit strong nonlinearity, complex boundary conditions, and unknown dynamics. Achieving accurate control of such processes poses a significant challenge. In light of this, a data-driven spatiotemporal least squares support vector machine (LS-SVM) inverse control method has been developed specifically for complex DPSs. First, a spatiotemporal LS-SVM model is proposed to capture the dynamics of DPSs by leveraging available data. Subsequently, by employing Taylor expansion on this spatiotemporal model, a state model is derived to explicitly establish the relationship between the control input and output variables. Building upon this foundation, an explicit control input is obtained through inversion and spatial fuzzy strategy, allowing for effective tracking of spatiotemporal dynamics. This control approach takes into account the influence of each input on all spatial points, thereby ensuring a favorable control effect for DPSs. Theoretical analysis and stability proofs affirm the stability of the proposed control approach for nonlinear DPSs. Furthermore, the efficacy of this controller is demonstrated through two actual experiments. First, the proposed approach exhibits superior control performance, as evidenced by a nearly threefold improvement in tracking accuracy on several sensors compared to the fuzzy controller. Second, the proposed controller maintains a smaller error during the tracking process, with deviations bounded within 1 degrees C even in the presence of disturbances.

Automated summary

This article proposes a data-driven inverse control method for complex distributed parameter systems (DPSs) using spatiotemporal least squares support vector machine (LS-SVM) model and spatial fuzzy strategy, effectively tracking the dynamics of DPSs. The efficacy and stability of this method are demonstrated through actual experiments.