A data-driven spatiotemporal model predictive control strategy for nonlinear distributed parameter systems

Many distributed parameter systems (DPSs) have strongly nonlinear spatiotemporal dynamics, unknown parameters and complex boundary conditions, which make it difficult to obtain accurate prediction and control in actual practice. In this paper, a data-driven spatiotemporal model predictive control (MPC) strategy is proposed for nonlinear DPSs. It first develops a low-order nonlinear spatiotemporal model by using kernel principal component analysis to reconstruct the nonlinear spatial dynamics, so that the spatial nonlinearity is better reserved in contrast with the traditional data-driven DPS modeling methods. On this basis, a spatiotemporal MPC is proposed for nonlinear DPSs. In this control strategy, a new objective function is constructed with consideration of errors on not only time but also space, which overcomes the shortcoming of the traditional MPC due to the ignorance of nonlinear spatial dynamics. The stability and effectiveness of the proposed spatiotemporal control strategy are demonstrated by mathematical stability and comparative case studies.