MPC strategy with mobile controllers in distributed parameter systems based on SVD-RBFNN reduced-order model

To address the challenges of high-dimensional computational bottlenecks and limited spatial flexibility of controllers in distributed parameter systems induced by spatiotemporal coupling, this paper proposes a model predictive control (MPC) strategy with mobile controllers based on the singular value decomposition-radial basis function neural network (SVD-RBFNN) reduced-order model. This strategy enables the simultaneous dynamic co-optimization of control inputs and controller positions. First, a high-accuracy reduced-order model is constructed by integrating SVD with RBFNN, effectively capturing the dominant system dynamics while significantly alleviating computational load. Then, multiple types of motion constraints including feasibility, motion smoothness, and coordination are incorporated into the design of controllers. Using the reduced-order model as a predictor, a multi-objective cost function is formulated that jointly optimizes control inputs and controller positions, which is efficiently solved via the sequential least squares quadratic programming (SLSQP) algorithm. Subsequently, strict theoretical analysis establish a uniform upper bound on the approximation error of the reduced-order model, thereby guaranteeing closed-loop feasibility and stability. Finally, two sets of comparative experiments are designed for linear and nonlinear systems, respectively, to validate the proposed method.