In this work, a two-dimensional (2D) kernel-based Gaussian process regression (GPR) method for the identification of batch process is proposed. Under the GPR framework, the estimate of the time-varying impulse response is a realization from a zero-mean Gaussian process (GP), wherein the kernel function encodes the possible structural dependencies. However, the existing kernels designed for system identification are one-dimensional (1D) kernels and underutilize the 2D data information of batch process. Utilizing the 2D correlation property of batch process impulse response, we propose the amplitude modulated 2D locally stationary kernel by means of addition / multiplication operation based on coordinate decomposition. Then, a nonparametric identification method using 2D kernel-based GPR for batch process is developed. Furthermore, the properties of the proposed 2D kernel are analyzed. Finally, we demonstrate the effectiveness of the proposed identification method in two examples.

Inaccurate models limit the performance of model-based real-time optimization (RTO) and even cause system instability. Therefore, a RTO framework that can guarantee global convergence with the presence of plant-model mismatch is desired. In this regard, the trust-region framework is simple to implement and guarantees globally convergent for unconstrained problems. However, it remains to be seen if the trust-region strategy can handle inequality constraints directly with the common model adaptation method. This paper addresses this issue and proposes a novel composite-step trust-region framework that guarantees global convergence for constrained RTO problems. The trial step is decomposed into a normal step that improves feasibility and a tangential step that reduces the cost function. In each iteration, the model optimization problem with relaxed constraints is solved. The proof of the global convergence property under structural plant-model mismatch is given.