We design moving horizon state estimators for a general model of bioprocesses. The underlying optimization is nonconvex due to the microbial growth kinetics, which are modeled as nonlinear functions. We relax the nonconvex growth constraints so that the optimization becomes a second-order cone program, which can be solved efficiently at large scales. Unfortunately, solutions to the relaxation can be inexact and thus lead to inaccurate state estimates. To recover feasible, albeit potentially locally optimal solutions, we use the concave–convex procedure, which here takes the form of a sequence of second-order cone programs. We find that the moving horizon state estimators outperform the unscented Kalman filter on numerical examples based on the gradostat and anaerobic digestion when there is high process noise or parameter error.

我们为生物过程的一般模型设计移动水平状态估计器。由于微生物生长动力学，潜在的优化是非凸的，它被建模为非线性函数。我们放宽了非凸增长约束，使优化成为一个二阶锥程序，可以在大尺度上有效地求解。不幸的是，松弛的解决方案可能不精确，从而导致状态估计不准确。为了恢复可行的，尽管可能是局部最优解，我们使用凹凸过程，这里采用一系列二阶锥程序的形式。我们发现，当存在高过程噪声或参数误差时，移动水平状态估计器在基于梯度恒温器和厌氧消化的数值示例上优于无迹卡尔曼滤波器。