Nonlinear modeling, estimation and predictive control in APMonitor

This paper describes nonlinear methods in model building, dynamic data reconciliation, and dynamic optimization that are inspired by researchers and motivated by industrial applications. A new formulation of the ℓ1-norm objective with a dead-band for estimation and control is presented. The dead-band in the objective is desirable for noise rejection, minimizing unnecessary parameter adjustments and movement of manipulated variables. As a motivating example, a small and well-known nonlinear multivariable level control problem is detailed that has a number of common characteristics to larger controllers seen in practice. The methods are also demonstrated on larger problems to reveal algorithmic scaling with sparse methods. The implementation details reveal capabilities of employing nonlinear methods in dynamic applications with example code in both Matlab and Python programming languages.