Adaptive steady-state target optimization using iterative modified gradient-based methods in linear non-square MPC

An important feature of linear model predictive control (MPC) is the ability to provide offset-free control through integral action. Linear MPC can utilize a steady-state target optimizer (SSTO) in conjunction with a dynamic optimization in order to manage systems that are non-square, have integrating modes, or encounter infeasible setpoints. Integral action does not ensure that the feasible steady-state target is closest to the true optimum when the desired setpoint is infeasible. This paper describes the modifications necessary to linear state-space MPC algorithms in order to address this problem (assuming systems with no integrating modes). The solution employs features of the integrated system optimization and parameter estimation (ISOPE) algorithm: the SSTO cost is modified by a term that results in matching of the true plant and model conditions necessary for optimality. This work combines well with prior work which has determined the situations where the modification is actually necessary.