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 [19], [20] which has determined the situations where the modification is actually necessary.