Robust Model Predictive Control for Input Saturated and Softened State Constraints

Abstract

This paper starts with a brief review of robust model predictive control (RMPC) algorithsms for uncertain systems using linear matrix inequalities (LMIs) subject to input and/or output saturated constraints. However when RMPC has both input and state constraints, a difficulty will arise due to the inability of the optimizer to satisfy the state constraints due to the constraints on inputs. Therefore, a novel RMPC scheme is presented that softens the state constraints as penalty terms are added to its objective function. These terms maintain state violation at low values until a constrained solution is returned. The state violation can be regulated by changing the value of the weighting factor. A novel robust predictive controller for input saturated and softened state constraints for linear time varying (LTV) systems with polytopic model uncertainties is presented.

Regression Models and Fuzzy Logic Prediction of TBM Penetration Rate

“…Fuzzy logic algorithms and calculations are based on [9] and [10]. The stochastic models and distributions are referred to as in [11] and [12]. The contents of this paper are as follows: Section 2 introduces the database distribution analyses; Section 3 develops four statistical regression models; Section 4 presents the development of fuzzy logic model and the performances comparison; Section 5 is the conclusion.…”

Robust Model Predictive Control Schemes for Tracking Setpoints

“…Based on the above infinite horizon RMPC scheme, Casavola et al [15] formulated a finite horizon RMPC scheme for the input-saturated constraints. Then, Minh and Afzulpurkar [16] developed a finite horizon RMPC scheme for the input-saturated and the softened state constraints. The idea to develop an RMPC scheme with the softened state constraints comes from the reality that RMPC regulator is designed for an online implementation; any infeasible solution of the optimization problem cannot be tolerated.…”

“…In this paper, we extend the RMPC algorithm in [16] for tracking setpoint RMPC algorithm. The new RMPC algorithm allows the system to track a reference output trajectory different from the origin.…”

“…Since the RMPC regulator is designed for online implementation, any infeasible solution of the optimization problems cannot be tolerated. To guarantee the system stability once the state space violates the constraints, Minh and Afzulpurkar [16] have developed an RMPC algorithm for input-saturated and softened state constraints using penalty terms added into the objective function. These terms keep the state violation at low values until a constrained solution is returned.…”

“…The RMPC algorithm in Minh and Afzulpurkar [16] was restricted to the finite horizon regulator with a zero target or nontracking setpoint. In this paper, we extend the RMPC algorithm in [16] for tracking setpoint RMPC algorithm.…”