Hierarchical decentralized reference governor using dynamic constraint tightening for constrained cascade systems

Abstract This paper proposes a hierarchical decentralized reference governor for constrained cascade systems. The reference governor (RG) approach is reformulated in terms of receding horizon strategy such that a locally receding horizon optimization is obtained for each subsystem with a pre-established prediction horizon. The algorithm guarantees that not only the nominal overall closed-loop system without any constraint is recoverable but also the state and control constraints are satisfied in transient conditions. Also, considering unfeasible reference signals, the output of any subsystem goes locally to the nearest feasible value. The proposed dynamic constraint tightening strategy uses a receding horizon to reduce the conservatism of conventional robust RGs. Moreover, a decentralized implementation of the algorithms used to compute tightened constraints and output admissible sets is introduced that allow to deal with large scale systems. Furthermore, a set of dynamic constraints are presented to preserve recursive feasibility of distributed optimization problem. Feasibility, stability, convergence, and robust constraint satisfaction of the proposed algorithm are also demonstrated. The proposed approach is verified by simulating a system composed of three cascade jacketed continuous stirred tank reactors.

[1]  Marcello Farina,et al.  An MPC-based reference governor approach for offset-free control of constrained linear systems , 2013, Int. J. Control.

[2]  Emanuele Garone,et al.  Distributed coordination-by-constraint strategies for multi-agent networked systems , 2011, 2011 50th IEEE Conference on Decision and Control and European Control Conference.

[3]  Marcello Farina,et al.  A Robust MPC Algorithm for Offset-Free Tracking of Constant Reference Signals , 2012, IEEE Transactions on Automatic Control.

[4]  Vicenç Puig,et al.  Non-linear economic model predictive control of water distribution networks , 2017 .

[5]  Frank Allgöwer,et al.  Economic and Distributed Model Predictive Control: Recent Developments in Optimization-Based Control , 2017 .

[6]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[7]  Emanuele Garone,et al.  A Distributed Command Governor based on Graph Colorability Theory , 2018 .

[8]  Jan Lunze,et al.  Feedback control of large-scale systems , 1992 .

[9]  Stefano Di Cairano,et al.  Reference governor for Network Control Systems subject to variable time-delay , 2015, Autom..

[10]  Stefano Di Cairano,et al.  Coordinating Controllers for Constrained Linear Systems by Virtual State Governors , 2015, IEEE Transactions on Automatic Control.

[11]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[12]  Eduardo F. Camacho,et al.  Robust tube-based MPC for tracking of constrained linear systems with additive disturbances , 2010 .

[13]  Riccardo Scattolini,et al.  A stabilizing model-based predictive control algorithm for nonlinear systems , 2001, Autom..

[14]  Emanuele Garone,et al.  Sensorless supervision of linear dynamical systems: The Feed-Forward Command Governor approach , 2011, Autom..

[15]  Emanuele Garone,et al.  The Distributed Command Governor Approach in a Nutshell , 2014 .

[16]  Paola Falugi.  Model predictive control for tracking randomly varying references , 2015, Int. J. Control.

[17]  Julio E. Normey-Rico,et al.  A practical approach for hybrid distributed MPC , 2017 .

[18]  Ilya V. Kolmanovsky,et al.  Decentralized constraint enforcement using reference governors , 2013, 52nd IEEE Conference on Decision and Control.

[19]  Alberto Bemporad,et al.  Reference governor for constrained nonlinear systems , 1998, IEEE Trans. Autom. Control..

[20]  M. A. Henson,et al.  Nonlinear Model Reference Adaptive Control with Embedded Linear Models , 2000 .

[21]  Seyyed Hossein Ghenaati,et al.  Modeling and MPC-based Method for Planning Transportation of Multiple Oil Products in Pipeline Network , 2019, 2019 27th Iranian Conference on Electrical Engineering (ICEE).

[22]  Emanuele Garone,et al.  A parallel distributed supervision strategy for multi-agent networked systems , 2016, Syst. Control. Lett..

[23]  David Q. Mayne,et al.  Generalized Stabilizing Conditions for Model Predictive Control , 2016, J. Optim. Theory Appl..

[24]  Fabio A. de Almeida,et al.  Reference Management for Fault-Tolerant Model Predictive Control , 2010 .

[25]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[26]  Vicenç Puig,et al.  A Supervisory Active Fault Tolerant Control Framework for Constrained Linear Systems* , 2020, 2020 European Control Conference (ECC).

[27]  K. T. Tan,et al.  Discrete‐time reference governors and the nonlinear control of systems with state and control constraints , 1995 .

[28]  Panagiotis D. Christofides,et al.  Networked and Distributed Predictive Control: Methods and Nonlinear Process Network Applications , 2011 .

[29]  Emanuele Garone,et al.  Distributed Reference Management Strategies for Networked Water Distribution Systems , 2011 .

[30]  Emanuele Garone,et al.  A Distributed Parallel Command Governor Strategy for the Coordination of Multi-Agent Networked Systems , 2012 .

[31]  B. Anderson,et al.  Digital control of dynamic systems , 1981, IEEE Transactions on Acoustics, Speech, and Signal Processing.

[32]  Stefano Di Cairano,et al.  Reference and command governors: A tutorial on their theory and automotive applications , 2014, 2014 American Control Conference.

[33]  Dragoslav D. Šiljak,et al.  Decentralized control of complex systems , 2012 .

[34]  Carlos Bordons Alba,et al.  Model Predictive Control , 2012 .

[35]  Iven M. Y. Mareels,et al.  Control of Large-Scale Irrigation Networks , 2007, Proceedings of the IEEE.

[36]  David Q. Mayne,et al.  Invariant approximations of the minimal robust positively Invariant set , 2005, IEEE Transactions on Automatic Control.

[37]  Elmer G. Gilbert,et al.  Constrained linear systems with hard constraints and disturbances: An extended command governor with large domain of attraction , 2011, Autom..

[38]  Emanuele Garone,et al.  Distributed Coordination-by-Constraint Strategies for Networked Control Systems , 2009 .

[39]  Marcello Farina,et al.  An MPC algorithm for offset-free tracking of constant reference signals , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[40]  Stefano Di Cairano,et al.  Reference and command governors for systems with constraints: A survey on theory and applications , 2017, Autom..

[41]  Antonio Ferramosca,et al.  MPC for tracking of constrained nonlinear systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[42]  Ilya V. Kolmanovsky,et al.  Reference governors for linear systems with nonlinear constraints , 2011, IEEE Conference on Decision and Control and European Control Conference.

[43]  David Q. Mayne,et al.  Robust model predictive control of constrained linear systems with bounded disturbances , 2005, Autom..

[44]  Ilya Kolmanovsky,et al.  Maximal output admissible sets for discrete-time systems with disturbance inputs , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[45]  Marko Bacic,et al.  Model predictive control , 2003 .

[46]  E. Gilbert,et al.  Theory and computation of disturbance invariant sets for discrete-time linear systems , 1998 .