+ Reference and Extended Command Governors

FIGURE 1: Reference/extended command governor protects the system against violating state and control constraints by minimally modifying commands to closed-loop systems to ensure safety.

See Survey Paper by E. Garone, S. Di Cairano and I.V. Kolmanovsky, "Reference and command governors for systems with constraints: A survey on theory and applications," Automatica, 2017.

With the increasing trend towards system downsizing and the growing stringency of requirements, constraint handling and limit protection are becoming both increasingly important and critical for engineered systems. Constraints can reflect actuator limits, safety requirements (e.g., process temperature or pressure must not exceed a safe value) or obstacle avoidance requirements.

Reference governors and extended command governors are control schemes (i.e., algorithms that are implemented in software) that can be augmented to already existing control systems in order to provide constraint handling/limit protection capabilities. These add-on schemes exploit prediction and optimization to supervise and minimally modify operator (e.g., pilot or driver) commands, or other closed-loop signals, whenever there is a danger of future constraint violations. As compared to the conventional reference governor, the extended command governor provides a less conservative solution at the cost of increased computational complexity.

Our recent research focus has been on advancing methods and design procedures for rigorous constraint enforcement based on low-order system models thereby leading to more practically appealing and computationally efficient solutions with guaranteed constraint protection properties. Furthermore, novel methods and governor design procedures have been developed for decentralized constraint enforcement in distributed/large scale systems, for prioritized constraint handling in cases when it is not feasible to enforce all constraints at once, for systems affected by large unmeasured disturbances, systems with time-varying constraints and time-varying references, and systems operated with commands sent over communication networks. In addition, constraint enforcement techniques based on reference governors and more general model predictive control solutions have been developed for systems with nonlinear dynamics evolving on non-Euclidian configuration spaces (i.e., on manifolds) which emerge in various applications such as spacecraft control and robotics. Finally, results and design techniques for reference governors placed to modify signals other than commands within the control loop have been established and schemes where in addition to reference command modifications the internal controller states may be reset have been proposed.

Our research also synergistically combines advances in theory and the treatment of specific applications to aerospace and automotive systems. Simulation-based and experimental studies have served to demonstrate the potential and quantify the benefits of the reference and extended command governor schemes, that have been enhanced with novel theoretical results that we have developed, for constraint handling (limit protection) and to establish directions and requirements for further theoretical advances to satisfy the needs of these applications. Specific applications we have considered included downsized fuel efficient turbocharged automotive engines, aircraft gas turbine engines, high altitude long endurance very flexible aircraft that may provide an alternative to communication satellites, hypersonic vehicles, flying wind energy generation turbines, constrained spacecraft relative motion control with obstacle/debris avoidance, constrained control of spacecraft attitude while protecting sensitive sensors and maintaining communication links, assuring safe operation of aircraft gas turbine engines, maintaining safe operation of advanced automotive Free Piston Engines (FPE) intended for hybrid hydraulic and electric vehicles, and vehicle rollover avoidance. In all of these applications, avoiding constraint violation is essential to be able to maintain safe operation of the system and reference and extended command governors provide attractive solutions.

FIGURE 2: Experimental in-vehicle results [37]. Preventing compressor surge in downsized engines using reference governor.

Survey Papers

[1] Garone, E., Di Cairano, S., and Kolmanovsky, I.V., "Reference and command governors for systems with constraints: A survey of their theory and applications," Automatica, vol. 75, pp. 306-328, 2017.

[2] Kalabic, U., “Reference governors: Theoretical extensions and practical applications,” Ph.D. dissertation, The University of Michigan, August, 2015.

[3] Kolmanovsky, I.V., Kalabic, U., and Gilbert, E.G., “Developments in constrained control using reference governors,’’ Proceedings of the 2012 IFAC Conference on Nonlinear Model Predictive Control (NMPC), Noordwijkerhout, the Netherlands, August 23 - 27, pp. 282-290, 2012.

[4] Kolmanovsky, I.V., Garone, E., and Di Cairano, S., “Reference and command governors: A tutorial on their theory and automotive applications,” Proceedings of American Control Conference, Portland, Oregon, pp. 226-241, 2014.

[5] Kolmanovsky, I., and Li, N., "Protecting systems from violating constraints using reference governors," Springer Nature Computer Science, 3, 478, 2022.

Parameter Governing

[6] Kolmanovsky, I.V. and Sun, J., 2006. Parameter governors for discrete-time nonlinear systems with pointwise-in-time state and control constraints. Automatica, 42(5), pp.841-848.

[7] Gupta, R., and Kolmanovsky, I.V., “Governing parameter changes in nonlinear parameter-dependent optimization problems,” Proceedings of ASME Dynamic Systems and Control Conference, Paper DSCC2013-3845, Palo Alto, California, 2013.

Reference Governors and Model Predictive Control (MPC) on Manifolds

[8] Kalabic, U.V., Gupta, R., Di Cairano, S., Bloch, A.M., and Kolmanovsky, I.V., "Constrained spacecraft attitude control on SO(3) using reference governors and nonlinear Model Predictive Control," Proceedings of American Control Conference, Portland, Oregon, pp. 5586-5593, 2014.

[9] Gupta, R., Kalabic, U., Di Cairano, S., Bloch, A., and Kolmanovsky, I.V., “Constrained spacecraft attitude control on SO(3) using fast nonlinear Model Predictive Control,” Proceedings of American Control Conference, Chicago, IL, USA, pp. 2980-2986, 2015.

[10] Kalabic, U.V., Gupta, R., Di Cairano, S., Bloch, A.M., and Kolmanovsky, I.V., "MPC on manifolds with applications to the control of systems on matrix Lie groups," Automatica, vol. 76, pp. 293-300, 2017.

[11] Kalabic, U., Gupta, R., Di Cairano, S., and Bloch, A., and Kolmanovsky, I.V., "MPC on manifolds with an application to SE(3)," Proceedings of American Control Conference, Boston, MA, pp. 7-12, 2016.

[12] Lee, D.-Y., Gupta, R., Kalabic, U., Di Cairano, S., Bloch, A.M., Cutler, J.W., and Kolmanovsky, I.V., ``Constrained attitude maneuvering of a spacecraft with reaction wheel assembly by nonlinear Model Predictive Control, Proceedings of American Control Conference, Boston, MA, pp. 4960-4965, 2016.

[13] Lee, D.-Y., Gupta, R., Kalabić, U., Di Cairano, S., Bloch, A.M., Cutler, J.W., and Kolmanovsky, I.V., "Geometric mechanics based nonlinear model predictive spacecraft attitude control with reaction wheels," Journal of Guidance, Control, and Dynamics 40, no. 2 (2017): 309-319.

Reference governors for linear systems with nonlinear constraints

[14] Kalabic, U., Kolmanovsky, I.V., and Gilbert, E.G., “Reference governors for linear systems with nonlinear constraints,” Proceedings of 50th IEEE Conference on Decision and Control, Orlando, Florida, pp. 2680-2686, 2011.

[15] Burlion, L., Schieni, R., and Kolmanovsky, I.V., "A reference governor for linear systems with polynomial constraints," Automatica, vol. 142, 110313, 2022.

Reduced order reference governors

[16] Kalabic, U., Kolmanovsky, I.V., Buckland, J., and Gilbert, E.G., "Reduced order reference governor," Proceedings of 51st IEEE Conference on Decision and Control, pp. 3245-3251, Maui, Hawaii, December, 2012.

[17] Kalabic, U., Kolmanovsky, I.V., and Gilbert, E.G., "Reduced order extended command governor," Automatica, vol. 50, no. 5, pp. 1466–1472, 2014.

[18] Li, Q., Kalabic, U., Kolmanovsky, I.V., "Fast reference governors for second-order linear systems with constraints and an input time-delay," Automatica, vol. 50, no. 2, pp. 641–645, 2014.

Prioritization reference governor schemes

[19] Kalabic, U., Chitalia, Y., Buckland, J., and Kolmanovsky, I.V., "Prioritization schemes for reference and command governors," Proceedings of European Control Conference, Zurich, Switzerland, pp. 2734 – 2739, 2013.

Reference and command governors for systems with slowly time-varying references and time-dependent constraints

[20] Kalabic, U., and Kolmanovsky, I.V., “Reference and command governors for systems with slowly time-varying references and time-dependent constraints,” Proceedings of the 53rd IEEE Conference on Decision and Control, Los Angeles, Ca, December 15-17, 6701-6706, 2014.

Inner loop reference governors

[21] Kalabic, U., and Kolmanovsky, I.V., “Inner loop reference governors: Placing reference governors inside the control loop by using passivity,” Proceedings of IEEE Conference on Decision and Control, Osaka, Japan, pp. 3019-3025, 2015.

Networked reference governor

[22] Di Cairano, S., and Kalabic, U., "Further developments and applications of network reference governor for constrained systems," Proceedings of American Control Conference, Montreal, Canada, pp. 3907-3912, 2012.

[23] Di Cairano, S., Kalabic, U., and Kolmanovsky, I.V., "Reference governor for network control systems subject to variable time-delay," Automatica, 2016.

[24] Li, Q., Kalabic, U., and Kolmanovsky, I.V., "Predictor-based reference governor for second-order linear constrained systems operated over a communication network," Proceedings of the 11th World Congress on Intelligent Control and Automation (WCICA), Shenyang, China, pp. 1700-1704, 2014.

Reference governors for systems with large disturbances

[25] Poloni, T., Kalabic, U., McDonough, K., and Kolmanovsky, I.V., “Disturbance canceling control based on simple input observers with constraint enforcement for aerospace applications,’’ Proceedings of the IEEE Multi-conference on Systems and Control, Antibes, France, pp. 158-165, 2014.

Controller state and reference governor

[26] McDonough, K., and Kolmanovsky, I.V., “Controller state and reference governors for discrete-time linear systems with pointwise-in-time state and control constraints,” Proceedings of American Control Conference, Chicago, IL, pp. 3607-3612, 2015.

[27] McDonough, K., and Kolmanovsky, I.V., ``Fast computable recoverable sets and their use for aircraft loss-of-control handling," AIAA Journal of Guidance, Control and Dynamics, 2016.

[28] Li, N., Girard, A., and Kolmanovsky, I.V., "Chance-constrained controller state and reference governor," Automatica, vol. 133, 109864, 2021.

Decentralized reference governor

[29] Kalabic, U., and Kolmanovsky, I.V. “Decentralized constraint enforcement using reference governors,” Proceedings of IEEE Conference on Decision and Control, Decision and Control (CDC), Firenze, Italy, pp. 6415-6421, 2013.

Applications to hypersonic vehicles

[30] Baldwin, M., and Kolmanovsky, I.V., “Constrained inner-loop control of a hypersonic glider using extended command governor,” Proceedings of American Control Conference, Washington DC, pp. 5576-5581.

[31] Petersen, C., Baldwin, M., and Kolmanovsky, I.V., “Model Predictive Control guidance with extended command governor inner-loop flight control for hypersonic vehicles,” Proceedings of AIAA Guidance, Navigation and Control Conference, Boston, MA, AIAA Paper 2013-5028, 2013.

Applications to spacecraft relative motion control

[32] Baldwin, M., and Kolmanovsky, I.V., “Robust controller for constrained relative motion maneuvering with disturbance rejection,” Proceedings of AIAA Guidance, Navigation and Control Conference, Boston, MA, AIAA Paper 2013-4721, pp. 1-14, 2013.

[33] Petersen, C., Jaunzemis, A., Baldwin, M., Holzinger, M.J., and Kolmanovsky, I.V., “Model Predictive Control and extended command governor for improving robustness of relative motion guidance and control,” Proceedings of AAS/AIAA Space Flight Mechanics Meeting, Paper AAS 14-249, Santa Fe, NM, January 2014.

[34] Petersen, C., and Kolmanovsky, I.V., “Coupled translational and rotational dynamics for precise constrained rendezvous and docking with periodic reference governors, Proceedings of 26^th AAS/AIAA Space Flight Mechanics Meeting, Napa, CA, February 14-18, 2016, Advances in Astronautical Sciences, vol. 158, Paper AAS 16-507.

Applications to spacecraft attitude control

[35] Weiss, A., Leve, F., Baldwin, M., Forbes, J., and Kolmanovsky, I.V., “Spacecraft constrained attitude control using positively invariant constraint admissible sets on SO(3)xR^3,” Proceedings of American Control Conference, Portland, Oregon, pp. 4955-4960, 2014.

Applications to Very Flexible Aircraft (VFA)

[35] Dillsaver, M., Kalabic, U., Kolmanovsky, I.V., and Cesnik, C., "Constrained control of a Very Flexible Aircraft using reference and extended command governors," Proceedings of American Control Conference, Washington DC, pp. 1611-1614, 2013.

[36] Gong, X., Zaseck, K., Kolmanovsky, I.V., and Chen, H., "Modeling and predictive control of free piston engine generator," Proceedings of 2015 American Control Conference, Chicago, IL, pp. 4735-4740, 2015.

[37] Gong, X., Zaseck, K., Kolmanovsky, I.V., and Chen, H., "Dual-loop control of free piston engine generator," Proceedings of IFAC E-COSM Workshop on Engine and Powertrain Control, Simulation and Modeling, Columbus, Ohio, 2015.

[38] Zaseck, K., Kolmanovsky, I.V., and Brusstar, M., “Constraint enforcement of piston motion in a free-piston engine,” Proceedings of 2014 American Control Conference, Portland, Oregon, pp. 1487-1492, 2014.

[39] Zaseck, K., Kolmanovsky, I.V., and Brusstar, M., “Stability, control, and constraint enforcement of piston motion in a hydraulic free-piston engine,” IEEE Transactions on Control Systems Technology, 2017.

Applications to wind energy/flying wind turbines

[40] Kalabic, U., Vermillion, C., and Kolmanovsky, I.V., “Reference governor design for computationally efficient attitude and tether tension constraint enforcement on a lighter than air wind energy system,” Proceedings of European Control Conference, Zurich, Switzerland, pp. 1004-1010, 2013.

Applications to gasoline turbocharged direct injection engines with experimental results

[41] Kalabic, U., Buckland, J., Cooper, S.L., Wait, S.K., and Kolmanovsky, I.V., “Reference governors for enforcing compressor surge constraints,” IEEE Transactions on Control Systems Technology, vol. 24, no. 5, pp. 1729-1739, 2016.

Synergistic input observers to facilitate engine reference governor implementation

[42] Kalabic, U., Kolmanovsky, I.V., and Buckland, J., "Multi-input observer for estimation of compressor flow," Proceedings of 2013 Dynamic Systems and Control Conference, V001T04A002-V001T04A002, Palo Alto, California, USA, October 21–23, 2013.

Applications to gas turbine engines

[43] Kolmanovsky, I.V., Jaw, L., Merrill, W., and H.-T. Tran, "Robust control and limit protection in aircraft gas turbine engines," Proceedings of IEEE Multi-conference on Systems and Control, Dubrovnik Palace Hotel, Dubrovnik, Croatia, October 3-5, pp. 812-819, 2012.

[44] Kolmanovsky, I.V., and Merill, W. "Limit protection in gas turbine engines based on reference and extended command governors," Proceedings of 50th AIAA/ASME/SAE/ASEE Joint Propulsion and Energy Forum and Exposition, Cleveland, Ohio, 2014.

[45] Tian, Y., and Kolmanovsky, I.V. “Reduced order and prioritized reference governors for limit protection in aircraft gas turbine engines,” Proceedings of AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2014-1149, pp. 1-19, 2014.

Fast reference governor for linear systems

[46] Nicotra, M., Garone, E., and Kolmanovsky, I.V., “A fast reference governor for linear systems,” AIAA Journal of Guidance, Control, and Dynamics, 2016.

Applications to loss of control of aircraft

[47] Di Donato, P.F.A., Balachandran, S., McDonough, K., Atkins, E., and Kolmanovsky, I.V., "Envelope-aware flight management for loss of control prevention given rudder jam," AIAA Journal of Guidance, Control, and Dynamics, 2016.

[44] Bencatel, R., Girard, A., and Kolmanovsky, I.V., "Reference governor strategies for vehicle rollover avoidance", IEEE Transactions on Control Systems Technology, 2017.

Matlab software files

We are developing a Matlab package to implement reference governor computations. Example files implementing robust reference governor, command governor and reduced reference governor are found here Sim Reference Governor

VIDEO: Rollover avoidance using reference governor