Hybrid Systems

Hybrid systems have been the subject of intensive study in the past few years by both the control and the computer-science communities. Particular emphasis has been placed on a unified representation of hybrid models rooted in rigorous mathematical foundations. Some classical problems such as reachability analysis, stability and safety have been investigated and tools for their solutions, i.e. HyTech, Kronos, Checkmate, developed. However, since the class of hybrid control problems is extremely broad (it contains continuous control problems as well as discrete event control problems as special cases), it is very difficult to devise a general yet effective strategy to solve them. In our opinion, it is important to address significant application domains to develop further understanding of the implications of the hybrid model on control algorithms and to evaluate whether using this formalism can be of substantial help in solving complex, real-life, control problems.

In this research, we focus on an application domain for hybrid system theory that is of great industrial interest: automotive engine and power-train control.  The engine control problem is very complex. The system can be decomposed into a chain of basic processes. Air intake and fuel injection can be controlled to yield the desired mix to deliver to the combustion process.  The timing of the sparks generated by the spark plugs determines the start of the combustion process that takes place in the cylinders.  The torque and the emissions generated by the combustion process depend on the fuel mix (quantity of fuel and its dynamics) and on the spark ignition timing. The torque is then delivered to the power-train and the emissions to the exhaust subsystem. The goals for the control strategy are, in general, given in terms of emissions and torque but it is often the case that sub-goals are given by car manufacturers on all the processes in the chain. Unfortunately even these goals are quite complex to specify since they depend on the behavior that the driver requests the car to have.

Based on the data from sensors measuring emissions and car dynamics, embedded controllers compute the control actions to apply. The ever increasing computational power of micro-controllers has made it possible to extend the performance and the functionality of these embedded controllers to limits that were unthinkable only a few years ago.  This opportunity has exposed the need for control algorithms with guaranteed properties that can reduce substantially emissions and gas consumption while maintaining the performance of the car.  To do so, we believe that it is important to use more accurate models than the ones proposed so far. An accurate model of a four-stroke gasoline engine has a ``natural'' hybrid representation because

• pistons have four modes of operation corresponding to the stroke they are in. Hence their behavior can be represented with a finite state model;

• power-train and air dynamics are continuous-time processes.

In addition, these processes interact tightly. In fact, the timing of the transitions between two phases of the pistons is determined by the continuous motion of the power-train, which in turn, depends on the torque produced by each piston.  In engine control literature, the discrete part of the engine behavior is converted into a more familiar and easy-to-handle continuous model where only the average values of the appropriate physical quantities are modeled.

The hybrid nature of the problem of engine control does not come only from the use of digital control laws, but it is rooted in the plant to be controlled. This characteristic complicates the modeling problem since several components with different mathematical properties are needed to capture the behavior of the engine and of the power-train. In fact, we use the term hybrid model for engine and power-train in a somewhat more general sense than it is common since our model includes interacting Finite State Machines, Discrete Event Systems and Continuous Time Systems.  We believe that the interactions among the different parts of a hybrid model of this type have not always been correctly described and characterized.  For these reasons, we review the concept of models of computation, which is commonly used in the embedded system design literature, and describe a modeling framework called the recently-proposed Tagged Signal Model that addresses explicitly time and partial orders among events, and is particularly suited to represent modality of interaction.  Our control algorithms applied to the hybrid model for engine and power-train share the same basic idea: relax the hybrid control problem to a simpler one and, then, modify appropriately the control law determined for the simpler problem to solve the original hybrid problem.

Publications:

A. Balluchi, L. Benvenuti, M. D. Di Benedetto, and A. L. Sangiovanni-Vincentelli. Idle Speed Controller Synthesis Using an Assume--Guarantee Approach. In Nonlinear and Hybrid Control in Automotive Applications, Lecture Notes in Computer Science. Springer-Verlag, 2002. 

A. Balluchi, L. Benvenuti, M. D. Di Benedetto, and A. L. Sangiovanni-Vincentelli. Design of Observers for Hybrid Systems. In C. J. Tomlin and M. R. Greenstreet, editors, Hybrid Systems: Computation and Control, volume ? of Lecture Notes in Computer Science, pages ?. Springer-Verlag, New York, U.S.A., 2002.

A. Balluchi, L. Benvenuti, M. D. Di Benedetto, and A. L. Sangiovanni-Vincentelli. Hybrid Control of Force Transients for Multi-point Injection Engines. International Journal of Robust and Nonlinear Control, 11, ``Special Issue on Hybrid Systems'' (invited paper):515--539, April 2001.

A. Balluchi, P. Souˆres, and A. Bicchi. Hybrid Feedback Control for Path Tracking by a Bounded--Curvature Vehicle. In M. D. Di Benedetto and A. L. Sangiovanni-Vincentelli, editors, Hybrid Systems: Computation and Control, volume 2034 of Lecture Notes in Computer Science, pages 133--146. Springer-Verlag, New York, U.S.A., 2001. 

P. Souˆres, A. Balluchi, and A. Bicchi. Optimal Feedback Control for Route Tracking with a Bounded--Curvature Vehicle. International Journal of Control, 74(10):1009-19, July 2001. 

M. D. Di Benedetto and A. L. Sangiovanni-Vincentelli, editors. Hybrid Systems: Computation and Control, volume 2034 of Lecture Notes in Computer Science, Rome, March 2001. Springer-Verlag, Heidelberg, Germany.

A. Balluchi, L. Benvenuti, M. D. Di Benedetto, G. M. Miconi, U. Pozzi, T. Villa, H. Wong-Toi, and A. L. Sangiovanni-Vincentelli. Maximal Safe Set Computation for Idle Speed Control of an Automotive Engine. In Nancy Lynch and Bruce H. Krogh, editors, Hybrid Systems: Computation and Control, volume 1790 of Lecture Notes in Computer Science, pages 32--44. Springer-Verlag, New York, U.S.A., 2000. 

A. Balluchi, L. Benvenuti, M. D. Di Benedetto, C. Pinello, and A. L. Sangiovanni-Vincentelli. Automotive Engine Control and Hybrid Systems: Challenges and Opportunities. Proceedings of the IEEE, 88, ``Special Issue on Hybrid Systems'' (invited paper)(7):888-912, July 2000. 

M. Broucke, M. Di Benedetto, and A. Sangiovanni-Vincentelli. Theory of Optimal Control Using Bisimulations. In N. Lynch and B. H. Krogh, editors, Hybrid Systems: Computation and Control, volume 1790, pages 89-102. Springer-Verlag, New York, U.S.A., 2000.

A. Balluchi, M. D. Di Benedetto, C. Pinello, C. Rossi, and A. L. Sangiovanni-Vincentelli. Hybrid Control in Automotive Applications: the Cut-off Control. Automatica, 35, (invited paper) Special Issue on Hybrid Systems(3):519--535, March 1999. 

A. Balluchi, M. D. Di Benedetto, C. Pinello, and A. L. Sangiovanni-Vincentelli. Hybrid Control in Automotive Applications. In D. S. Gilliam G. Picci, editor, Dynamical Systems, Control, Coding, Computer Vision, volume 25 of Progress in Systems and Control Theory, pages 449--479. Birkh„user, Basel, Boston, Berlin, 1999. 

A. Balluchi, M. D. Di Benedetto, C. Pinello, C. Rossi, and A. L. Sangiovanni-Vincentelli. Hybrid Control for Automotive Engine Management: The Cut-Off Case. In T.A. Henzinger and S. Sastry, editors, Hybrid Systems: Computation and Control, volume 1386 of Lecture Notes in Computer Science, pages 13--32. Springer-Verlag, London, U.K., 1998.

A. L. Sangiovanni-Vincentelli. Control Using Logic-Based Switching. In A.S. Morse, editor, Embedded System Design and Hybrid Systems, pages 17-38. Springer-Verlag, U.K., 1997.

A. Balluchi, L. Benvenuti, M. D. Di Benedetto, G. Girasole, and A. L. Sangiovanni-Vincentelli. Idle Speed Control Design and Verification for an Automotive Engine. In Proc. International Workshop on ``Modeling, Emissions and Control in Automotive Engines'', MECA'01, Salerno, Italy, September 2001. 

A. Balluchi, L. Benvenuti, M. D. Di Benedetto, and A. L. Sangiovanni-Vincentelli. A Hybrid Observer for the Driveline Dynamics. In Proc. 6th European Control Conference, ECC2001, Porto, Portugal, September 2001. 

A. Balluchi, M. D. Di Benedetto, C. Pinello, and A. L. Sangiovanni-Vincentelli. Mixed Models of Computation in the Design of Automotive Engine Control. In Proc. 40th IEEE Conference on Decision and Control, Orlando, Florida, December 2001. (invited paper). 

A. Balluchi, L. Benvenuti, M. D. Di Benedetto, C. Pinello, and A. L. Sangiovanni-Vincentelli. Automotive Engine and Power-Train Control: a Comprehensive Hybrid Model. In Proc. 8th Mediterranean Conference on Control and Automation - MED2000, Patras, Greece, July 2000. (invited paper). 

A. Balluchi, L. Benvenuti, M. D. Di Benedetto, T. Villa, H. Wong-Toi, and A. L. Sangiovanni-Vincentelli. Hybrid Controller Synthesis for Idle Speed Management of an Automotive Engine. In Proc. 2000 IEEE American Control Conference, volume 2, Chicago, IL, USA, pages 1181--1185, June 2000. (invited paper). 

A. Balluchi, A. Bicchi, C. Caterini, C. Rossi, and A. L. Sangiovanni-Vincentelli. Hybrid Tracking Control for Spark--Ignition Engines. In Proc. 39th IEEE Conference on Decision and Control, volume 4, Sydney, NSW, Australia, pages 3126-31, December 2000. 

A. Balluchi, A. Bicchi, B. Piccoli, and P. Souˆres. Stability and Robustness of Optimal Synthesis for Route Tracking by Dubins' Vehicles. In Proc. 39th IEEE Conference on Decision and Control, volume 1, Sydney, Australia, pages 581-6, December 2000. (invited paper). 

P. Souˆres, A. Balluchi, and A. Bicchi. Optimal Feedback Control for Route Tracking with a Bounded--Curvature Vehicle. In Proc. 2000 IEEE International Conference on Robotics and Automation, San Francisco, California, USA, pages 2473--2478, April 2000. 

A. Balluchi, L. Benvenuti, M. D. Di Benedetto, C. Cardellino, C. Rossi, and A. L. Sangiovanni-Vincentelli. Hybrid Control of the Air-fuel Ratio in Force Transients for Multi-point Injection Engines. In Proc. 38th IEEE Conference on Decision and Control, Phoenix, Arizona, USA, pages 316--321, December 1999. 

A. Balluchi, L. Benvenuti, T. Villa, H. Wong-Toi, and A. L. Sangiovanni-Vincentelli. Controller Synthesis for Hybrid Systems with Lower Bounds on Event Separation. In Proc. 38th IEEE Conference on Decision and Control, Phoenix, Arizona, USA, pages 3984--3989, December 1999. 

A. Balluchi, L. Benvenuti, H. Wong-Toi, T. Villa, and A. L. Sangiovanni-Vincentelli. A Case Study of Hybrid Controller Synthesis of a Heating System. In Proc. 5th European Control Conference, ECC99, Karlsruhe, Germany, September 1999. 

A. Balluchi, L. Benvenuti, M. D. Di Benedetto, A. Ferrari, C. Pinello, C. Rossi, and A. L. Sangiovanni-Vincentelli. The Design of Embedded Controllers for Automotive Engine Management: the Cut-off Case. In Proc. Cadence Technical Conference 1998, S. Antonio, Texas, USA, pages 183--190, May 1998.

A. Balluchi, A. Bicchi, G. Padroni, C. Rossi, and A. L. Sangiovanni-Vincentelli. Hybrid Optimization Problems in Automotive Applications. In Proc. IFAC International Workshop on Motion Control, Grenoble, France, pages 273--278, September 1998. 

A. Balluchi, M. D. Di Benedetto, C. Pinello, and A. L. Sangiovanni-Vincentelli. A Hybrid Approach to the Fast Positive Force Transient Tracking Problem in Automotive Engine Control. In Proc. 37th IEEE Conference on Decision and Control, Tampa, Florida, USA, pages 3226--3231, December 1998. 

T. Villa, H. Wong-Toi, A. Balluchi, J. Preussig, A. L. Sangiovanni-Vincentelli, and Y. Watanabe. Formal Verification of an Automotive Engine Controller in the Cutoff Mode. In Proc. Cadence Technical Conference 1998, S. Antonio, Texas, USA, pages 586--592, May 1998. 

T. Villa, H. Wong-Toi, A. Balluchi, J. Preussig, A. L. Sangiovanni-Vincentelli, and Y. Watanabe. Formal Verification of an Automotive Engine Controller in the Cutoff Mode. In Proc. 37th IEEE Conference on Decision and Control, Tampa, Florida, USA, pages 4271--4276, December 1998. 

A. Balluchi, M. D. Di Benedetto, C. Pinello, C. Rossi, and A. L. Sangiovanni-Vincentelli. Cut-off in Engine Control: a Hybrid System Approach. In Proc. 36th IEEE Conference on Decision and Control, San Diego, California, USA, pages 4720--4725, December 1997.

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