My main current research interests

 

BOOLEAN CONTROL NETWORKS

Collaborations with: NICOLETTA BOF, ETTORE FORNASINI, GAL HOCHMA, MICHAEL MARGALIOT.

TOPIC DESCRIPTION: Research   in  Boolean networks (BNs)  and Boolean control networks (BCNs) has a   long tradition. The  renewed interest witnessed in recent times, however, must be mainly credited to two reasons: on the one hand, BNs and BCNs  have  proved to be  effective modeling tools for a number of rapidly evolving research topics,  like  genetic regulation networks  and consensus problems.

On the other hand, the  algebraic framework   developed by D. Cheng and co-authors has allowed   to  cast  both BNs and BCNs into the framework of linear state-space models (operating  on canonical vectors), thus benefitting of a  number of powerful algebraic tools, in addition to   traditional graph-based techniques.

PROBLEMS INVESTIGATED: CONTROLLABILITY, STABILIZATION TO AN EQUILIBRIUM POINT OR TO A LIMIT CYCLE, OPTIMAL CONTROL, OUTPUT FEEDBACK STABILIZATION, CONNECTIONS WITH SYMBOLIC DYNAMICS, OBSERVABILITY, FAULT DETECTION, INPUT/OUTPUT DECOUPLING.

RELATED JOURNAL PUBLICATIONS

(go to the publications section for the full list and related files)

  1. A. Fornasini, M.E. Valcher "Observability, reconstructibility and state observers  of Boolean Control Networks", IEEE Transactions on Automatic Control, Volume 58, Issue 6, pp. 1390 - 1401, 2013.

  2. B. G. Hochma, M. Margaliot, E. Fornasini and   M.E.  Valcher  "Symbolic Dynamics of  Boolean Control Networks", Automatica, vol. 49, no.8, pp. 2525–2530, 2013.

  3. C. E. Fornasini, M.E. Valcher "On the periodic trajectories of Boolean Control Networks", Automatica, vol. 49, pp. 1506-1509, 2013.

  4. D. E. Fornasini, M.E. Valcher "Optimal control of Boolean control networks", IEEE Transactions on Automatic Control, vol. 59, no. 5, pp. 1258-1270, May 2014

  5. E. E. Fornasini, M.E. Valcher, "Identification problems for Boolean networks and Boolean control networks", Proceedings of the IFAC World Conference (IFAC 2014), Cape Town (South Africa), pp. 5399-5404, August 24-29, 2014.

  6. F. N. Bof, E. Fornasini and Maria Elena Valcher, "Output feedback stabilization of Boolean control networks", Automatica, vol. 57, pp. 21-28, July 2015.

  7. G. E. Fornasini, M.E. Valcher "Fault detection analysis of Boolean control networks", IEEE Transactions on Automatic Control, Vol. 60, no. 10, pp. 2734-2739, 2015.

  8. H. E. Fornasini, M.E. Valcher "Fault detection problems for Boolean networks and Boolean control networks", Proceedings of the 34th Chinese Conference, pp. 1-8, Hangzhou, China, July 28-30, 2015.

  9. I. E. Fornasini, M.E. Valcher, “Recent developments in Boolean Control Networks”, (SurveyPaper) Journal of Control and Decision, special issue “Selected Keynotes and Distinguished Lectures of 2015 Chinese Control and Decision Conference”, vol. 3, issue 1, pp. 1-18, 2016




POSITIVE SWITCHED SYSTEMS

Collaborations with: FRANCO BLANCHINI, PATRIZIO COLANERI, ETTORE FORNASINI, JOHN LYGEROS, FRANCESCA PARISE, IRENE ZORZAN.

TOPIC DESCRIPTION: LINEAR SWITCHED SYSTEMS, WITH THE POSITIVITY CONSTRAINT ON THE STATE AND INPUT VARIABLES, HAVE BEEN THE OBJECT OF A SIGNIFICANT NUMBER OF CONTRIBUTIONS IN THE LAST TEN YEARS. THE INTEREST IN THIS CLASS OF SYSTEMS IS PRIMARILY MOTIVATED BY THE NUMBER OF APPLICATION AREAS WHERE THEY HAVE BEEN FRUITFULLY EMPLOYED. TO MENTION THE MOST SIGNIFICANT ONES: WIRELESS POWER CONTROL, CONGESTION CONTROL, SYSTEM BIOLOGY, HIV MITIGATION THERAPY AND PHARMACOKINETIC.

ON THE OTHER HAND, THE INVESTIGATION OF POSITIVE SWITCHED SYSTEMS OFFERS A GOOD NUMBER OF CHALLENGING PROBLEMS, SINCE THE POSITIVITY CONSTRAINT ON THE STATE AND INPUT VARIABLES MAKES IT IMPOSSIBLE TO RESORT TO TECHNIQUES AND RESULTS BASED ON FINITE-DIMENSIONAL VECTOR SPACES, AND DEMANDS FOR THE INVOLVEMENT OF LESS SETTLED APPROACHES, BASED ON CONES AND POLYTOPES. THIS IS THE CASE, FOR INSTANCE, WHEN DEALING WITH REACHABILITY AND CONTROLLABILITY OF POSITIVE SWITCHED SYSTEMS, TWO TOPICS THAT ARE STILL MOSTLY UNEXPLORED.

WHEN ADDRESSING STABILITY AND STABILIZABILITY PROBLEMS, ON THE OTHER HAND, THE RESULTS OBTAINED FOR STANDARD LINEAR SWITCHED SYSTEMS CAN BE FRUITFULLY EMPLOYED BUT IN GENERAL THEY REPRESENT CONSERVATIVE RESULTS, AND AD-HOC TOOLS, BASED ON COPOSITIVE (CONTROL) LYAPUNOV FUNCTIONS AND ON CHARACTERIZATIONS INVOLVING THE CONVEX COMBINATIONS OF THE SUBSYSTEM MATRICES, TURN OUT TO BE MORE APPROPRIATE

PROBLEMS INVESTIGATED: REACHABILITY/CONTROLLABILITY, STABILITY AND STABILIZATION, STABILITY AND STABILIZATION OF SPECIAL CLASSES OF POSITIVE SWITCHED SYSTEMS INCLUDING COMPARTMENTAL SWITCHED SYSTEMS.

RELATED JOURNAL PUBLICATIONS

(go to the publications section for the full list and related files)

  1. A. P.Santesso, M.E. Valcher “Monomial reachability and zero-controllability of discrete-time positive switched systems”, Systems and Control Letters, vol. 57, pp.340-347, 2008.

  2. B. M.E. Valcher, P.Santesso  “Reachability properties of single-input continuous-time positive switched systems”, IEEE Transactions on Automatic Control, pp. 1117-1130, vol. 55, no.5, May 2010.

  3. C. E. Fornasini, M.E. Valcher "Reachability  of a class of discrete-time positive switched  systems", SIAM J. on Control and Optimization, vol. 49, no.1, pp 162-184, 2011.

  4. D. E. Fornasini, M.E. Valcher "Linear  copositive Lyapunov functions for continuous-time positive switched  systems", IEEE Transactions on Automatic Control, pp. 1933-1937, vol. 55, no.8, August 2010.

  5. E. E. Fornasini, M.E. Valcher "Asymptotic stability and stabilizability of special classes of discrete-time positive switched  systems", Linear Algebra and its Appl., Special Issue on ILAS 2010, vol. 438, pp. 1814-1831, February 2013.

  6. F. E. Fornasini, M.E. Valcher "Stability and stabilizability criteria for discrete-time positive switched  systems", IEEE Transactions on Automatic Control, vol. 57, no.5, pp. 1208-1221, 2012.

  7. G. F. Blanchini, P. Colaneri, M.E. Valcher "Co-positive Lyapunov functions for the stabilization of positive  switched systems", IEEE Transactions on Automatic Control, vol. 57, no.12, pp. 3038-3050, December 2012.

  8. H. E. Fornasini, M.E. Valcher "On the stability of continuous-time  positive switched systems with rank one difference", Control & Cybernetics, special issue for the  80th birthday of Tadeusz Kaczorek, vol. 42, no. 1, pp. 47-62, 2013.

  9. I.E. Fornasini, M.E. Valcher "Stability properties of a class of positive switched systems with rank one difference", Systems and Control Letters, vol. 64, pp.12-19, February 2014.

  10. J.M.E. Valcher, I. Zorzan "On the stabilizability of continuous-time compartmental  switched systems", Proceedings of the 54th IEEE Conf. on Decision and Control, Osaka, Japan, pp. 4246-4251, December 15-18, 2015.

  11. K.F. Parise, M.E. Valcher, J. Lygeros "Reachability analysis for switched affine systems and its application to controlled stochastic biochemical reaction networks", Proceedings of the 55th IEEE Conf. on Decision and Control, pp. 746- 751, Las Vegas, Nevada, December 12-14, 2016.

  12. L.M.E. Valcher, I. Zorzan "Stability and stabilizability of continuous-time compartmental switched systems", IEEE Transactions on Automatic Control, vol. 61, no. 12, pp. 3885 - 3897, 2016