Interpolating Control Toolbox

ICT is a free and open-source MATLAB toolbox for computing interpolation-based control of linear time-invariant (LTI) and time-varying (LTV) systems subject to local state and control constraints. The technique behind it is based on the interpolating control (IC) scheme introduced by [3-5] and later extended by [8-10] for decentralised (robust) IC. The main idea of IC is to blend a local high-gain (inner) controller, which satisfies some user-desired performance specifications, with a global low-gain (outer) controller via interpolation. The two controllers are defined in some invariant sets that are determined offline; the applied control is determined on-line with an inexpensive interpolation between the two controllers. For the interpolation, a low-dimensional linear programming (LP) problem is solved at each time instant.

Relevant Publications

  1. F. Blanchini and S. Miani, Set-Theoretic Methods in Control. Birkhäuser Basel, 2008.
  2. F. Blanchini, "Set invariance in control," Automatica, vol. 35, pp. 1747-1767, 1999.
  3. E. C. Kerrigan, "Robust constraint satisfaction: Invariant sets and predictive control," Ph.D. dissertation, University of Cambridge, United Kingdom, 2000.
  4. H.-N. Nguyen, Constrained Control of Uncertain, Time-Varying, Discrete-Time Systems. Cham, Switzerland: Springer, 2014.
  5. H.-N. Nguyen, P.-O. Gutman, S. Olaru, and M. Hovd, "Implicit improved vertex control for uncertain, time-varying linear discrete-time systems with state and control constraints," Automatica, vol. 49, no. 9, pp. 2754-2759, 2013.
  6. H.-N. Nguyen, P.-O. Gutman, and R. Bourdais, "More efficient interpolating control," in Proc. 2014 European Control Conference (ECC), 2014, pp. 2158–2163.
  7. E. G. Gilbert and K. T. Tan, “Linear systems with state and control constraints: the theory and application of maximal output admissible sets," IEEE Transactions on Automatic Control, vol. 36, no. 9, pp. 1008–1020, 1991.
  8. P.-O. Gutman and M. Cwikel, “Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and states,” IEEE Transactions on Automatic Control, vol. 31, no. 4, pp. 373–376, 1986.
  9. S. Scialanga and K. Ampountolas, "Interpolating constrained control of interconnected systems," IFAC-PapersOnLine, vol. 51, no. 9, pp. 7–12, 2018. DOI: 10.1016/j.ifacol.2018.07.002
  10. S. Scialanga and K. Ampountolas, "Robust constrained Interpolating Control of interconnected systems," In: 57th IEEE Conference on Decision and Control (CDC), Fontainebleau, Miami Beach, FL, USA, Dec. 17-19, 2018, pp. 7016-7021. doi:10.1109/cdc.2018.8619513
  11. S. Scialanga and K. Ampountolas, "Interpolating Control Toolbox (ICT)," In: 2019 18th European Control Conference (ECC), Naples, Italy, June 25–28, 2019, pp. 2510–2515. doi:10.23919/ecc.2019.8796000
  12. S. Scialanga, S. Olaru, K. Ampountolas, "Reduced-complexity interpolating control with periodic invariant sets". International Journal of Control, doi:doi:10.1080/00207179.2021.2013540, 2021.