The regulator problem for both discrete-time and continuous-time linear systems is considered. The control and its increments are under non-symmetrical constraints and the domain of constraints includes the origin on its boundary. We derive necessary and sufficient conditions which ensure the satisfaction of all the constraints and also the asymptotic stability by a state feedback. An illustrative example shows the application of our method.
- Wang L. Model Predictive Control System Design and Implementation Using MATLAB. London, Springer (2009).
- Chen H. Stability and Robustness Considerations in Nonlinear Model Predictive Control. Ph.D. Thesis. Germany, University of Stuttgart (1997).
- Gutman P. O., Hagander P. A new design of constrained controllers for linear systems. IEEE Transactions on Automatic Control. 30 (1), 22–33 (1985).
- Benzaouia A., Hmamed A., Tadeo F. Stabilization of controlled positive delayed continuous time systems. International Journal of Systems Science. 41 (12), 1473–1479, (2010).
- Hmamed A., Ait Rami M., Benzaouia A., Tadeo F. Stabilization under constrained states and controls of positive systems with time delays. European Journal of Control. 18 (2), 182–190 (2012).
- Bensalah H., Baron L. Positive invariance of constrained linear continuous-time delay system with delay dependence. Proceedings of the international conference of control, dynamic systems and robotics. Ottawa, Ontario, Canada. 179 (2015).
- El Bhih A., Benfatah Y., Ghazaoui A., Rachik M. On the maximal output set of fractional-order discrete-time linear systems. Mathematical Modeling and Computing. 9 (2), 262–277 (2022).
- Dórea C. E., Olaru S., Niculescu S.-I. Delay-dependent polyhedral invariant sets for continuous-time linear systems. IFAC-PapersOnline. 55 (34), 108–113 (2022).
- Benzaouia A., Burgat C. Regulator problem for linear discrete-time systems with non-symmetrical constrained control. International Journal of Control. 48 (6), 2441–2451 (1988).
- Clarcke D. W., Mohtadi C., Tuffs P. S. Generalised predictive control – Part I. The basic algorithm. Automatica. 23 (2), 137–148 (1987).
- Clarcke D. W., Mohtadi C., Tuffs P. S. Generalised predictive control – Part II. Extension and Interpretations. Automatica. 23 (2), 149–160 (1987).
- Gilbert E. G., Tan K. T. Linear systems with state and control constraints: on the theory of maximal output admissible sets. IEEE Transactions on Automatic Control. 36 (9), 1008–1020 (1991).
- Zakary O., Rachik M., Tridane A., Abdelhak A. Identifying the set of all admissible disturbances: discrete-time systems with perturbed gain matrix. Mathematical Modeling and Computing. 7 (2), 293–309 (2020).
- Biannic J.-M., Tarbouriech S. Optimization and implementation of dynamic anti-windup compensators with multiple saturations in flight control systems. Control Engineering Practice. 17 (6), 703–713 (2009).
- Brieger O., Kerr M., Leissling D., Postlethwaite I., Sofrony J., Turner M. C. Flight testing of a rate saturation compensation scheme on the ATTAS aircraft. Aerospace Science and Technology. 13 (2–3), 92–104 (2009).
- Syafiie S., Tadeo F., Villafin M., Alonso A. A. Learning control for batch thermal sterilization of canned foods. ISA Transactions. 50 (1), 82–90 (2011).
- Mhaskar P., Keneddy A. B. Robust model predictive control of nonlinear process systems: Handling rate constraints. Chemical Engineering Science. 63 (2), 366–375 (2008).
- Valencia-Palomo G., Rossiter J. A. Programmable logic controller implementation of an auto-tuned predictive control based on minimal plant information. ISA Transactions. 50 (1), 92–100 (2011).
- Prívara S., Široký J., Ferkl L., Cigler J. Model predictive control of a building heating system: The first experience. Energy and Buildings. 43 (2–3), 564–572 (2011).
- Parker R. S., Doyle F. J., Peppas N. A. A model-based algorithm for blood glucose control in Type I diabetic patients. IEEE Transactions on Biomedical Engineering. 46 (2), 148–157 (1999).
- Schuster E., Walker M. L., Humphreys D. A., Krstić M. Plasma vertical stabilization with actuation constraints in the DIII-D tokamak. Automatica. 41 (7), 1173–1179 (2005).
- Blanco E., De Prada C., Cristea S., Casas J. Nonlinear predictive control in the LHC accelerator. Control Engineering Practice. 17 (10), 1136–1147 (2009).
- Mesquine F., Tadeo F., Benzaouia A. Regulator problem for linear systems with constraints on the control and its increments or rate. Automatica. 40 (8), 1387–1395 ( 2004).
- Mesquine F., Tadeo F., Benzaouia A. Constrained Control and Rate or Increment for Linear Systems with Additive Disturbances. Mathematical Problems in Engineering. 2006, 037591 (2006).
- Bitsoris G., Olaru S. Further results on the linear constrained regulation problem. 21st Mediterranean Conference on Control and Automation. 824–830 (2013).
- Bitsoris G., Olaru S., Vassilaki M. On the linear constrained regulation problem for continuous-time systems. IFAC Proceedings Volumes. 47 (3), 4004–4009 (2014).
- Fernandez-Camacho E., Bordons-Alba C. Model Predictive Control in the Process Industry. Springer Verlag (2004).
- Bitsoris G. Positively invariant polyedral sets of discrete-time linear systems. International Journal of Control. 47 (6), 1713–1726 (1988).
- Henrion D., Tarbouriech S., Kučera V. Control of linear systems subject to input constraints: a polynomial approach. Automatica. 36 (4), 597–604 (2001).
- Benzaouia A., Hmamed A. Regulator problem of linear continuous-time systems with non-symmetrical constrained control. IEEE Transaction on Automatic Control. 38 (10), 1550–1560 (1993).
- Mesquine F., Tadeo F., Benzaouia A. Regulator problem for linear systems with constraints on control and its increment. IFAC Proceedings Volumes. 35 (1), 85–90 (2002).
- Benzaouia A. Resolution of equation XA+XBX=HX and the pole assignment problem. IEEE Transaction on Automatic Control. 39 (10), 2091–2095 (1994).