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A numerically robust state-space approach to stable-predictive control strategies. (English) Zbl 0913.93022
The stable general predictive control (SGPC) transfer function framework is extended to a state-space representation which has significant computational and numerical advantages in the case of an open-loop unstable plant. The key idea is prestabilization of the plant before the predictions (for the SGPC algorithms) are computed. Prestabilization ensures stable and bounded predictions which improves numerical conditioning hence the use of matrices with very large elements associated with unstable predictions is avoided. Prestabilization is later removed through optimization. It is shown that the proposed alternative to a SGPC algorithmic formulation for state-space control laws does not suffer from poor conditioning and meets most terminal constraints imposed by the SGPC approach.

93B51 Design techniques (robust design, computer-aided design, etc.)
93B40 Computational methods in systems theory (MSC2010)
Full Text: DOI
[1] Bemporad, A.; Mosca, E., Constraint fulfillment in control systems via predictive reference management, (), 3017-3022
[2] Chisci, L.; Lombardi, A.; Mosca, E.; Rossiter, J.A., Stochastic state-space approach to stabilizing predictive control, Int. J. control, 65, 4, 619-637, (1996) · Zbl 0863.93088
[3] Chisci, L.; Rossiter, J.A., Stabilizing predictive control: static vs dynamic programming approach, IEE control 96, 1368-1373, (1996), Exeter, UK
[4] Clarke, D.W.; Scattolini, R., Constrained receding horizon predictive control, (), 347-354, (4) · Zbl 0743.93063
[5] Gossner, J.R.; Kouvaritakis, B.; Rossiter, J.A., Cautious stable predictive control: a guaranteed stable predictive control algorithm with low input activity and good robustness, Int. J. control, 67, 5, 675-697, (1997) · Zbl 0882.93025
[6] Keerthi, S.S.; Gilbert, E.G., Optimal, infinite horizon feedback laws for a general class of constrained discrete-time systems: stability and moving horizon approximations, J. optim. theory appl., 57, 2, 265-293, (1988) · Zbl 0622.93044
[7] Kouvaritakis, B.; Rossiter, J.A.; Chang, A.O.T., Stable generalized predictive control: an algorithm with guarenteed stability, (), 349-362, (4) · Zbl 0765.93065
[8] Michalska, H.; Mayne, D., Robust receding horizon control of constrained nonlinear systems, IEEE trans autmat. control, 38, 1623-1633, (1993) · Zbl 0790.93038
[9] Mosca, E.; Zhang, J., Stable redesign of predictive control, Automatica, 28, 6, 1229-1233, (1992) · Zbl 0775.93056
[10] Rawlings, J.B.; Muske, K.R., The stability of constrained receding horizon control, IEEE trans. automat. control, 38, 10, 1512-1516, (1993) · Zbl 0790.93019
[11] Rossiter, J.A.; Gossner, J.R.; Kouvaritakis, B., Infinite horizon stable predictive control, IEEE trans. automat. contract, 41, 10, 1522-1527, (1996) · Zbl 0863.93037
[12] Rossiter, J.A.; Kouvaritakis, B., Constrained generalized predictive control, (), 243-254, (4) · Zbl 0786.93005
[13] Rossiter, J.A.; Kouvaritakis, B., Numerical robustness and efficiency of generalised predictive control algorithms with guaranted stability, (), 154-162, (3) · Zbl 0799.93049
[14] Rossiter, J.A.; Kouvaritakis, B.; Gossner, J.R., Feasibility and stability results for constrained stable generalised predictive control, Automatica, 31, 6, 863-877, (1995) · Zbl 0830.93067
[15] Scokaert, P.O.M.; Rawlings, J.B., Infinte horizon linear quadratic control with constraints, (), 109-114
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