模型预测控制及其应用研究
摘要
模型预测控制(MPC)是近三十年来飞速发展、取得了广泛应用的一种控制方法。它的当前控制作用是在每一个采样瞬间通过求解一个有限时域开环最优控制问题而获得。过程的当前状态作为最优控制问题的初始状态，解得的最优控制序列只实施第一个控制作用。这种控制方法的一个重要优点是它能够处理操作变量和状态的约束。模型预测控制已经被广泛地应用于石油化工及其相关工业。在这些工业过程中，满足约束是非常重要的。因为经济效益要求控制作用和状态接近其所允许的边界。
本文的主要内容包括：
1．系统地回顾了模型预测控制的发展历史，并对具有代表性的几种模型预测控制方法进行了简要的介绍和分析。
2．提出了模型预测控制的本质特点是其独有的实施方式。对传统的模型预测控制的三个特点说(预测模型、滚动优化、反馈校正)进行了分析和超越。
3．利用Lyapunov方法给出了模型预测控制闭环稳定性的4个基本条件。
4．简要分析了模型预测控制的鲁棒性和可行性。
5．对几个典型的控制系统进行了模型预测控制的仿真研究。一个是锅炉系统的汽包水位控制，这是一个不稳定的非最小相位系统。一个是三槽液位系统，这是一个不稳定的非线性系统。
Model predictive control is a form of control that developed rapidly and gained
extensive application in recent years. Its current control action is obtained by solving,
at each sampling instant, a finite horizon open-loop optimal control problem, using
the current state of the plant as initial state; the optimization yields an optimal control
sequence and the first control in this sequence is applied to the plant. An important
advantage of this type of control is its ability to cope with hard constraints on controls
and states. It has, therefore, been widely applied in petro-chemical and related
industries where satisfaction of constrains is particularly important because efficiency
demands operating points on or close to the boundary of the set of admissible states
and controls.
The main contents of this thesis are stated as follows:
I. It completely reviewed the development of model predictive control and
introduced and analyzed the main types of model predictive control in the
literature.
2. It pointed out that the main characteristic of the MIPC is its implementation.
It analyzed and overrided the traditional doctrine of the three characteristics
of the MIPC(model for prediction, receding horizon optimization, feedback).
3. It obtained the four axioms of the close loop stability of the MPG by using
the Lyapunov method.
4. It concisely analyzed the robustness and feasibility of the MIPC.
5. It emulated some classical plant with the model predictive control. One is
the level control of the boiler system, which is a unstable non-minimum
phase system; the other is a three-tank system, which is a unstable
non-linear system.
本文的主要内容包括：
1．系统地回顾了模型预测控制的发展历史，并对具有代表性的几种模型预测控制方法进行了简要的介绍和分析。
2．提出了模型预测控制的本质特点是其独有的实施方式。对传统的模型预测控制的三个特点说(预测模型、滚动优化、反馈校正)进行了分析和超越。
3．利用Lyapunov方法给出了模型预测控制闭环稳定性的4个基本条件。
4．简要分析了模型预测控制的鲁棒性和可行性。
5．对几个典型的控制系统进行了模型预测控制的仿真研究。一个是锅炉系统的汽包水位控制，这是一个不稳定的非最小相位系统。一个是三槽液位系统，这是一个不稳定的非线性系统。
Model predictive control is a form of control that developed rapidly and gained
extensive application in recent years. Its current control action is obtained by solving,
at each sampling instant, a finite horizon open-loop optimal control problem, using
the current state of the plant as initial state; the optimization yields an optimal control
sequence and the first control in this sequence is applied to the plant. An important
advantage of this type of control is its ability to cope with hard constraints on controls
and states. It has, therefore, been widely applied in petro-chemical and related
industries where satisfaction of constrains is particularly important because efficiency
demands operating points on or close to the boundary of the set of admissible states
and controls.
The main contents of this thesis are stated as follows:
I. It completely reviewed the development of model predictive control and
introduced and analyzed the main types of model predictive control in the
literature.
2. It pointed out that the main characteristic of the MIPC is its implementation.
It analyzed and overrided the traditional doctrine of the three characteristics
of the MIPC(model for prediction, receding horizon optimization, feedback).
3. It obtained the four axioms of the close loop stability of the MPG by using
the Lyapunov method.
4. It concisely analyzed the robustness and feasibility of the MIPC.
5. It emulated some classical plant with the model predictive control. One is
the level control of the boiler system, which is a unstable non-minimum
phase system; the other is a three-tank system, which is a unstable
non-linear system.
引文
1． Lee, E.B., & Markus, L. (1967) . Foundations of Optimal Control Theory. New York: Wiley.
2． Bellman, R. (1957) . Dynamic Programming. Princeton: Princeton University Press.
3． Kalman, R.E. (1960) . Contributions to the theory of optimal control. Boletin Sociedad Matematica Mexicana, 5, 102-119．
4． Kleinman, B.L. (1970) . An easy way to stabilize a linear constant system. IEEE Transactions on Automatic Control, 15(12) , 693．
5． Thomas, Y.A. (1975) . Linear quadratic optimal estimation and control with receding horizon. Electronics Letters, 11, 19-21．
6． Kwon, W.H., & Pearson, A.E. (1977) . A modified quadratic cost problem and feedback stabilization of a linear system. IEEE Transactions on Automatic Control, 22(5) , 838-842．
7． Kwon, W.H., Bruckstein, A.M., & Kailath, T. (1983) . Stabilizing state-feedback design via the moving horizon method. International Journal of Control, 37(3) , 631-643．
8． Richalet, J., Rault, A., Testud, J.L., & Papon, J. (1976) . Algorithmic control of industrial processes. Proceedings of the Fourth IFAC symposium on identification and system parameter estimation.
9． Propoi, A.I. (1963) . Use of linear programming methods for synthesizing sampled data automatic systems. Automation and remote Control, 24(7) , 837-844．
10． Cutler, C.R., & Ramaker, B.L. (1980) . Dynamic matrix control-a computer control algorithm. Proceedings Joint Automatic Control Conference, San Francisco, CA.
11． Garcia, C.E., & Morshedi, A.M. (1986) . Quadratic programming solution of dynamic matrix control(QDMC). Chemical Engineering Communications, 46．
12． Qin, S.J., & Badgwell, T.A. (1997) . An overview of industrial model predictive control technology. In: J.C Kantor, C.E. Garcia, & B. Carnahan(Eds.), Fifth
International Conference on Chemical Process Control, CACHE, AICHE, (pp.232-256) .
13． Garcia, C.E., Prett, D.M., & Morari, M. (1989) . Model predictive control: theory and practice-a survey. Automatica, 25(3) , 335-348．
14． Jay H. Lee, Manfred Morari & Carlos E. Garcia (1994) . State-space Interpretation of Model Predictive Control, Automatica, 30(4) , pp.707-717．
15． P. Lundstrom, J.H. Lee, M. Morari & S. Skogestad (1995) . Limitations of Dynamic Matrix Control. Computers Chem. Eng. (19) 4:409-421．
16． Richalet J., et al. Model Predictive Heuristic Control: Application Industrial Processes. Automatica. 1978, 14(5) :413-428．
17． Rouhani R, Mehra R.K. Model Algorithmic Control, Based Theoretical Properties. Automatica. 1982, 18(4) :401-414．
18． Garcia, C.E. & M. Morari (1982) . Internal Model Control-1． A unifying review and some new results. Ind. Engng Chem. Process Des. Dev., 21, 4308-323．
19． Mehra, R.K. & R. Rouhani (1980) . Theoretical considerations on model algorithmic control for non-minimum phase systems. Proc. Joint Aut. Control Conf, San Francisco, California.
20． Garcia, C.E. & M. Morari (1985a). Internal Model Control-2． Design procedure for multivariable systems. Ind. Engng Chem. Process Des. Dev., 24, 472-484．
21． Garcia, C.E. & M. Morari (1985b). Internal Model Control-3． Multivariable control law computation and tuning guidelines. Ind. Engng Chem. Process Des. Dev., 24, 484-494．
22． Richalet J. et al. Predictive Functional Control-Application to Fast and Accurate Robots. IFAC 10th Triennial World Conference.
23． D.W. Clarke, C. Mohtadi & PS. Tuffs. Generalized Predictive Control-Part 1． The basic algorithm. Automatica, Vol. 23, No.2, pp137-148．
24． D.W. Clarke, C. Mohtadi & PS. Tuffs. Generalized Predictive Control-Part 2． Extensions and Interpretations. Automatica, Vol. 23, No.2, pp149-160．
25． Astrom, K.J. (1970) . Introduction to stochastic control theory, New York, USA: Academic Press.
26． Bitmead, R.R., Gevers, M., & Wertz, V. (1990) . Adaptive optimal control-The thinking man's GPC. Englewood Cliffs, NJ: Prentice-Hall.
27． Soeterboek, R. (1992) . Predictive control-a unified approach. Englewood Cliffs, NJ: Prentice-Hall.
28． 席裕庚，预测控制。北京：国防出版社，1993。
29． D.Q. Mayne, J.B. Rawlings, C.V. Rao & P.O.M. Scokaert (2000) . Constrained model predictive control: stability and optimality. Automatica 36, 789-814．
30． Mosca, E., Lemos, J.M., & Zhang, J. (1990) . Stabilizing I/O receding horizon control. Proceedings 29th IEEE conference on decision and control, Honolulu, pp.2518-2523．
31． Clarke, D.W. & Scattolini, R. (1991) . Constrained receding horizon predictive control. Proceedings of the IEE, part D, Control theory and application, 138, 344-354．
32． Mosca, E., & Zhang, J. (1992) . Stable redesign of predictive control. Automatica, 28(6) , 1229-1233．
33． Chen, C.C., & Shaw, L. (1982) . On receding horizon feedback control. Automatica, 18, 349-352．
34． Mayne, D.Q., & Michalska, H. (1990) . Receding horizon control of non-linear systems. IEEE Transactions on Automatic Control, 35(4) , 814-824．
35． Keerthi, S.S., & Gilbert, E.G. (1988) . Optimal, infinite horizon feedback laws for a general class of constrained discrete time systems: Stability and moving-horizon approximations. Journal of Optimization Theory and Application, 57, 265-293．
36． Meadows, E.S., Henson, M.A., Eaton, J.W., & Rawlings, J.B. (1995) . Receding horizon control and discontinuous state feedback stabilization. International Journal of Control, 62, 1271-1229．
37． Chisci, L., & Mosca, E. (1994) . Stabilizing I/O receding horizon control of CARMA plants. IEEE Transactions on Automatic Control, 39(3) , 614-618．
38． Bemporad, A., Chisci, L., & Mosca, E. (1995) . On the stabilizing property of SIORHC. Automatica, 30, 2013-2015
39． De Nicolao, G, Magni, L., & Scattolini, R. (1996a). On the robustness of receding
horizon control with terminal constraints. IEEE Transactions on Automatic Control, 41,451-453．
40． Magni, L., & Sepulchre, R. (1997) . Stability margins of nonlinear receding horizon control via inverse optimality. Systems & Control Letters, 32, 241-245．
41． Bitmead, R.R., Gevers, M, & Wertz, V. (1990) . Adaptive optimal control-The thinking man's GPC. Englewood Cliffs, NJ: Prentice-Hall.
42． Rawlings, J.B., & Muske, K.R. (1993) . Stability of constrained receding horizon control. IEEE Transactions on Automatic control, AC-38(10) , 1512-1516．
43． Gauthier, J.P., & Bernard, G. (1983) . Commande multivariable en presence de constraints de type inegalite. Revue of Automatique d'informatique et de Recherche Operationnelle (RAIRO), 17(3) , 205-222．
44． Alamir, M., & Bernard, G. (1995) . Stability of a truncated infinite constrained receding horizon scheme: The general discrete nonlinear case. Automatica, 31(9) , 1353-1356．
45． Michalska, H., & Mayne, D.Q. (1993) . Robust receding horizon control of constrained nonlinear systems. IEEE Transaction on Automatic Control, 38, 1623-1632．
46． Chisci, L., Lombardi, A., & Mosca, E. (1996) . Dual receding horizon control of constrained discrete-time systems. European Journal of Control, 2, 278-285．
47． Scokaert, P.O.M., Mayne, D.Q., & Rawlings, J.B. (1999) . Suboptimal model predictive control (feasibility implies stability). IEEE Transaction on Automatic Control, 44(3) , 648-654．
48． Sznaier, M., & Damborg, M.J. (1990) . Heuristically enhanced feedback control of constrained discrete time linear systems. Automatica, 26, 521-532．
49． Sznaier, M., & Damborg, M.J. (1987) . Suboptimal control of linear systems with state and control inequality constraints, Proceedings of the 26th IEEE conference on decision and control, Los Angeles (pp. 761-762) .
50． Chmielewski, D., & Manousiouthakis, V. (1996) . On constrained infinite time linear quadratic optimal control. Systems & Control Letters, 29, 121-129．
51． Scokaert, P.O.M., & Rawlings, J.B. (1999) . Constrained linear quadratic
regulation. IEEE Transaction on Automatic Control, 43(8) , 1163-1169．
52． Parisini, T., & Zoppoli, R. (1995) . A receding horizon regulator for nonlinear systems and a neural approximation. Automatica, 31(10) , 1443-1451．
53． Jadbabaie, A., Yu, J., & Hauser, J. (1999) . Unconstrained receding horizon control of nonlinear systems. IEEE Transactions on Automatic Control.
54． De Nicolao, G, Magni, L., & Scattolini, R. (1996c). Stabilizing non-linear receding horizon control via a non-quadratic penalty. Proceedings of the IMACS multi-conference CESA, vol. 1, Lille, France (pp. 185-187) .
55． Chen, H., & Allgower, F. (1998b). A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica, 14(10) , 1205-1217．
56． Zafiriou, E. (1990) . Robust Model Predictive Control of Processes with hard constraints. Computers Chem. Engng, 14: 359-371．
57． Allgower, F, & Zheng, A. (1999) . Model predictive control: Assessment and future directions. Proceedings of international workshop on model predictive control, Ascona, 1998, Berlin: Springer.
58． 郑大钟编著，线性系统理论，清华大学出版社，1990。
59． Chen, H., & Allgower, F. (1998a). Nonlinear model predictive control schemes with guaranteed stability. In: R. Berber, C. Kravaris (Eds.). NATO ASI on nonlinear model based process control (pp. 465-494) .
60． De Nicolao, G, Magni, L., & Scattolini, R. (1996b). Robust predictive control of systems with uncertain impulse response. Automatica, 32(10) , 1475-1476．
61． De Nicolao, G, & Sepulchre, R. (1997) . Fake Ricatti equations for stable receding horizon control. Proceedings of ECC conference.
62． Meadows, E.S. (1997) . Dynamic programming and model predictive control. Proceedings of American Control Conference, Albuquerque (pp. 1635-1639) .
63． Primbs, J.A., & Nevistic, V. (1997) . Constrained finite receding horizon linear quadratic control. Technical Report CIT-CDS 97-002, California Institute of Technology, Pasadena, CA
64． D Q. Mayne, J.B. Rawlings, C.V. Rao & P.O.M. Scokaert (2001) Correction to
"Constrained model predictive control: stability and optimality". Automatica, 37 p483．
65． Allwright, J.C., (1993) . On min-max model based predictive control. Proceedings Oxford symposium on advances in model based predictive control, Oxford. pp.4153-426．
66． Zheng, A. & Morari, M. (1993) . Robust stability of constrained model predictive control, Proceedings of the American control conference. pp379-383．
67． Genceli, H., & Nikolaou, M. (1993) . Robust stability analysis of constrained l1 norm model predictive control. AICHE. Journal, 39(12) , 1954-1965．
68． De Nicolao, G, Magni, L., & Scattolini, R. (1996b). Robust predictive control of systems with uncertain impulse response. Automatica, 32(10) , 1475-1479．
69． Magni, L., & Sepulchre, R. (1997) . Stability margins of nonlinear receding horizon control via inverse optimality. Systems & Control Letters, 32, 241-245．
70． Mayne, D.Q. (1995) . Optimization in model based control, Proceedings of the IFAC symposium on dynamics and control chemical reactors and batch processes(Dycord+'95) , Helsingor, Denmark(pp.229-242) .
71． Chen, H., Scherer, C., & Allgower, F (1997) . A game theoretic approach to nonlinear robust receding horizon control of constrained systems. Proceedings of the American control conference. Albuquerque, NM.
72． Magni, L., Nijmeijer, H., & van der Schaft, A. (1999b). A receding horizon approach to the nonlinear ∞ problem. Automatica.
73． De Nicolao, G, Magnani, L., Magni, L., & Scattolini, R. (1999a). On stability receding horizon control for nonlinear discrete time systems. Proceedings of 38th IEEE conference on decision and control.
74． 席裕庚、耿晓军、陈虹(2000) 。预测控制性能研究的新进展，控制理论与应 用，Vol．17，No.4．
75． Scokaert, P.M. & Clarke, D.W. Stability and feasibility in constrained predictive control [A], In: Clarke, D.W. (ed.). Advances in model based predictive control [C], Oxford: Oxford University Press, 1994, 217-229．
76． Chen H. Stability and Robustness Consideration in Nonlinear Model Predictive
Control [M]. Duesseldorf: VDI Verlag, 1997．
77． Scokaert, P.O.M. Constrained predictive control [D]. Oxford: Dept. of Eng. Science, Oxford University, 1994．
78． Scokaert, P.M. & Clarke. Stabilizing properties of constrained predictive control [J]. IEE Proc. Part D, 1994,141(5) ; 295-304．
79． Chen H. & Allgoewer. F. A quasi-infinite horizon predictive control scheme for constrained nonlinear systems [J]. Control Theory and Applications, 1999, 16(3) , 313-319．
80． Scokaert. P.O.M. & Rawlings. J.B. On infeasibilities in model predictive control [A]. In: Kantor J C, Garcia C.E. & Carnahan B (eds.). Chemical Process Control-V: Proceedings of Fifth international Conference on Chemical Process Control [C], California, 1997, 331-334．
81． Manfred Morari & N. Lawrence Ricker. Model predictive control toolbox-for use with matlab. The Math Works Inc.
82． L.R. Petzold, A description of DASSL: A differential/algebraic system solver. Sandia National Laboratories, Livermore, CA, Tech. Rep. 82-8637, 1982．
83． P.E. Gill, W. Murray, M.A. Saunders, & M.H. Wright. User's guide for NPSOL, 5． 0． A FORTRAN package for nonlinear programming. Stanford Univ, Tech. Rep., Nov. 1994．
84． 王骥程，祝和云主编，化工过程控制工程(第二版)，化学工业出版社，北京， 1991．
85． Berlin, F., Frank, P.M., Design and Realization of a MIMO predictive controller for a 3-Tank system. Advances in Model Based Predictive Control. Oxford University Press., Inc., New York, NY, 1994．
86． Robertson, D., & Lee, J. (1996) . Statistical interpretation of constrained moving horizon estimation. Proceedings of A.I.Ch.E annual meeting, Chicago, IL.
87． Robertson, D., Lee, J.H. & Rawlings, J.B. (1996) . A moving horizon based approach for least squares state estimation. A.I.Ch.E. Journal, 42(8) , 2209-2224．
2． Bellman, R. (1957) . Dynamic Programming. Princeton: Princeton University Press.
3． Kalman, R.E. (1960) . Contributions to the theory of optimal control. Boletin Sociedad Matematica Mexicana, 5, 102-119．
4． Kleinman, B.L. (1970) . An easy way to stabilize a linear constant system. IEEE Transactions on Automatic Control, 15(12) , 693．
5． Thomas, Y.A. (1975) . Linear quadratic optimal estimation and control with receding horizon. Electronics Letters, 11, 19-21．
6． Kwon, W.H., & Pearson, A.E. (1977) . A modified quadratic cost problem and feedback stabilization of a linear system. IEEE Transactions on Automatic Control, 22(5) , 838-842．
7． Kwon, W.H., Bruckstein, A.M., & Kailath, T. (1983) . Stabilizing state-feedback design via the moving horizon method. International Journal of Control, 37(3) , 631-643．
8． Richalet, J., Rault, A., Testud, J.L., & Papon, J. (1976) . Algorithmic control of industrial processes. Proceedings of the Fourth IFAC symposium on identification and system parameter estimation.
9． Propoi, A.I. (1963) . Use of linear programming methods for synthesizing sampled data automatic systems. Automation and remote Control, 24(7) , 837-844．
10． Cutler, C.R., & Ramaker, B.L. (1980) . Dynamic matrix control-a computer control algorithm. Proceedings Joint Automatic Control Conference, San Francisco, CA.
11． Garcia, C.E., & Morshedi, A.M. (1986) . Quadratic programming solution of dynamic matrix control(QDMC). Chemical Engineering Communications, 46．
12． Qin, S.J., & Badgwell, T.A. (1997) . An overview of industrial model predictive control technology. In: J.C Kantor, C.E. Garcia, & B. Carnahan(Eds.), Fifth
International Conference on Chemical Process Control, CACHE, AICHE, (pp.232-256) .
13． Garcia, C.E., Prett, D.M., & Morari, M. (1989) . Model predictive control: theory and practice-a survey. Automatica, 25(3) , 335-348．
14． Jay H. Lee, Manfred Morari & Carlos E. Garcia (1994) . State-space Interpretation of Model Predictive Control, Automatica, 30(4) , pp.707-717．
15． P. Lundstrom, J.H. Lee, M. Morari & S. Skogestad (1995) . Limitations of Dynamic Matrix Control. Computers Chem. Eng. (19) 4:409-421．
16． Richalet J., et al. Model Predictive Heuristic Control: Application Industrial Processes. Automatica. 1978, 14(5) :413-428．
17． Rouhani R, Mehra R.K. Model Algorithmic Control, Based Theoretical Properties. Automatica. 1982, 18(4) :401-414．
18． Garcia, C.E. & M. Morari (1982) . Internal Model Control-1． A unifying review and some new results. Ind. Engng Chem. Process Des. Dev., 21, 4308-323．
19． Mehra, R.K. & R. Rouhani (1980) . Theoretical considerations on model algorithmic control for non-minimum phase systems. Proc. Joint Aut. Control Conf, San Francisco, California.
20． Garcia, C.E. & M. Morari (1985a). Internal Model Control-2． Design procedure for multivariable systems. Ind. Engng Chem. Process Des. Dev., 24, 472-484．
21． Garcia, C.E. & M. Morari (1985b). Internal Model Control-3． Multivariable control law computation and tuning guidelines. Ind. Engng Chem. Process Des. Dev., 24, 484-494．
22． Richalet J. et al. Predictive Functional Control-Application to Fast and Accurate Robots. IFAC 10th Triennial World Conference.
23． D.W. Clarke, C. Mohtadi & PS. Tuffs. Generalized Predictive Control-Part 1． The basic algorithm. Automatica, Vol. 23, No.2, pp137-148．
24． D.W. Clarke, C. Mohtadi & PS. Tuffs. Generalized Predictive Control-Part 2． Extensions and Interpretations. Automatica, Vol. 23, No.2, pp149-160．
25． Astrom, K.J. (1970) . Introduction to stochastic control theory, New York, USA: Academic Press.
26． Bitmead, R.R., Gevers, M., & Wertz, V. (1990) . Adaptive optimal control-The thinking man's GPC. Englewood Cliffs, NJ: Prentice-Hall.
27． Soeterboek, R. (1992) . Predictive control-a unified approach. Englewood Cliffs, NJ: Prentice-Hall.
28． 席裕庚，预测控制。北京：国防出版社，1993。
29． D.Q. Mayne, J.B. Rawlings, C.V. Rao & P.O.M. Scokaert (2000) . Constrained model predictive control: stability and optimality. Automatica 36, 789-814．
30． Mosca, E., Lemos, J.M., & Zhang, J. (1990) . Stabilizing I/O receding horizon control. Proceedings 29th IEEE conference on decision and control, Honolulu, pp.2518-2523．
31． Clarke, D.W. & Scattolini, R. (1991) . Constrained receding horizon predictive control. Proceedings of the IEE, part D, Control theory and application, 138, 344-354．
32． Mosca, E., & Zhang, J. (1992) . Stable redesign of predictive control. Automatica, 28(6) , 1229-1233．
33． Chen, C.C., & Shaw, L. (1982) . On receding horizon feedback control. Automatica, 18, 349-352．
34． Mayne, D.Q., & Michalska, H. (1990) . Receding horizon control of non-linear systems. IEEE Transactions on Automatic Control, 35(4) , 814-824．
35． Keerthi, S.S., & Gilbert, E.G. (1988) . Optimal, infinite horizon feedback laws for a general class of constrained discrete time systems: Stability and moving-horizon approximations. Journal of Optimization Theory and Application, 57, 265-293．
36． Meadows, E.S., Henson, M.A., Eaton, J.W., & Rawlings, J.B. (1995) . Receding horizon control and discontinuous state feedback stabilization. International Journal of Control, 62, 1271-1229．
37． Chisci, L., & Mosca, E. (1994) . Stabilizing I/O receding horizon control of CARMA plants. IEEE Transactions on Automatic Control, 39(3) , 614-618．
38． Bemporad, A., Chisci, L., & Mosca, E. (1995) . On the stabilizing property of SIORHC. Automatica, 30, 2013-2015
39． De Nicolao, G, Magni, L., & Scattolini, R. (1996a). On the robustness of receding
horizon control with terminal constraints. IEEE Transactions on Automatic Control, 41,451-453．
40． Magni, L., & Sepulchre, R. (1997) . Stability margins of nonlinear receding horizon control via inverse optimality. Systems & Control Letters, 32, 241-245．
41． Bitmead, R.R., Gevers, M, & Wertz, V. (1990) . Adaptive optimal control-The thinking man's GPC. Englewood Cliffs, NJ: Prentice-Hall.
42． Rawlings, J.B., & Muske, K.R. (1993) . Stability of constrained receding horizon control. IEEE Transactions on Automatic control, AC-38(10) , 1512-1516．
43． Gauthier, J.P., & Bernard, G. (1983) . Commande multivariable en presence de constraints de type inegalite. Revue of Automatique d'informatique et de Recherche Operationnelle (RAIRO), 17(3) , 205-222．
44． Alamir, M., & Bernard, G. (1995) . Stability of a truncated infinite constrained receding horizon scheme: The general discrete nonlinear case. Automatica, 31(9) , 1353-1356．
45． Michalska, H., & Mayne, D.Q. (1993) . Robust receding horizon control of constrained nonlinear systems. IEEE Transaction on Automatic Control, 38, 1623-1632．
46． Chisci, L., Lombardi, A., & Mosca, E. (1996) . Dual receding horizon control of constrained discrete-time systems. European Journal of Control, 2, 278-285．
47． Scokaert, P.O.M., Mayne, D.Q., & Rawlings, J.B. (1999) . Suboptimal model predictive control (feasibility implies stability). IEEE Transaction on Automatic Control, 44(3) , 648-654．
48． Sznaier, M., & Damborg, M.J. (1990) . Heuristically enhanced feedback control of constrained discrete time linear systems. Automatica, 26, 521-532．
49． Sznaier, M., & Damborg, M.J. (1987) . Suboptimal control of linear systems with state and control inequality constraints, Proceedings of the 26th IEEE conference on decision and control, Los Angeles (pp. 761-762) .
50． Chmielewski, D., & Manousiouthakis, V. (1996) . On constrained infinite time linear quadratic optimal control. Systems & Control Letters, 29, 121-129．
51． Scokaert, P.O.M., & Rawlings, J.B. (1999) . Constrained linear quadratic
regulation. IEEE Transaction on Automatic Control, 43(8) , 1163-1169．
52． Parisini, T., & Zoppoli, R. (1995) . A receding horizon regulator for nonlinear systems and a neural approximation. Automatica, 31(10) , 1443-1451．
53． Jadbabaie, A., Yu, J., & Hauser, J. (1999) . Unconstrained receding horizon control of nonlinear systems. IEEE Transactions on Automatic Control.
54． De Nicolao, G, Magni, L., & Scattolini, R. (1996c). Stabilizing non-linear receding horizon control via a non-quadratic penalty. Proceedings of the IMACS multi-conference CESA, vol. 1, Lille, France (pp. 185-187) .
55． Chen, H., & Allgower, F. (1998b). A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica, 14(10) , 1205-1217．
56． Zafiriou, E. (1990) . Robust Model Predictive Control of Processes with hard constraints. Computers Chem. Engng, 14: 359-371．
57． Allgower, F, & Zheng, A. (1999) . Model predictive control: Assessment and future directions. Proceedings of international workshop on model predictive control, Ascona, 1998, Berlin: Springer.
58． 郑大钟编著，线性系统理论，清华大学出版社，1990。
59． Chen, H., & Allgower, F. (1998a). Nonlinear model predictive control schemes with guaranteed stability. In: R. Berber, C. Kravaris (Eds.). NATO ASI on nonlinear model based process control (pp. 465-494) .
60． De Nicolao, G, Magni, L., & Scattolini, R. (1996b). Robust predictive control of systems with uncertain impulse response. Automatica, 32(10) , 1475-1476．
61． De Nicolao, G, & Sepulchre, R. (1997) . Fake Ricatti equations for stable receding horizon control. Proceedings of ECC conference.
62． Meadows, E.S. (1997) . Dynamic programming and model predictive control. Proceedings of American Control Conference, Albuquerque (pp. 1635-1639) .
63． Primbs, J.A., & Nevistic, V. (1997) . Constrained finite receding horizon linear quadratic control. Technical Report CIT-CDS 97-002, California Institute of Technology, Pasadena, CA
64． D Q. Mayne, J.B. Rawlings, C.V. Rao & P.O.M. Scokaert (2001) Correction to
"Constrained model predictive control: stability and optimality". Automatica, 37 p483．
65． Allwright, J.C., (1993) . On min-max model based predictive control. Proceedings Oxford symposium on advances in model based predictive control, Oxford. pp.4153-426．
66． Zheng, A. & Morari, M. (1993) . Robust stability of constrained model predictive control, Proceedings of the American control conference. pp379-383．
67． Genceli, H., & Nikolaou, M. (1993) . Robust stability analysis of constrained l1 norm model predictive control. AICHE. Journal, 39(12) , 1954-1965．
68． De Nicolao, G, Magni, L., & Scattolini, R. (1996b). Robust predictive control of systems with uncertain impulse response. Automatica, 32(10) , 1475-1479．
69． Magni, L., & Sepulchre, R. (1997) . Stability margins of nonlinear receding horizon control via inverse optimality. Systems & Control Letters, 32, 241-245．
70． Mayne, D.Q. (1995) . Optimization in model based control, Proceedings of the IFAC symposium on dynamics and control chemical reactors and batch processes(Dycord+'95) , Helsingor, Denmark(pp.229-242) .
71． Chen, H., Scherer, C., & Allgower, F (1997) . A game theoretic approach to nonlinear robust receding horizon control of constrained systems. Proceedings of the American control conference. Albuquerque, NM.
72． Magni, L., Nijmeijer, H., & van der Schaft, A. (1999b). A receding horizon approach to the nonlinear ∞ problem. Automatica.
73． De Nicolao, G, Magnani, L., Magni, L., & Scattolini, R. (1999a). On stability receding horizon control for nonlinear discrete time systems. Proceedings of 38th IEEE conference on decision and control.
74． 席裕庚、耿晓军、陈虹(2000) 。预测控制性能研究的新进展，控制理论与应 用，Vol．17，No.4．
75． Scokaert, P.M. & Clarke, D.W. Stability and feasibility in constrained predictive control [A], In: Clarke, D.W. (ed.). Advances in model based predictive control [C], Oxford: Oxford University Press, 1994, 217-229．
76． Chen H. Stability and Robustness Consideration in Nonlinear Model Predictive
Control [M]. Duesseldorf: VDI Verlag, 1997．
77． Scokaert, P.O.M. Constrained predictive control [D]. Oxford: Dept. of Eng. Science, Oxford University, 1994．
78． Scokaert, P.M. & Clarke. Stabilizing properties of constrained predictive control [J]. IEE Proc. Part D, 1994,141(5) ; 295-304．
79． Chen H. & Allgoewer. F. A quasi-infinite horizon predictive control scheme for constrained nonlinear systems [J]. Control Theory and Applications, 1999, 16(3) , 313-319．
80． Scokaert. P.O.M. & Rawlings. J.B. On infeasibilities in model predictive control [A]. In: Kantor J C, Garcia C.E. & Carnahan B (eds.). Chemical Process Control-V: Proceedings of Fifth international Conference on Chemical Process Control [C], California, 1997, 331-334．
81． Manfred Morari & N. Lawrence Ricker. Model predictive control toolbox-for use with matlab. The Math Works Inc.
82． L.R. Petzold, A description of DASSL: A differential/algebraic system solver. Sandia National Laboratories, Livermore, CA, Tech. Rep. 82-8637, 1982．
83． P.E. Gill, W. Murray, M.A. Saunders, & M.H. Wright. User's guide for NPSOL, 5． 0． A FORTRAN package for nonlinear programming. Stanford Univ, Tech. Rep., Nov. 1994．
84． 王骥程，祝和云主编，化工过程控制工程(第二版)，化学工业出版社，北京， 1991．
85． Berlin, F., Frank, P.M., Design and Realization of a MIMO predictive controller for a 3-Tank system. Advances in Model Based Predictive Control. Oxford University Press., Inc., New York, NY, 1994．
86． Robertson, D., & Lee, J. (1996) . Statistical interpretation of constrained moving horizon estimation. Proceedings of A.I.Ch.E annual meeting, Chicago, IL.
87． Robertson, D., Lee, J.H. & Rawlings, J.B. (1996) . A moving horizon based approach for least squares state estimation. A.I.Ch.E. Journal, 42(8) , 2209-2224．