Worst-case formulations of model predictive control for systems with bounded parameters

Abstrad-Two different predictive control formulations are developed based on minimization of the worst-case quadratic cost for systems with bounded parameters. The two formulations differ on the assumptions made about the future inputs in optimizing the current input: one assumes open-mop control, while the other considers closed-loop control. Their closed-loop properties such as asymptotic stability are examined. We then focus on a moving average model with an integrator, and derive computationally simpler suboptimal algorithms.

[1]  E. M. Wright,et al.  Adaptive Control Processes: A Guided Tour , 1961, The Mathematical Gazette.

[2]  Takashi Yahagi Optimal feedback control by PID action , 1973 .

[3]  C. R. Cutler,et al.  Dynamic matrix control¿A computer control algorithm , 1979 .

[4]  A. V. Balakrishnan Optimal Control Theory , 1981 .

[5]  Y. F. Huang,et al.  On the value of information in system identification - Bounded noise case , 1982, Autom..

[6]  M. Milanese,et al.  Estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors: Linear families of models and estimators , 1982 .

[7]  Manfred Morari,et al.  Robust Model Predictive Control , 1987, 1987 American Control Conference.

[8]  Sigurd Skogestad,et al.  Robust control of ill-conditioned plants: high-purity distillation , 1988 .

[9]  E. Gilbert,et al.  Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations , 1988 .

[10]  Graham C. Goodwin,et al.  Quantification of Uncertainty in Estimation using an Embedding Principle , 1989, 1989 American Control Conference.

[11]  H. Michalska,et al.  Receding horizon control of nonlinear systems , 1988, Proceedings of the 28th IEEE Conference on Decision and Control,.

[12]  Manfred Morari,et al.  Model predictive control: Theory and practice - A survey , 1989, Autom..

[13]  Gustavo Belforte,et al.  Parameter estimation algorithms for a set-membership description of uncertainty , 1990, Autom..

[14]  Stephen P. Boyd,et al.  Linear controller design: limits of performance , 1991 .

[15]  B. L. Cooley,et al.  Stable min-max control for state-space systems with bounded input matrix , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[16]  竹内 裕喜,et al.  非線形 Receding Horizon 勾配法 , 2004 .