New Algorithm for Complex Optimization Problem with Inequality Constraints

Abstract In this paper, a new procedure is developed to solve complex constrained linear quadratic optimal control problem. To do that, the problem is fustly decomposed and reformulated to an equivalent optimization one. Then, the resulted necessary conditions of optimality are solved within atwo-level structure. Under the assumption that the original problem has a solution, the convergence behavior of the algorithm is investigated. It is shown that the algorithm converges to the optimal solution. Simulation results of the paper-machine design problem are given to illustrate the effectiveness of the developed technique.

[1]  Gene F. Franklin,et al.  Digital control of dynamic systems , 1980 .

[2]  M. Morari,et al.  Stability of model predictive control with mixed constraints , 1995, IEEE Trans. Autom. Control..

[3]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..

[4]  Manfred Morari,et al.  Controller design with actuator constraints , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[5]  J. Park.  Control of state-constrained linear dynamical systems: anti-reset windup approach , 2000 .

[6]  T. A. Badgwell,et al.  An Overview of Industrial Model Predictive Control Technology , 1997 .

[7]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[8]  M. Morari,et al.  Global stabilization of linear discrete-time systems with bounded controls-a model predictive control approach , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[9]  M. Morari,et al.  The explicit solution of constrained LP-based receding horizon control , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[10]  Hee Yong Youn,et al.  Dynamic anti-windup based control method for state constrained systems , 2003, Autom..

[11]  Magdi S. Mahmoud,et al.  Large-scale control systems : theories and techniques , 1985 .

[12]  Janusz Kowalik,et al.  Nonlinear programming procedures and design optimization , 1966 .

[13]  Alberto Bemporad,et al.  Min-max control of constrained uncertain discrete-time linear systems , 2003, IEEE Trans. Autom. Control..

[14]  Manfred Morari,et al.  LQ control for constrained continuous-time systems: an approach based on singular value decomposition , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).