Optimization Based Design and Control

Abstract The use of optimization for the design of control systems with many, competing design objectives, is explored.A canonical form for the design problem is presented, and it is shown how a variety of design objectives may be transcribed into this form. Methods for solving the resulting mathematical programming problem are presented. The effective handling of control and state constraints requires a nonlinear controller. Receding horizon, or model predictive (optimization based) control is an effective method of achieving nonlinearcontrol of constrained systems when the plant is sufficiently slow to permit, online, approximate solution of openloop optimal control problems. Recent research that enhances the applicability of this type of control to constrained nonlinear systems is described.

[1]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[2]  E. Polak.  Basics of Minimax Algorithms , 1989 .

[3]  D. Mayne,et al.  An outer approximations algorithm for computer-aided design problems , 1979 .

[4]  John C. Doyle,et al.  Guaranteed margins for LQG regulators , 1978 .

[5]  Elijah Polak,et al.  Finite-termination schemes for solving semi-infinite satisfycing problems , 1991 .

[6]  Stephen P. Boyd,et al.  Structured and Simultaneous Lyapunov Functions for System Stability Problems , 1989 .

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

[8]  G. Stein,et al.  Multivariable feedback design: Concepts for a classical/modern synthesis , 1981 .

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

[10]  C. C. Gonzaga,et al.  On Constraint Dropping Schemes and Optimality Functions for a Class of Outer Approximations Algorithms , 1979 .

[11]  Abdelfatah M. Mohamed,et al.  Conical magnetic bearings with radial and thrust control , 1992 .

[12]  D. Mayne,et al.  An implementable receding horizon controller for stabilization of nonlinear systems , 1990, 29th IEEE Conference on Decision and Control.

[13]  D. Mayne,et al.  Robust receding horizon control of constrained nonlinear systems , 1993, IEEE Trans. Autom. Control..

[14]  J. Pearson,et al.  l^{1} -optimal feedback controllers for MIMO discrete-time systems , 1987 .

[15]  D. Mayne,et al.  Algorithms for the design of control systems subject to singular value inequalities , 1982 .

[16]  Charles A. Desoer,et al.  Necessary and sufficient condition for robust stability of linear distributed feedback systems , 1982 .

[17]  E. Polak,et al.  On the design of linear multivariable feedback systems via constrained nondifferentiable optimization in H/sup infinity / spaces , 1989 .

[18]  H. Kwakernaak.  Minimax frequency domain performance and robustness optimization of linear feedback systems , 1985 .

[19]  Elijah Polak,et al.  On the design of stabilizing compensators via semi-infinite optimization , 1989 .

[20]  D. Mayne,et al.  Receding horizon control of nonlinear systems , 1990 .

[21]  A. L. Tits,et al.  Optimization-based controller design for rotorcraft , 1993 .

[22]  Mathukumalli Vidyasagar,et al.  Optimal rejection of persistent bounded disturbances , 1986 .

[23]  Kenneth O. Kortanek,et al.  Semi-Infinite Programming: Theory, Methods, and Applications , 1993, SIAM Rev..

[24]  W. Kwon,et al.  A modified quadratic cost problem and feedback stabilization of a linear system , 1977 .

[25]  J. Rawlings,et al.  The stability of constrained receding horizon control , 1993, IEEE Trans. Autom. Control..

[26]  E. Polak.  On the mathematical foundations of nondifferentiable optimization in engineering design , 1987 .