Covariance-based hardware selection-Part I: globally optimal actuator selection

A new covariance based formulation of the actuator selection problem is presented. The proposed optimization problem is aimed at finding the set of minimum cost actuator arrays such that there exists a linear feedback for which all closed-loop signals will satisfy pre-specified variance bounds. Through a linear matrix inequality (LMI) based transformation we exactly convert the original problem into a computationally attractive mixed integer convex program (MICP). The resulting MICP leads to the first computational scheme capable of calculating globally optimal solutions to the covariance based actuator selection problem. It is further shown that the formulation is general enough to incorporate extensions to the actuator noise and actuator dynamics cases. Finally, a set of examples are presented to illustrate the scheme as well as the scalability of required computational effort.

[1]  Sigeru Omatu,et al.  Optimization of sensor and actuator locations in a distributed parameter system , 1983 .

[2]  M L DeLorenzo.  Selection of Noisy Sensors and Actuators for Regulation of Linear Systems. , 1983 .

[3]  R. Skelton,et al.  Robust H/sub 2//LQG control for systems with finite-signal-to-noise uncertainty: a convergent algorithm , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[4]  Zongli Lin,et al.  On the problem of general structural assignments of linear systems through sensor/actuator selection , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[5]  A. Arbel.  Controllability measures and actuator placement in oscillatory systems , 1981 .

[6]  H. Weber,et al.  Analysis and optimization of certain qualities of controllability and observability for linear dynamical systems , 1972 .

[7]  Atsunobu Ichikawa,et al.  Sensor and controller location problems for distributed parameter systems , 1979, Autom..

[8]  Singiresu S Rao,et al.  Thermopiezoelectric control design and actuator placement , 1997 .

[9]  Michel Gevers,et al.  Optimal point-wise discrete control and controllers' allocation strategies for stochastic distributed systems , 1976 .

[10]  Panagiotis D. Christofides,et al.  Integrating nonlinear output feedback control and optimal actuator/sensor placement for transport-reaction processes , 2001 .

[11]  Wodek Gawronski,et al.  Simultaneous placement of actuators and sensors , 1999 .

[12]  C. D. Johnson,et al.  Optimization of a Certain Quality of Complete Controllability and Observability for Linear Dynamical Systems , 1969 .

[13]  Michael A. Demetriou,et al.  Optimal location of sensors and actuators for an active noise control problem , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[14]  M. Amouroux,et al.  On the optimal pointwise control and parametric optimization of distributed parameter systems , 1978 .

[15]  L. Vandenberghe,et al.  Algorithms and software for LMI problems in control , 1997 .

[16]  Miguel J. Bagajewicz.  Process Plant Instrumentation: Design and Upgrade , 2000 .

[17]  Robert E. Skeltm,et al.  Integrated Instrumentation and Control Design Using Finite Signal-to-noise Models* , 1998 .

[18]  Wodek Gawronski.  Almost-balanced structural dynamics , 1997 .

[19]  Robert E. Skelton,et al.  Space structure control design by variance assignment , 1985 .

[21]  D. Chmielewski,et al.  On the Tuning of Predictive Controllers: Inverse Optimality and the Minimum Variance Covariance Constrained Control Problem , 2004 .

[22]  Panagiotis D. Christofides,et al.  Computation of optimal actuator locations for nonlinear controllers in transport-reaction processes , 2000 .

[23]  John D. Perkins,et al.  Economic analysis of different structures of on-line process optimization systems , 1998 .

[24]  Pennung Warnitchai,et al.  Optimal placement and gains of sensors and actuators for feedback control , 1994 .

[25]  R. E. Kalman,et al.  Controllability of linear dynamical systems , 1963 .

[26]  Robert E. Skelton,et al.  Economic design problem: integrating instrumentation and control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[27]  R. Skelton,et al.  Selection of Dynamic Sensors and Actuators in the Control of Linear Systems , 1989 .

[28]  M. Amouroux,et al.  On optimization of zones of action for an optimal control problem for distributed parameter systems , 1979 .

[29]  J. Perkins,et al.  A systematic method for optimum sensor selection in inferential control systems , 1999 .

[30]  M. A. Demetriou,et al.  Numerical investigation on optimal actuator/sensor location of parabolic PDEs , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[31]  Singiresu S Rao,et al.  Optimal placement of actuators in actively controlled structures using genetic algorithms , 1991 .

[32]  R. Braatz,et al.  A tutorial on linear and bilinear matrix inequalities , 2000 .

[33]  Panagiotis D. Christofides,et al.  Optimal actuator/sensor placement for nonlinear control of the Kuramoto-Sivashinsky equation , 2003, IEEE Trans. Control. Syst. Technol..

[34]  L Padula Sharon,et al.  Optimization Strategies for Sensor and Actuator Placement , 1999 .

[35]  G. Dullerud,et al.  A Course in Robust Control Theory: A Convex Approach , 2005 .

[36]  Carlos S. Kubrusly,et al.  Sensors and controllers location in distributed systems - A survey , 1985, Autom..

[37]  P. Christofides,et al.  Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes , 2002 .

[38]  Josip Lončarić.  Sensor/Actuator Placement via Optimal Distributed Control of Exterior Stokes Flow , 1998 .

[39]  Karolos M. Grigoriadis,et al.  A unified algebraic approach to linear control design , 1998 .

[40]  M. Athans,et al.  On the determination of the optimal constant output feedback gains for linear multivariable systems , 1970 .

[41]  L. Vandenberghe,et al.  Applications of semidefinite programming in process control , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).