The use of observability and controllability gramians or functions for optimal sensor and actuator location in finite-dimensional systems

Abstract

In this paper, we discuss the optimal location of sensors and actuators for both linear and nonlinear dynamical systems, in both the continuous-time and discrete-time case, on the basis of observability and controllability functions. The optimal location of sensors can be viewed as the problem of maximizing the output energy generated by a given state. On the other hand, the optimal location of actuators can be viewed as the problem of minimizing the input energy required to reach a given state. Such design problems occur in many applications, such as the control of distributed parameter systems, arising in mechanical, hydraulic or chemical processes. In this paper, some new results on observability and controllability functions for nonlinear systems are also provided. Furthermore, we propose a general procedure for computing the optimal design parameters, based on both integer programming and a branch and bound method, suitable for large-scale systems. The effectiveness of this approach is demonstrated for a practical example.