Sensitivity Equations for the Design of Control Systems

J. Borggaard and J. Vance (USA)


Optimization, Actuator Placement, Sensitivity Equations, Distributed Parameter Systems


Systematic strategies for optimal actuator and sensor loca tions require finding extrema of control performance mea sures. When the control is designed for a distributed pa rameter system, these performance measures frequently in volve the kernel of the Riccati operator or that of the feed back operator. For example, measuring the optimal lin ear quadratic regulator (LQR) cost over a range of initial data involves the Riccati operator. To aid in the design process, we consider sensitivity equations for Riccati and Chandrasekhar equations. The latter is well-suited for com puting feedback kernels when there are a small number of control inputs and control outputs. As we demonstrate, the sensitivity of these kernels to actuator positions can lead to efficient computation of gradients for optimization algo rithms. Numerical examples corresponding to placing an actuator in the heat equation are provided.

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