Best tracking and regulation performance under control effort constraint

This paper studies optimal tracking and regulation control problems, in which objective functions of tracking error and regulated response, defined by integral square measures, are to be minimized jointly with the control effort, where the latter is measured by the plant input energy. The problems are solved explicitly by deriving analytical expressions for the best achievable performance. Besides the plant nonminimum phase zeros, time delays, and unstable poles, the results reveal and quantify how the lightly damped poles, the anti-resonant zeros, and the bandwidth of the plant may all affect the performance. These effects are nonexistent when the control effort is not taken into account.