Convex analysis and global optimization of joint actuator location and control problems

It is shown that the optimal value of the continuous-time linear-quadratic problem regarded as a function of the system model and index parameters exhibits properties (convexity, concavity, and monoticity) specially suitable for optimization purposes. Based on this fact, a procedure for the global solution determination of eventually nonconvex problems, involving the above-mentioned function, is proposed. Such problems embody some known designs, such as filtering under noise uncertainty or precision constraints and optimal actuator/sensor location. The last problem is deeply analyzed, and two practical applications, namely satellite attitude control and large flexible system control, are included