Stochastic Optimal Control of a Servo Motor with a Lifetime Constraint

We consider a linear quadratic optimal regulation problem of a servo motor in the presence of stochastic load disturbance subject to a constraint that establishes a desired motor winding lifetime. To satisfy the constraint, a family of LQR control designs is parameterized with a single scalar performance weight that establishes a trade-off between performance and control power. Power analysis approach is then used to find the optimal value of the parameter that provides maximum disturbance rejection control in the given LQR family subject to the desired motor lifetime constraint