Control of the Pareto Optimality of Systems with Unknown Disturbances

In this paper we treat the classical linear-quadratic regulator (LQR) design as an online multi-objective optimization problem where the compromise between the multiple objective functions is not resolved until run-time. For this purpose the unknown Pareto front is locally approximated by the gradient of the objective functions. Then, using a superordinated control loop, the Pareto optimality is adjusted to an arbitrary point on the Pareto front. This makes it possible to react to unknown or slowly varying stochastic disturbances or changing optimality requirements. Also, the control engineer is no longer concerned with determining suitable weighting matrices as in the classical LQR design. Instead, a compromise between the contradicting objectives is sought by means of physically or economically interpretable rules. It is shown that the gradients of the objective functions that depend on the currently effective disturbances can be computed from the system state through fictitious outputs. This allows a very efficient implementation of the proposed regulator scheme without knowledge of the disturbances.