Model predictive control allocation for overactuated systems - stability and performance

Overactuated systems often arise in automotive, aerospace, and robotics applications, where for reasons of redundancy or performance constraints, it is beneficial to equip a system with more control inputs than outputs. This necessitates control allocation methods that distribute control effort amongst many actuators to achieve a desired effect. Until recently, most methods have treated the control allocation as static in the sense that different dynamic authorities of the actuators were not taken into account. Recent advances have used model predictive control allocation (MPCA) to consider the dynamic authorities of the actuators over a receding horizon. In this paper, we consider the dynamic control allocation problem for overactuated systems where each actuator has different dynamic control authority and hard saturation limits. A modular control design approach is proposed, where the controller consists of an outer loop controller that synthesizes a desired virtual control input signal and an inner loop controller that uses MPCA to achieve the desired virtual control signal. We derive sufficient stability conditions for the composite feedback system and show how these conditions may be realized by imposing an additional constraint on the MPCA design. An automotive example is provided to illustrate the effectiveness of the proposed algorithm.