Proxy-based optimal dynamic control allocation for multi-input, multi-output over-actuated systems

In over-actuated systems, an output can be realized through various control effort combinations. It is desirable to allocate the control efforts dynamically (as opposed to statically) in an optimal manner. In this paper, a proxy-based control allocation approach is proposed for multi-input, multioutput over-actuated systems. Instead of using real-time optimization for control allocation, the proposed method establishes an energy optimal subspace; it then defines a causally implementable proxy to accurately measure the deviation of the controlled system from the energy optimal subspace using matrix fraction description and spectral factorization. The control allocation problem is thus converted to a regulation problem, and is solved using a standard H∞ approach. The proposed method is validated through simulation examples, in comparison with an existing dynamic control allocation method. Significant improvements in energy efficiency without affecting the controlled output are demonstrated.