Passivity-based robust control of systems with redundant sensors and actuators

Abstract

This paper considers passivity-based control of a class of uncertain linear, time-invariant systems having redundant sensors and actuators. The approach consists of robustly 'passifying'(i.e. rendering passive) the system, which is assumed to have affine parametric uncertainties in the system matrix as well as the input and output matrices. The passification is accomplished by finding constant matrices to be placed at the input and output of the system which will appropriately combine the sensor signals and distribute the control signals to the actuators. Sufficient conditions are first obtained for the system to remain passive for all parameter values that lie in a hyper-rectangular region in the parameter space. The conditions take the form of a set of linear matrix inequalities (LMIs). Next, the problem of finding an optimal sensor blending matrix is considered, which will maximize the region in the parameter space in which the system remains robustly passive. The dual problem of optimal control allocation is also considered, and a method is given for combined sensor blending and control allocation for robust passification. A method for reduction of the number of LMIs is investigated, and a numerical example is given for demonstrating the approach.