LMI Control Design With Input Covariance Constraint for a Tensegrity Simplex Structure

The Input Covariance Constraint (ICC) control problem is an optimal control problem that minimizes the trace of a weighted output covariance matrix subject to multiple constraints on the input (control) covariance matrix. ICC control design using the Linear Matrix Inequality (LMI) approach was proposed and applied to a tensegrity simplex structure in this paper. Since it has been demonstrated that the system control variances are directly associated with the actuator sizes for a given set of ℒ₂ disturbances, the tensegrity simplex design example is used to demonstrate the capability of using the ICC controller to optimize the system performance in the sense of output covariance with a given set of actuator constraints. The ICC control design was compared with two other control design approaches, pole placement and Output Covariance Constraint (OCC) control designs. Simulation results show that the proposed ICC controllers optimize the system performance (the trace of a weighted output covariance matrix) for the given control covariance constraints whereas the other two control design methods cannot guarantee the feasibility of the designed controllers. Both, state feedback and full-order dynamic output feedback controllers have been considered in this work.