Computation of Low-Complexity Control-Invariant Sets for Systems with Uncertain Parameter Dependence
This paper proposes two new algorithms to compute low-complexity robust control-invariant (LC-RCI) sets along with associated static linear state-feedback laws. The RCI set is assumed to be symmetric around the origin and described by the same number of affine inequalities as twice the dimension of the state vector. The proposed algorithms are applicable to systems with rational parameter dependence, which cannot be handled by the existing algorithms in the literature without introducing additional conservatism. The state and control input constraints are reformulated as simple scalar inequalities, while the invariance condition is relaxed into two alternative sets of (standard and dilated) linear matrix inequality (LMI) conditions. Based on the tractable formulations of the system constraints and invariance condition, both one-step and iterative algorithms are developed for the computation of LC-RCI sets of desirably large/small volumes. The iterative algorithms are constructed in a way to ensure recursive feasibility and convergence to a stationary point.The potential benefits of the proposed algorithms are demonstrated with reference to the existing literature via an illustrative example.
Linear matrix inequalities (LMI)
Semi-definite program, Linear fractional transformation (LFT).