Cardinality Constrained Robust Optimization Applied to a Class of Interval Observers

Abstract

We propose a linear programming-based method of interval observer design for systems with uncertain but bounded model parameters and initial conditions. We assume that each uncertain parameter in the system model is bounded by conservative guaranteed bounds, and tighter conditional bounds. We define a class of systems by the number of conservative bounds required to bound all uncertain parameters. Using robust optimization, we solve a single linear program per class of systems to obtain gains for the interval observer. A conservative upper bound on the worst-case steady-state performance of the interval observers over the specified class of systems is minimized.