Reference management using state observers

Abstract

The reference management algorithm is an auxiliary system which modifies the reference signal to fulfil the state and control constraints. In the previous works, most of such algorithms require the assumption that the state vector of the closed-loop system including the plant state is directly measurable, which may be unrealistic for some applications. In this paper, we develop a new reference management algorithm for discrete-time constrained systems with unmeasurable plant states. The present algorithm assures the constraints fulfilment when an ellipsoidal set of possible plant state vectors is available instead of the plant state itself. It is shown that the set of possible plant states can be obtained from the measured outputs by using the Luenberger-type observer or the set-valued observer. The effectiveness of the present method is demonstrated by a numerical example.

Reference and command governors for systems with constraints: A survey on theory and applications

“…In [5], some sufficient conditions to ensure that these outer approximations still lead to a positively invariant, tightened version ofÕ ∞ have been highlighted. A very relevant case is when a Luenberger observer [39,122] is used to estimate the state. In this case, starting from an initial estimatex(0) and given an initial uncertain setÊ(0), the set-valued observer becomeŝ…”

An off‐line design method of compensation law for constrained linear systems

“…Also the reference governor techniques, which shape the reference signal before the signal is applied to the closed-loop system, have been reported by [9][10][11][12]. In [13], the parameter governor is introduced to ensure the constraints fulfilment and improve the transient response in the discrete-time setting.…”