Interval peak-to-peak observers for continuous- and discrete-time systems with persistent inputs and delays
This work provides a computationally tractable solution to a previously difficult optimal control problem for interval observers, benefiting control engineers working on robust state estimation.
The paper proposes a novel non-conservative approach for designing interval observers that achieve minimum peak-to-peak gain for linear systems with persistent inputs and delays, formulated as tractable finite-dimensional linear programs. The method is shown to be uniform over all possible mappings, and is extended to time-delay and discrete-time systems.
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the error dynamics. Indeed, by exploiting several recent results on positive systems, we propose a novel and non-conservative approach formulated in terms of tractable finite-dimensional linear programs for designing a class of interval observers achieving minimum peak-to-peak gain. The optimal observer is notably shown to be uniform over the set of all possible mappings between observation errors and their weighted versions, which parallels a recent result on the stabilization of linear positive systems. Results pertaining on the interval observation of time-delay and discrete-time systems are then obtained as a direct application of the proposed method, emphasizing then its versatility. Several examples on the interval observation of linear and nonlinear systems are finally given for illustration.