Time-Invariant and Optimal Interval Observers viaMixed-Monotone Embeddings скачать в хорошем качестве

Time-Invariant and Optimal Interval Observers viaMixed-Monotone Embeddings

Speaker: Tarun Pati (Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA) Abstract: In this seminar, we present a unified interval framework for guaranteed state estimation of uncertain systems with bounded disturbances and noise, where set-valued estimates are constructed to enclose the true state, making the approach particularly suitable for safety-critical applications. First, we introduce a time-invariant polytopic and interval observer design for all detectable linear systems using a non-square coordinate transformation and mixed-monotone embeddings, establishing the existence of correct-by-construction and input-to-state stable (ISS) observers without requiring positivity or time-varying transformations. Second, we develop computationally efficient $\mathcal{H}_\infty$- and $\mathcal{L}_1$-optimal interval observer synthesis methods for nonlinear continuous- and discrete-time systems by eliminating mixed-integer formulations and reducing the design to linear or semidefinite programs without added conservatism, together with a new continuous-time mixed-monotone decomposition that tightens nonlinear bounds and reduces estimation error.