Thach Ngoc Dinh

Gia Quoc Bao Tran, Thach Ngoc Dinh, Zhenhua Wang

We provide a systematic interval observer design method for detectable linear time-invariant (LTI) systems, where a part of the state is observable from the measured output. An observability-based invertible LTI transformation decomposes the state into two parts. The first part is decoupled from the other and observable from the output, while the second is affected by the first, does not appear in the output, but is detectable. A Sylvester-based LTI interval observer is designed for the first part. For the second part, a Jordan-based linear time-varying interval observer is built, treating the interaction from the first part as inputs with known bounds. The intervals in the original coordinates are constructed either by inverting the decomposition online for the intervals in the transformed coordinates or by directly implementing the observer written in the original coordinates. Academic examples illustrate the interest of our approach.

Shyam Kamal, Baby Diana, Sunidhi Pandey et al.

This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The optimization variables are treated as states and the Lagrange multipliers as control input, with equality constraints defined as sliding manifold. The resulting design guarantees exact constraint enforcement with finite time convergence, independent of objective convexity, and exhibits robustness to matched disturbance, structural uncertainty and bounded measurement noise. To accelerate the convergence, a nonsingular terminal sliding mode based normed gradient flow is introduced, ensuring both finite time convergence to optimal solution and constraint satisfaction. Rigorous Lyapunov analysis establishes closed loop stability and convergence. Numerical studies across diverse benchmark problems demonstrate superior accuracy and robustness over classical continuous time optimization method, highlighting effectiveness under disturbance.