S. Janardhanan

Atul Sharma, Chayan Kumar Paul, S. Janardhanan

This paper presents a novel position control strategy for a single-link flexible manipulator, tailored for applications where precise position must be achieved within strict time constraints. To accomplish this objective, firstly, a nested non-singular terminal sliding mode controller is designed for the system, enabling precise and robust control. Furthermore, a fixed-time sliding mode observer is designed to estimate unmeasured system states accurately in a fixed time, thereby enabling closed-loop control implementation. A stability analysis is presented to guarantee the robustness and efficacy of the proposed composite control algorithm. The effectiveness of the proposed fixed-time controller is demonstrated through numerical simulation on accuracy, stability, and convergence speed. The proposed controller's performance is also compared with that of other state-of-the-art control schemes. The proposed controller is further validated through experiments conducted on a real hardware setup.

Rudra Prakash, S. Janardhanan, Shaunak Sen

This paper analyses the computational complexity of validated interval methods for uncertain nonlinear systems. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its adoption is often limited by computational cost in high dimensions. We develop an algorithm-level worst-case framework that makes the dependence on the initial search volume $\mathrm{Vol}(X_0)$, the target tolerance $\varepsilon$, and the costs of validated primitives explicit (inclusion-function evaluation, Jacobian evaluation, and interval linear algebra). Within this framework, we derive worst-case time and space bounds for interval bisection, subdivision$+$filter, interval constraint propagation, interval Newton, and interval Krawczyk. The bounds quantify the scaling with $\mathrm{Vol}(X_0)$ and $\varepsilon$ for validated steady-state enclosure and highlight dominant cost drivers. We also show that determinant and inverse computation for interval matrices via naive Laplace expansion is factorial in the matrix dimension, motivating specialised interval linear algebra. Finally, interval Newton and interval Krawczyk have comparable leading-order costs; Krawczyk is typically cheaper in practice because it inverts a real midpoint matrix rather than an interval matrix. These results support the practical design of solvers for validated steady-state analysis in applications such as biochemical reaction network modelling, robust parameter estimation, and other uncertainty-aware computations in systems and synthetic biology.