arXiv subjects

Shyam Kamal

Publications and source records attributed to Shyam Kamal.

6 recordsLinked to original sources

arXiv2026

A Fixed-Time Sliding-Mode Framework for Constraint Optimization

This paper develops a robust fixed time optimization framework for constrained problems that guarantees exact constraint satisfaction and convergence to KKT points within fixed time , independent of initial conditions. The approach treats the Lagrange multipliers as control inputs, composed of an equivalent control and a switching control, with the system states representing the decision variables. An equivalent control steers the gradient flow to a local KKT point asymptotically for nonconvex objectives and to unique global optimum in fixed time for convex objectives. Constraint enforcement is achieved by embedding the equality constraints directly as a sliding manifold, with a fixed time switching control ensuring rapid and reliable feasibility. The framework further accounts for the matched disturbances, providing robustness guarantees that are theoretically characterized and illustrated using spherical constraints. Numerical studies on a 3-bus AC optimal power flow problem and distributed consensus=based parameter estimation problem demonstrate the effectiveness, scalability and robustness of proposed approach.

math.OC↗

arXiv2026

Robust Constrained Optimization via Sliding Mode Control

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.

math.OC↗

arXiv2026

Novel Stability Criteria for Discrete and Hybrid Systems via Ramanujan Inner Products

This paper introduces a Ramanujan inner product and its corresponding norm, establishing a novel framework for the stability analysis of hybrid and discrete-time systems as an alternative to traditional Euclidean metrics. We establish new $ε$-$δ$ stability conditions that utilize the unique properties of Ramanujan summations and their relationship with number-theoretic concepts. The proposed approach provides enhanced robustness guarantees and reveals fundamental connections between system stability and arithmetic properties of the system dynamics. Theoretical results are rigorously proven, and simulation results on numerical examples are presented to validate the efficacy of the proposed approach.

eess.SY↗

arXiv2019

Chattering-Free Implementation of Continuous Terminal Algorithm with Implicit Euler Method

This paper proposes an efficient implementation for a continuous terminal algorithm (CTA). Although CTA is a continuous version of the famous twisting algorithm (TA), the conventional implementations of this CTA still suffer from chattering, especially when the gains and the time-step sizes are selected very large. The proposed implementation is based on an implicit Euler method and it totally suppresses the chattering. The proposed implementation is compared with the conventional explicit Euler implementation through simulations. It shows that the proposed implementation is very efficient and the chattering is suppressed both in the control input and output.

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arXiv2019

Vector Contraction Analysis for Nonlinear Dynamical Systems

This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently induces a vector distance between any pair of trajectories of the system, offers an amenable framework as each component of vector-valued norm function satisfies fewer strict conditions as that of standard contraction analysis. Particularly, every element of vector-valued norm derivative need not be strictly negative definite for convergence of any pair of trajectories of the system. Moreover, vector-valued norm derivative satisfies a component-wise inequality employing some comparison system. In fact, the convergence analysis is performed by comparing the relative distances between any pair of the trajectories of the original nonlinear system and the comparison system. Comparison results are derived by utilizing the concepts of quasi-monotonicity property of the function and vector differential inequalities. Moreover, the results are also derived in the framework of the cone ordering instead of utilizing component-wise inequalities between vectors. In addition, the proposed framework is illustrated by examples.

math.OC↗

arXiv2018

Adaptive Gains to Super-Twisting Technique for Sliding Mode Design

This paper studies the super-twisting algorithm (STA) for adaptive sliding mode design. The proposed method tunes the two gains of STA on line simultaneously such that a second order sliding mode can take place with small rectifying gains. The perturbation magnitude is obtained exactly by employing a third-order sliding mode observer in opposition to the conventional approximations by using a first order low pass filter. While driving the sliding variable to the sliding mode surface, one gain of the STA automatically converges to an adjacent area of the perturbation magnitude in finite time. The other gain is adjusted by the above gain to guarantee the robustness of the STA. This method requires only one parameter to be adjusted. The adjustment is straightforward because it just keeps increasing until it fulfills the convergence constraints. For large values of the parameter, chattering in the update law of the two gains is avoided by employing a geometry based backward Euler integration method. The usefulness is illustrated by an example of designing an equivalent control based sliding mode control (ECBC-SMC) with the proposed adaptive STA for a perturbed LTI system.

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