Shyam Kamal

Xiaogang Xiong, Shyam Kamal, Shanhai Jin

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.

Baby Diana, Priyanka Singh, Shyam Kamal et al.

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.

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.

Xiaogang Xiong, Wei Chen, Guohua Jiao et al.

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.