This note proposes a reaching law based on difference equation with minima, for discrete-time sliding mode control, providing solution that has properties of modified Gao's when far away from the origin and Utkin's equivalent control close to origin. On one hand, proposed approach eliminates chattering makes system states stay hyperplane perfectly, while other it restricts rate change variable by tuning design parameter. As result, derived this is not as aggressive law, very large initial...

In this brief, a minimum operator (MO) based approach is proposed for discrete-time super-twisting-like algorithm which has different roots unlike its contemporaries, most of are on Euler-discretization (ED). The both unperturbed and perturbed cases. application further explored the super-twisting observer (STO) that yields finite-time estimation system states. An illustrative example pendulum with known as well unknown input considered state observation problem. Simulation results show...

This brief deals with the design of discrete sliding mode control incorporating difference equation minima. It discusses two reaching laws having hybrid structure respect to Gao's law and Utkin's law. approach overcomes limitations both methods, which are primarily chattering in former overly large action latter case. These crafted for systems without perturbation. In case undisturbed system, switching variable converges zero within a finite-time step, while perturbed remains close vicinity...

This article explores the theory of discrete-time gradient systems that converge in a finite amount time and are governed by difference equation with minima. Two algorithms distinct structures discussed, both aimed at achieving finite-time stabilization these systems. These gradient-based have significant applications solving optimization problems. Using convergent techniques discussed article, quadratic programming problem is solved, an optimal solution obtained within frame. The...

Neural network (NN) control approach is an efficient method to approximate unknown nonlinear functions in dynamical systems ensuring uniform ultimate boundedness of the closed loop system. Nevertheless, problem arbitrary time unsolved most existing results. In this paper, we implement neural scheme show that states system and NN weighted error converge compact set are semi-globally uniformly ultimately bounded guaranteeing existence set. Specifically, it ensured after time, valid estimation...

In this paper, we have designed a new observer utilizing the fact that some class of systems possesses at least one fast varying measured state variable along with sluggish unmeasured plant variables. This is introducing which proportional to combination variables and output. A velocity estimation problem finite dimensional linear time-invariant model brushed permanent magnet DC (PMDC)motor has been considered as case study. Simulation result shows effectiveness proposed reduced order...

This paper introduces optimal sliding mode control with a predefined upper bound of settling time (PUBST) for stabilizing uncertain nonlinear dynamical systems. Sufficient conditions optimality are given, which involve Lyapunov function that satisfies certain differential inequality guaranteeing PUBST. Further, it also the Hamilton-Jacobi-Bellman equation. Moreover, an integral is integrated PUBST to make system insensitive matched type bounded perturbations. The validity proposed method...

Gradient flow systems provide effortless continuous time optimization. Such have inherent property that their solutions move in the direction of descent. This paper proposes a modified gradient technique to reach optimal point an objective function within priori chosen predefined time. A least square estimation problem and quadratic programming are solved using proposed continuous-time optimization approach. Simulation results aforementioned problems show efficacy method. Further, obtained...

In this paper, a minimum operator based law for discrete-time sliding mode control is proposed which stands between the Gao's reaching and Utkin's law, alleviating limitations of both types, i.e., primarily chattering in former overly large action latter case. The designed first-order second-order perturbed systems. Further, twisting-like algorithm developed ensures band free convergence system states finite time. Simulation results show efficacy methodology.

This article discusses the sliding mode control problem, where reaching phase is achieved non-monotonically, and can be either monotonically or non-monotonically. Once completed, state variables slide on manifold then reach equilibrium point. A practical second-order example of ball motion model considered to show non-monotonic phase. Simulation results verify behavior