This paper introduces an online LiDAR-based discrete-time barrier function combined with a dynamic obstacle avoidance algorithm to ensure system safety by keeping the state within an invariant set and minimizing collision risks. The online LiDAR-based discrete-time barrier function is a lowlevel safety controller, particularly in unknown environments, enabling safe navigation under set-based constraints and ensuring safety with both dynamic and static obstacles. The method synthesizes the online LiDAR-based discrete-time barrier function for safe control input corrections. Experimental validation with TurtleBot3 simulations and hardware tests on the Quanser QBot platform demonstrates the effectiveness of the LiDARbased online LiDAR-based discrete-time barrier function for safe navigation in real-world scenarios.

This article presents a solution to the problem of achieving optimal prescribed-time stability and stabilization for nonlinear dynamical systems. In contrast to existing prescribed-time control methods, this article initiates by establishing sufficient conditions for prescribed-time stability through the use of continuous Lyapunov candidate functions. Building upon these conditions, we introduce an optimal prescribed-time stabilization method that incorporates specific differential inequalities. This method complies with the Hamilton-Jacobi-Bellman steady-state equation, ensuring both optimality and prescribed-time stability. Furthermore, we derive a set of optimal prescribed-time stabilizing control laws for a class of affine nonlinear dynamical systems. Finally, we demonstrate the effectiveness of the proposed approach through simulations and experiments involving the reference level tracking of a coupled tank system, thus ensuring that the tracking performance aligns with practical user specificationsNote to Practitioners—This article was instigated by the challenge of devising optimal feedback control strategies for a specific class of nonlinear dynamical systems at predetermined time instances. In recent years, there has been a growing interest in prescribed time stability and stabilization approaches, driven by their potential applications across diverse fields, including control engineering, robotics, and aerospace engineering. These methods facilitate the regulation of nonlinear dynamical systems to reach a desired steady state within a predefined finite time, offering a valuable solution for situations demanding rapid stabilization. In this article, we introduce a novel optimal prescribed-time stabilization method that relies on specific differential inequalities. This method not only adheres to the Hamilton-Jacobi-Bellman steady-state equation but also guarantees both optimality and prescribed-time stability. Furthermore, we derive a family of optimal prescribed-time stabilizing control laws tailored to a particular class of affine nonlinear dynamical systems. To validate the effectiveness of our proposed stabilization approach, we conduct experiments focusing on tracking the desired water level within a coupled tank system. Ultimately, the presented prescribed-time optimal feedback control strategy marks a significant stride forward in the advancement of optimal and efficient control methods for nonlinear dynamical systems, offering solutions that hold immense promise in practical applications.

A second-order sliding mode control (SMC) is applied to regulate the third-order two-switch forward converter (FC) in continuous conduction mode which is suitable for wide input voltage range applications e.g. for DC supply to power electronic subsystem in a high voltage Battery Management System (BMS) of Li-ion batteries. The relative degree approach is used for indirect control of output load voltage in the presence of model uncertainties. Super-twisting control is applied to two-switch FC to avoid the disadvantage of chattering effect of first-order SMC. A detailed analysis of modelling and controlling is presented. The converter is simulated with a 550V to 1000V input voltage range to 15V constant output voltage. Simulation results show the advantages of STA such as good transient response and robustness to uncertainties in comparison with the conventional proportional-integral (PI) controller and compensated control system.

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

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, the problem of arbitrary time uniform boundedness is unsolved in most of the existing results. In this paper, we implement neural network control scheme to show that the states of the nonlinear system and the NN weighted error converge to the compact set in arbitrary time and are semi-globally uniformly ultimately bounded guaranteeing the existence of the compact set. Specifically, it is ensured that after this arbitrary time, valid estimation of the unknown function is achieved as the states remain in existing compact set. We implement this methodology on first-order and second-order systems. In the end, we provide academic and practical examples with simulations to show the efficacy of the mathematical results.

This paper addresses a new technique to cater to the nonlinear dynamics involved in a coupled tank system. Earlier approaches to designing a linear controller for a nonlinear system are two-fold. The first considers linearizing the plant around some operating point, thereby ignoring the dynamics posed by higher-order terms while the second approach is to represent the system nonlinearities in the form of model uncertainties, without any approximation of the higher order terms. The latter method forms the basis of design considered in this paper. The nonlinear model of a coupled tank system is represented in the form of a polytopic system that allows for the implementation of a linear controller. The variation in nonlinear term is treated as an uncertain parameter for the system representation. A R∞ based Proportional Integral (PI) controller is designed combined with pole placement in a desired Linear Matrix Inequality (LMI) region to ensure better transient behavior of the system. Experimental results have been provided and compared with conventional design to illustrate the efficacy of the proposed design method.

This paper investigates the implementation of output-delayed feedback control (ODFC) technique for controlling the sway angle of single pendulum gantry crane (SPGC) system. Linearized mathematical model of the SPGC in state space form is considered for the investigation. The designed ODFC has undergone complete stability analysis for a given controller gain.