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 paper considers the problem of estimating the states of a class of non-linear systems with a generalized class of uncertainties. Both matched and mismatched uncertainties have been considered in the system. An observer based on Super-Twisting Algorithm is designed to estimate the states of the system in finite time. The observer uses the estimated information of the mismatched uncertainties provided by an Extended State Observer which is designed separately. The finitetime stability of the designed observer is proved using Lyapunov technique. The designed approach ensures accuracy in estimating the states even in the presence of the generalized uncertainties which shows strong robustness. The technique is illustrated by taking the problem of State-of-Charge estimation of Lithium-ion Battery based on its simplified electrical equivalent circuit model. Simulation results are presented to highlight the effectiveness of the technique.

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.

This paper addresses the critical objective of achieving rapid state transfer in quantum systems. Increasing control gain to achieve fast convergence can result in poor convergence. To circumvent this, a novel continuous, nonsmooth control is devised, exploiting Lyapunov conditions for quantum systems described by von Neumann equations. This approach ensures swift convergence to the target eigenstate while minimizing control effort and enhancing fidelity compared to prevalent techniques such as bang-bang control, approximate bang-bang control, and standard Lyapunov control. Several illustrative examples are provided to corroborate and validate the efficacy of the proposed methodology.

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.

A robust decentralized control method is proposed in this paper for an islanded DC microgrid. A state-space model of the islanded DC microgrid system is derived based on the small-signal model of the system. Parametric uncertainties like load resistance, filter inductance and capacitance are modelled using the upper linear fractional transformation technique. A loop-shaping$H_{\infty}$controller is designed to ensure robust stability and satisfaction of desired performance criteria. The proposed control technique is applied to an islanded DC microgrid test system comprising a dispatchable distributed generation unit, a photovoltaic unit following the maximum power point tracking algorithm, and a battery energy storage system unit. Simulation studies validate the efficacy of the proposed control approach for an islanded DC microgrid.

Over the past few years, rated convergence has gained importance and has acquired tremendous interest from the research community. In this regard, some nomenclatures have emerged, broadly falling under the spectrum of finite time stability. However, these notions have certain aspects which differentiate them. Therefore it becomes imperative to bring out a comparative study among these notions. Moreover, such recent concepts are being applied to several application problems. Thus it is essential to understand even the small details associated with them. The purpose of the present paper is to address these objectives. In addition, the convergence of states and boundedness of the control in case of arbitrary time convergence has also been discussed.

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.

International audience

In complex urban environments, the Inertial Navigation System (INS) is important for navigating unmanned ground vehicles (UAVs) for its environment-independency and reliability of real-time localization. It is usually employed as the baseline in the case of other sensors failures, such as the GPS, Lidar, or Cameras. However, one problem for the INS is that its estimation error of localization accumulates over time, and thus the estimated trajectories of the UAVs continue to drift away from their ground truths. To solve this problem, this paper proposes an improved algorithm based on the Invariant Extended Kalman Filter (IEKF) for dead-reckoning of autonomous vehicles, which dynamically adjusts the process noise and the observation noise covariance matrixes through Attention mechanism and Recurrent Neural Network (RNN). The algorithm achieves more robust and accurate dead-reckoning localization in the experiments conducted on the KITTI dataset, reducing the translational error by about 45%compared to the baseline.

In this article, the free-will arbitrary time consensus is formulated for multiagent systems. This consensus protocol is independent of initial conditions and any other system parameters. With such a protocol, the multiagent system is shown to attain consensus as well as average consensus within the prespecified arbitrary time. Agents rendezvous can also be accomplished with the given protocol. Communication imperfections are easily handled with the designed protocol. Robust free-will arbitrary time consensus protocol is also designed. The stability of such nonlinear nonautonomous protocols is established using suitable Lyapunov functions. Simulation examples confirm the theoretical findings.

This paper proposes a guidance law based on super-twisting algorithm with adaptive gains. Planar geometry of missile-target engagement has been considered. With the proposed scheme, the Line-Of-Sight (LOS) rate converges to zero within finite time. The guidance law is designed considering the uncertainty associated with the maneuvering and non-maneuvering target. Further, the unknown target acceleration is estimated by using an extended state observer. The estimated information of the uncertain target acceleration is utilized in the design. Simulation results for a numerical example are presented which show satisfactory performance of the designed law.

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.