High-Order Control Barrier Function-Based Safety Control of Constrained Robotic Systems:An Augmented Dynamics Approach

Although constraint satisfaction approaches have achieved fruitful results,system states may lose their smoothness and there may be undesired chattering of control inputs due to switching characteristics.Furthermore,it remains a challenge when there are additional constraints on control torques of robotic systems.In this article,we propose a novel high-order control barrier function(HoCBF)-based safety control method for robotic systems subject to input-output constraints,which can maintain the desired smoothness of system states and reduce undesired chattering vibration in the control torque.In our design,augmented dynamics are introduced into the HoCBF by constructing its output as the control input of the robotic system,so that the constraint satisfaction is facilitated by HoCBFs and the smoothness of system states is maintained by the augmented dynamics.This proposed scheme leads to the quadratic program(QP),which is more user-friendly in implementation since the constraint satisfaction control design is implemented as an add-on to an existing tracking control law.The proposed closed-loop control system not only achieves the requirements of real-time capability,stability,safety and compliance,but also reduces undesired chattering of control inputs.Finally,the effectiveness of the proposed control scheme is verified by simulations and experiments on robotic manipulators.

Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles

This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.

High-order sliding mode attitude controller design for reentry flight

A novel high-order sliding mode control strategy is proposed for the attitude control problem of reentry vehicles in the presence of parametric uncertainties and external disturbances, which results in the robust and accurate tracking of the aerodynamic angle commands with the finite time convergence. The proposed control strategy is developed on the basis of integral sliding mode philosophy, which combines conventional sliding mode control and a linear quadratic regulator over a finite time interval with a free-final-state and allows the finite-time establishment of a high-order sliding mode. Firstly, a second-order sliding mode attitude controller is designed in the proposed high-order siding mode control framework. Then, to address the control chattering problem, a virtual control is introduced in the control design and hence a third-order sliding mode attitude controller is developed, leading to the chattering reduction as well as the control accuracy improvement. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.

Flight control for a flexible air-breathing hypersonic vehicle based on quasi-continuous high-order sliding mode

The focus of this paper is on control design and simulation for the longitudinal model of a flexible air-breathing hypersonic vehicle（FAHV）.The model of interest includes flexibility effects and intricate couplings between the engine dynamics and flight dynamics.To overcome the analytical intractability of this model,a nominal control-oriented model is constructed for the purpose of feedback control design in the first place.Secondly,the multi-input multi-output（MIMO） quasi-continuous high-order sliding mode（HOSM） controller is proposed to track step changes in velocity and altitude,which is based on full state feedback.The simulation results are presented to verify the effectiveness of the proposed control strategy.

An Improved Control Algorithm for High-order Nonlinear Systems with Unmodelled Dynamics

In this paper, we consider a class of high-order nonlinear systems with unmodelled dynamics from the viewpoint of maintaining the desired control performance （e,g., asymptotical stability） and reducing the control effort. By introducing a new reseating transformation, adopting an effective reduced-order observer, and choosing an ingenious Lyapunov function and appropriate design parameters, this paper designs all improved output-feedback controller. The output-feedback controller guarantees the globally asymptotieal stability of the closed-loop system. Subsequently, taking a concrete system for an example, the smaller critical values for gain parameter and resealing transformation parameter are obtained to effectively reduce the control effort.

High-Order Volterra Model Predictive Control and Its Application to a Nonlinear Polymerisation Process

Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order. Keywords Model predictive control - Volterra series - process control - nonlinear control Yun Li is a senior lecturer at University of Glasgow, UK, where has taught and researched in evolutionary computation and control engineering since 1991. He worked in the UK National Engineering Laboratory and Industrial Systems and Control Ltd, Glasgow in 1989 and 1990. In 1998, he established the IEEE CACSD Evolutionary Computation Working Group and the European Network of Excellence in Evolutionary Computing (EvoNet) Workgroup on Systems, Control, and Drives. In summer 2002, he served as a visiting professor to Kumamoto University, Japan. He is also a visiting professor at University of Electronic Science and Technology of China. His research interests are in parallel processing, design automation and discovery of engineering systems using evolutionary learning and intelligent search techniques. Applications include control, system modelling and prediction, circuit design, microwave engineering, and operations management. He has advised 12 Ph.D.s in evolutionary computation and has 140 publications.Hiroshi Kashiwagi received B.E, M.E. and Ph.D. degrees in measurement and control engineering from the University of Tokyo, Japan, in 1962, 1964 and 1967 respectively. In 1967 he became an Associate Professor and in 1976 a Professor at Kumamoto University. From 1973 to 1974, he served as a visiting Associate Professor at Purdue University, Indiana, USA. From 1990 to 1994, he was the Director at Computer Center of Kumamoto University. He has also served as a member of Board of Trustees of Society of Instrument and Control Engineers (SICE), Japan, Chairman of Kyushu Branch of SICE and General Chair of many international conferences held in Japan, Korea, Chin and India. In 1994, he was awarded SICE Fellow for his contributions to the field of measurement and control engineering through his various academic activities. He also received the Gold Medal Prize at ICAUTO’95 held in India. In 1997, he received the “Best Book Award” from SICE for his new book entitled “M-sequence and its application” written in Japanese and published in 1996 by Shoukoudou Publishing Co. in Japan. In 1999, he received the “Best Paper Award” from SICE for his paper “M-transform and its application to system identification”. His research interests include signal processing and applications, especially pseudorandom sequence and its applications to measurement and control engineering.

Fast self-adapting high-order sliding mode control for a class of uncertain nonlinear systems

A fast self-adapting high-order sliding mode(FSHOSM)controller is designed for a class of nonlinear systems with unknown uncertainties.As for uncertainty-free nonlinear system,a new switching condition is introduced into the standard geometric homogeneity.Different from the existing geometric homogeneity method,both state variables and their derivatives are considered to bring a reasonable effective switching condition.As a result,a faster convergence rate of state variables is achieved.Furthermore,based on the integral sliding mode(ISM)and above geometric homogeneity,a self-adapting high-order sliding mode(HOSM)control law is proposed for a class of nonlinear systems with uncertainties.The resulting controller allows the closed-loop system to conduct with the expected properties of strong robustness and fast convergence.Stable analysis of the nonlinear system is also proved based on the Lyapunov approach.The effectiveness of the resulting controller is verified by several simulation results.

Hybrid Predictive Control Based on High-Order Differential State Observers and Lyapunov Functions for Switched Nonlinear Systems

In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.

On iterative learning control design for tracking iteration-varying trajectories with high-order internal model

In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOlM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOlM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.

A force control high-order single-step-β method (HSM) for substructure pseudo-dynamic testing

This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept of equivalent shear stiffness which can meet the requirement of the HSM algorithm.A study is done to theoretically validate the technique by the numerical analysis of two-storey shear building structure,in comparison of the proposed substructure pseudo-dynamic testing algorithm with the central difference method(CDM).Then,a full-scale SPDT model,the three-storey frame-supported reinforced concrete short-limb masonry shear wall structure,is designed and tested to simulate the seismic response of the corresponding six-storey structure and verify the proposed force control HSM technique.Meanwhile,the techniques of both stiffness correction and force control are suggested to control algorithmic error,control error and measurement error.The results indicate that the force control HSM can be used in the full-scale multi-degree-of-freedom(MDOF)substructure pseudo-dynamic testing before descent segment of structure restoring force properties.

Tunable spectral continuous shift of high-order harmonic generation in atoms by a plasmon-assisted shaping pulse

We delve into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse.Our findings reveal an intriguing manipulation of the frequency peak position in the harmonic emission by adjusting the absolute phase parameter within the frequency domain of the shaping pulse.This phenomenon holds potential significance for experimental setups necessitating precisely tuned single harmonics.Notably,we observe a modulated shift in the created harmonic photon energy,spanning an impressive range of 1.2 eV.This frequency peak shift is rooted in the asymmetry exhibited by the rising and falling edges of the laser pulse,directly influencing the position of the peak frequency emission.Our study quantifies the dependence of this tuning range and the asymmetry of the laser pulse,offering valuable insights into the underlying mechanisms driving this phenomenon.Furthermore,our investigation uncovers the emergence of semi-integer order harmonics as the phase parameter is altered.We attribute this discovery to the intricate interference between harmonics generated by the primary and secondary return cores.This observation introduces an innovative approach for generating semi-integer order harmonics,thus expanding our understanding of high-order harmonic generation.Ultimately,our work contributes to the broader comprehension of complex phenomena in laser-matter interactions and provides a foundation for harnessing these effects in various applications,particularly those involving precise spectral control and the generation of unique harmonic patterns.

Electron correlation in two-electron atoms:A Bohmian analysis of high-order harmonic generation in high-frequency domain

In studying interactions between intense laser fields and atoms or molecules,the role of electron correlation effects on the dynamical response is an important and pressing issue to address.Utilizing Bohmian mechanics(BM),we have theoretically explored the two-electron correlation characteristics while generating high-order harmonics in xenon atoms subjected to intense laser fields.We initially employed Bohmian trajectories to reproduce the dynamics of the electrons and subsequently utilized time-frequency analysis spectra to ascertain the emission time windows for high-order harmonics.Within these time windows,we classified the nuclear region Bohmian trajectories and observed that intense high-order harmonics are solely generated when paired Bohmian particles(BPs)concurrently appear in the nuclear region and reside there for a duration within a re-collision time window.Furthermore,our analysis of characteristic trajectories producing high-order harmonics led us to propose a two-electron re-collision model to elucidate this phenomenon.The study demonstrates that intense high-order harmonics are only generated when both electrons are in the ground state within the re-collision time window.This work discusses the implications of correlation effects between two electrons and offers valuable insights for studying correlation in multi-electron high-order harmonic generation.

An Improved Control Algorithm of High-order Nonlinear Systems

这份报纸从在为一个具体例子维持需要的控制性能的前提减少控制努力的观点设计一个改进产量反馈控制器。产量反馈控制器保证全球性由介绍新重新可伸缩的转变，收养一个有效还原剂顺序观察员，并且选机灵的 Lyapunov 功能和适当设计为参数的靠近环的系统的 asymptotical 稳定性。从理论分析和一个具体例子，同时，为获得参数和重新可伸缩的转变参数的更小的批评价值被获得有效地比相关报纸的设计减少控制努力和控制器的变化的率。

Elliptically polarized high-order harmonic generation of Ar atom in an intense laser field

High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.

High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.

High-order harmonic generation of ZnO crystals in chirped and static electric fields

High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved(k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

Adaptive terminal sliding mode control for high-order nonlinear dynamic systems

An adaptive terminal sliding mode control (SMC) technique is proposed to deal with the tracking problem for a class of high-order nonlinear dynamic systems. It is shown that a function augmented sliding hyperplane can be used to develop a new terminal sliding mode for high-order nonlinear systems. A terminal SMC controller based on Lyapunov theory is designed to force the state variables of the closed-loop system to reach and remain on the terminal sliding mode, so that the output tracking error then converges to zero in finite time which can be set arbitrarily. An adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated. It is also shown that the stability of the closed-loop system can be guaranteed with the proposed control strategy. The simulation of a numerical example is provided to show the effectiveness of the new method.

Controlling the contributions to high-order harmonic generation from different nuclei of N_2 with an orthogonally polarized two-color laser field

The generation of high-order harmonic and the attosecond pulse of the N2 molecule with an orthogonally polarized two-color laser field are investigated by the strong-field Lewenstein model.We show that the control of contributions to high-order harmonic generation（HHG） from different nuclei is realized by properly selecting the relative phase.When the relative phase is chosen to be φ= 0.4π,the contribution to HHG from one nucleus is much more than that from another.Interference between two nuclei can be suppressed greatly; a supercontinuum spectrum of HHG appears from 40 e V to125 e V.The underlying physical mechanism is well explained by the time–frequency analysis and the semi-classical threestep model with a finite initial transverse velocity.By superposing several orders of harmonics,an isolated attosecond pulse with a duration of 80 as can be generated.

Satisfactory PI-P Controller Design for High-order Servo System

The paper presents an output feedback controller design method for high-order servo system with the constraints of multiple indices by using satisfactory control theory. The control strategy is to convert transfer-function form of two-loop servo system into state-space form and assign the system poles in the specified region and H_∞ attenuation degree in the given range with the Riccati matrix inequality so that the closed-loop system has good dynamics and robust quality. A numeric example is given to show the effectiveness of the proposed approach.