Robust output-feedback stabilization of a class of nonlinear systems with the nonlinearities of varied form

The back-stepping designs based on confine functions are suggested for the robust output-feedback global stabilization of a class of nonlinear continuous systems; the proposed stabilizer is efficient for the nonlinear continuous systems confined by a bound function, the nonlinearities of the systems may be of varied forms or uncertain; the designed stabilizer is robust means that a class of nonlinear continuous systems can be stabilized by the same output feedback stabilization schemes; numerical simulation examples are given.

Observer-based Output-feedback Stabilization Control Design for a Class of Nonlinear Uncertain Systems

The output-feedback stabilization control problem is investigated for a class of nonlinear uncertain systems. Based on the multivariable analog of circle criterion, an observer is designed to estimate the system states and hence the dynamical equations that the estimation error satisfies are derived first. Then, by using integral backstepping approach together with completing square technique, the output-feedback stabilization control is constructively designed such that the closed-loop system is asymptotically stable. Finally, an example is given to illustrate the main results of this paper.

A frequency servo SoC with output power stabilization loop technology for miniaturized atomic clocks

A frequency servo system-on-chip(FS-SoC)featuring output power stabilization technology is introduced in this study for high-precision and miniaturized cesium(Cs)atomic clocks.The proposed power stabilization loop(PSL)technique,incorporating an off-chip power detector(PD),ensures that the output power of the FS-SoC remains stable,mitigating the impact of power fluctuations on the atomic clock's stability.Additionally,a one-pulse-per-second(1PPS)is employed to syn-chronize the clock with GPS.Fabricated using 65 nm CMOS technology,the measured phase noise of the FS-SoC stands at-69.5 dBc/Hz@100 Hz offset and-83.9 dBc/Hz@1 kHz offset,accompanied by a power dissipation of 19.7 mW.The Cs atomic clock employing the proposed FS-SoC and PSL obtains an Allan deviation of 1.7×10^(-11) with 1-s averaging time.

Adaptive Output-Feedback Stabilization for PDE-ODE Cascaded Systems with Unknown Control Coefficient and Spatially Varying Parameter

This paper investigates the adaptive stabilization for a class of uncertain PDE-ODE cascaded systems. Remarkably, the PDE subsystem allows unknown control coefficient and spatially varying parameter, and only its one boundary value is measurable. This renders the system in question more general and practical, and the control problem more challenging. To solve the problem,an invertible transformation is first introduced to change the system into an observer canonical form,from which a couple of filters are constructed to estimate the unmeasurable states. Then, by adaptive technique and infinite-dimensional backstepping method, an adaptive controller is constructed which guarantees that all states of the resulting closed-loop system are bounded while the original system states converging to zero. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed method.

Adaptive Robust Servo Control for Vertical Electric Stabilization System of Tank and Experimental Validation

A tracking stability control problem for the vertical electric stabilization system of moving tank based on adaptive robust servo control is addressed.This paper mainly focuses on two types of possibly fast timevarying but bounded uncertainty within the vertical electric stabilization system:model parameter uncertainty and uncertain nonlinearity.First,the vertical electric stabilization system is constructed as an uncertain nonlinear dynamic system that can reflect the practical mechanics transfer process of the system.Second,the dynamical equation in the form of state space is established by designing the angular tracking error.Third,the comprehensive parameter of system uncertainty is designed to estimate the most conservative effects of uncertainty.Finally,an adaptive robust servo control which can effectively handle the combined effects of complex nonlinearity and uncertainty is proposed.The feasibility of the proposed control strategy under the practical physical condition is validated through the tests on the experimental platform.This paper pioneers the introduction of the internal nonlinearity and uncertainty of the vertical electric stabilization system into the settlement of the tracking stability control problem,and validates the advanced servo control strategy through experiment for the first time.

Minimal-order observer and output-feedback stabilization control design of stochastic nonlinear systems

A minimal-order observer and output-feedback stabilization control are given for single-input multi-output stochastic nonlinear systems with unobservable states, un- modelled dynamics and stochastic disturbances. Based on the observer designed, the estimates of all observable states of the system are given, and the convergence of the es- timation errors are analyzed. In addition, by using the integrator backstepping approach, an output-feedback stabilization control is constructively designed, and sufficient condi- tions are obtained under which the closed-loop system is asymptotically stable in the large or bounded in probability, respectively.

Stabilization Controller of An Extended Chained Nonholonomic System With Disturbance:An FAS Approach

This study examines the stabilization issue of extended chained nonholonomic systems(ECNSs)with external disturbance.Unlike the existing approaches,we transform the considered system into a fully actuated system(FAS)model,simplifying the stabilizing controller design.We implement a separate controller design and propose exponential stabilization controller and finite-time stabilization controller under finite-time disturbance observer(FTDO)for the two system inputs.In addition,we discuss the specifics of global stabilization control design.Our approach demonstrates that two system states exponentially or asymptotically converge to zero under the provided switching stabilization control strategy,while all other system states converge to zero within a finite time.

A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.

Output Feedback Stabilization of High-Order Nonlinear Time-Delay Systems With Low-Order and High-Order Nonlinearities

Dear Editor,to This letter deals with the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities.By constructing reduced-order observer,based on homogeneous domination theory together with the adding a power integrator method,an output feedback controller is developed guarantee the equilibrium of the closed system globally uniformly asymptotically stable.

Passivity-Based Stabilization for Switched Stochastic Nonlinear Systems

Dear Editor,This letter addresses the passivity-based mean square exponential stabilization problem for switched stochastic nonlinear systems.A concept of generalized small-time norm-observability is presented and an appropriate test condition is also provided.For pre-given passivity rate and average dwell time,a set of feedback controllers is designed by use of the passivity property.

Set Stabilization of Large-Scale Stochastic Boolean Networks:A Distributed Control Strategy

Dear Editor,This letter deals with the set stabilization of stochastic Boolean control networks(SBCNs)by the pinning control strategy,which is to realize the full control for systems by imposing control inputs on a fraction of agents.

Nonlinear Robust Stabilization of Ship Roll by Convex Optimization

Dear Editor,This letter presents a nonlinear robust controller design method for ship roll stabilization by combining the dual of Lyapunov's stability theorem with the sum of squares(SOS) technique. Varying initial metacentric height and ship speed are regarded as uncertainties, sea waves are considered as external disturbances, and then the robust nonlinear controller is designed. Taking a container ship as an example, simulations are performed to verify the effectiveness of the proposed design scheme.

Solidification/Stabilization of Chromium in Red Mud-based Geopolymer

Up to 1.5wt%of Cr(Ⅲ)salts(CrCl_(3),and Cr_(2)O_(3))and Cr(Ⅵ)salts(Na_(2)CrO_(4),and CaCr_(2)O_(7))were incorporated into red mud-based geopolymers,respectively.The solidification/stabilization,compressive strength,and durability of the Cr-containing geopolymers were investigated.The experimental results indicate that the red mud-based geopolymer could effectively solidify/stabilize different types of Cr salts with solidification/stabilization rates of above 99.61%.Geopolymers are environmentally safe when the dosage of CaCr_(2)O_(7)is≤1.0wt%,or the dosage of CrCl_(3),Cr_(2)O_(3),and Na_(2)CrO_(4)is≤1.5wt%,respectively.The effects of Cr salts on the compressive strength varies with the type and content of Cr salts.The freeze-thaw cycle is more destructive to geopolymer properties than sulfate attack or acid rain erosion.The solidification/stabilization of Cr is mainly attributed to the following reasons:a)The chemical binding of Cr is related to the formation of Cr-containing hydrates(eg,magnesiochromite((Mg,Fe)(Cr,Al)_(2)O_(4)))and doping into N-A-S-H gel and C-A-S-H gel framework;b)The physical effect is related to the encapsulation by the hydration products(e g,N-A-S-H gel and C-A-S-H gel).This study provides a reference for the treatment of hazardous Cr-containing wastes by solid waste-based geopolymers.

New results on global output-feedback stabilization for nonlinear systems with unknown growth rate

In this paper, the global asymptotic stabilization by output feedback is investigated for a class of uncertain nonlinear systems with unmeasured states dependent growth. Compared with the closely related works, the remarkableness of the paper is that either the growth rate is an unknown constant or the dimension of the closed-loop system is significantly reduced, mainly due to the introduction of a distinct dynamic high-gain observer based on a new updating law. Motivated by the related stabilization results, and by skillfully using the methods of universal control and backstepping, we obtain the design scheme to an adaptive output-feedback stabilizing controller to guarantee the global asymptotic stability of the resulting closed-loop system. Additionally, a numerical example is considered to demonstrate the effectiveness of the proposed method.

Nonlinear robust adaptive control for bidirectional stabilization system of all-electric tank with unknown actuator backlash compensation and disturbance estimation

Since backlash nonlinearity is inevitably existing in actuators for bidirectional stabilization system of allelectric tank,it behaves more drastically in high maneuvering environments.In this work,the accurate tracking control for bidirectional stabilization system of moving all-electric tank with actuator backlash and unmodeled disturbance is solved.By utilizing the smooth adaptive backlash inverse model,a nonlinear robust adaptive feedback control scheme is presented.The unknown parameters and unmodelled disturbance are addressed separately through the derived parametric adaptive function and the continuous nonlinear robust term.Because the unknown backlash parameters are updated via adaptive function and the backlash effect can be suppressed successfully by inverse operation,which ensures the system stability.Meanwhile,the system disturbance in the high maneuverable environment can be estimated with the constructed adaptive law online improving the engineering practicality.Finally,Lyapunov-based analysis proves that the developed controller can ensure the tracking error asymptotically converges to zero even with unmodeled disturbance and unknown actuator backlash.Contrast co-simulations and experiments illustrate the advantages of the proposed approach.

Structural and electrochemical stabilization enabling high-energy P3-type Cr-based layered oxide cathode for K-ion batteries

Layered-type transition metal(TM)oxides are considered as one of the most promising cathodes for K-ion batteries because of the large theoretical gravimetric capacity by low molar mass.However,they suffer from severe structural change by de/intercalation and diffusion of K^(+)ions with large ionic size,which results in not only much lower reversible capacity than the theoretical capacity but also poor power capability.Thus,it is important to enhance the structural stability of the layered-type TM oxides for outstanding electrochemical behaviors under the K-ion battery system.Herein,it is investigated that the substitution of the appropriate Ti^(4+)contents enables a highly enlarged reversible capacity of P3-type KxCrO_(2) using combined studies of first-principles calculation and various experiments.Whereas the pristine P3-type KxCrO_(2) just exhibits the reversible capacity of∼120 mAh g^(−1) in the voltage range of 1.5-4.0 V(vs.K^(+)/K),the∼0.61 mol K^(+)corresponding to∼150 mAh g^(−1) can be reversible de/intercalated at the structure of P3-type K0.71[Cr_(0.75)Ti_(0.25)]O_(2) under the same conditions.Furthermore,even at the high current density of 788 mA g^(−1),the specific capacity of P3-type K0.71[Cr_(0.75)Ti_(0.25)]O_(2) is∼120 mAh g^(−1),which is∼81 times larger than that of the pristine P3-type KxCrO_(2).It is believed that this research can provide an effective strategy to improve the electrochemical performances of the cathode materials suffered by severe structural change that occurred during charge/discharge under not only K-ion battery system but also other rechargeable battery systems.

Coupling effect of cement-stabilization and biopolymer-modification on the mechanical behavior of dredged sediment

Nowadays,biopolymer stabilization as a promising eco-friendly approach in soft ground improvement has attracted wide attentions.However,the feasibility of using biopolymer as a green additive of cementstabilized dredged sediment(CDS)with high water content is still unknown.In this study,guar gum(GG)and xanthan gum(XG)were adopted as typical biopolymers,and a series of unconfined compressive strength(UCS),splitting tensile strength(STS)and scanning electron microscopy(SEM)tests were performed to evaluate the mechanical and microstructural properties of XG-and GG-modified CDSs considering several factors including biopolymer modification,binderesoil ratio and wateresolid ratio.Furthermore,the micro-mechanisms revealing the evolutions of mechanical properties of biopolymermodified CDS were analyzed.The results indicate that the addition of XG can effectively improve the strength of CDS,while the GG has a side effect.The XG content of 9%was recommended,which can improve the 7 d-and 28 d-UCSs by 196%and 51.8%,together with the 7 d-and 28 d-STSs by 118.3%and 42.2%,respectively.Increasing the binderesoil ratio or decreasing the wateresolid ratio significantly improved the strength gaining but aggravated the brittleness characteristics of CDS.Adding XG to CDS contributed to the formation of microstructure with more compactness and higher cementation degrees of ordinary Portland cement(OPC)-XG-stabilized DS(CXDS).The micro-mechanism models revealing the interactions of multiple media including OPC cementation,biopolymer film bonding and bridging effects inside CXDS were proposed.The key findings confirm the feasibility of XG modification as a green and high-efficiency mean for improving the mechanical properties of CDS.

Release characteristics and stabilization of heavy metals in antimony tailings in Yunnan Province,China

The pollution caused by the mining and smelting of heavy metals is becoming an increasingly severe environmental problem.In this study,the environmental risks of mine tailings were explored using typical antimony tailings(the depth of the sample taken from the ground to the deepest position of 120 cm)from the Zuoxiguo mine in Yunnan Province,Southwest China.The tailings were examined to explore the geological background,distribution characteristics,and release characteristics of heavy metals.Additionally,stabilizer treatments for heavy metals were investigated in consideration of waste treatment.The results showed that the contents of Sb and As(8.93×103 and 425 mg/kg,respectively)in the tailings were considerably higher than the local soil background values,suggesting that these metals pose a considerable threat to the surrounding environment.The geological background values of Cr,Cd,Pb,Cu,and Zn were relatively low.The results of static release showed that Sb,As,Cd,and Cr leached from the tailings more easily than Cu,Zn,and Pb under acidic conditions(pH=2.98).Geo-accumulation indices and potential ecological risk indices showed that Sb,As,Cd,and Pb were highly enriched in the tailings,whereas Cu,Cr,and Zn contents were relatively low.The single factor ecological risk index of the mining area showed that Sb and As are high ecological risk factors,whereas Cr,Cu,Zn,Cd,and Pb are not.The results of the orthogonal test results showed that by adding 15.0%(m/m)fly ash and 15.0%(m/m)zeolite powder to the quicklime and curing for 28 d,a significant stabilization effect was observed for Sb,As,and Pb.This study helps determine the priority control components for characteristic heavy metals in antimony tailings,and provides valuable insights regarding the formulation of appropriate mitigation strategies.

Finite-Time Stabilization for Constrained Discrete-time Systems by Using Model Predictive Control

In this paper, a model predictive control(MPC)framework is proposed for finite-time stabilization of linear and nonlinear discrete-time systems subject to state and control constraints. The proposed MPC framework guarantees the finite-time convergence property by assigning the control horizon equal to the dimension of the overall system, and only penalizing the terminal cost in the optimization, where the stage costs are not penalized explicitly. A terminal inequality constraint is added to guarantee the feasibility and stability of the closed-loop system.Initial feasibility can be improved via augmentation. The finite-time convergence of the proposed MPC is proved theoretically,and is supported by simulation examples.