Practical Stability Analysis Research Articles

Pseudo-dynamic viscoelastic stability analysis of anti-dip bedding rock slopes

Earthquakes contribute to the failure of anti-dip bedding rock slopes (ABRSs) in seismically active regions. The pseudo-static method is commonly employed to assess the ABRSs stability. However, simplifying seismic effects as static loads often underestimates rock slope stability. The development of a practical stability analysis approach for ABRSs, particularly in slope engineering design, is imperative. This study proposes a stability evaluation model for ABRSs, incorporating the viscoelastic properties of rock, to quantitatively assess the safety factor and failure surface under seismic conditions. The mathematical description of the pseudo-dynamic method, derived in this study, accounts for the viscoelastic properties of ABRSs and integrates the Hoek–Brown failure criterion with the Kelvin-Voigt stress-strain relationship of rocks. Furthermore, to address concurrent translation-rotation failure in ABRSs, upper bound limit analysis is utilized to quantify the safety factor. Through a comparison with existing literature, the proposed method considers the effect of harmonic vibration on the stability of ABRSs. The obtained safety factor is lower than that of the quasi-static method, with the resulting percentage change exceeding 5%. The critical failure surface demonstrates superior positional accuracy compared to the Aydan and Adhikary basal planes, with minimal error observed between the physical model test and the numerical simulation test. The parameter sensitivity analysis reveals that the inclination of ABRSs exhibits the highest sensitivity (Sk) value across the three levels of horizontal seismic coefficient (kh). The study aims to devise an expeditious calculation approach for assessing the stability of ABRSs during seismic events, intending to offer theoretical guidance for their stability analysis.

Practical stability analysis of stochastic perturbed linear time-varying systems via integral inequality

In this paper, we investigate the problem of stability of linear time-varying stochastic perturbed systems. We present sufficient conditions ensuring the global practical uniform exponential stability of a different class of stochastic perturbed systems based on generalized integral inequalities of Gronwall type. Finally, we provide numerical examples to prove the usefulness of the main results of this paper.

Sliding Surface-Based Path Planning for Unmanned Aerial Vehicle Aerobatics

This paper exploits the concept of nonlinear sliding surfaces to be used as a basis in the development of aerial path planning projects involving aerobatic three-dimensional path curves in the presence of disturbances. This approach can be used for any kind of unmanned aerial vehicle aimed at performing aerobatic maneuvers. Each maneuver is associated with a nonlinear surface on which an aerial vehicle could be driven to slide. The surface design exploits the properties of Viviani’s curve and the Hopf bifurcation. A vector form of the super twisting algorithm steers the vehicle to the prescribed surfaces. A suitable switching control law is proposed to shift between surfaces at different time instants. A practical stability analysis that involves the descriptor approach allows for determining the controller gains. Numerical simulations are developed to illustrate the accomplishment of the suggested aerobatic flight.

Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays

This paper studies gene regulatory networks (GRNs) with distributed delays. The essential concept of practical stability of the genes is introduced. We investigate the problems of practical stability and global practical exponential stability of the GRN model under an impulsive control. New practical stability criteria are proposed by designing appropriate impulsive controllers via the Lyapunov functions approach. In the design of the impulsive controller, we consider the effect of impulsive perturbations at fixed times and distributed delays on the stability of the considered GRNs. Several numerical examples are also presented to justify the proposed criteria.

Dual‐mode event‐triggered predictive control for nonlinear systems with bounded disturbances

AbstractIn this article, we propose a dual‐mode event‐triggered predictive control method for nonlinear systems with bounded disturbances. The proposed method contains two triggering mechanisms, namely, the hybrid threshold‐based event‐triggered model predictive control (HETMPC) mechanism and the event‐triggered linear quadratic regulator mechanism. The former triggering mechanism is designed based on the error between the real state and the optimal state and also the disturbance information acted on the investigated system. Compared with the traditional fixed triggering threshold, the designed HETMPC has a fewer triggering numbers and reduces the computational burden of online real‐time optimization. This event‐triggered mechanism will be adopted before the states go into the terminal invariant set. The latter event‐triggered mechanism is designed based on the derivation of the system state and it will be adopted after the states enter the terminal invariant set. The feasibility and the input‐to‐state practical stability analysis of the designed strategy is presented. Some simulations, including the application to a mass‐spring‐damper system, are provided to show the correctness and feasibility of the designed algorithms.

Finite time course keeping control for unmanned surface vehicles with command filter and rudder saturation

This paper studies the problem of course keeping control for unmanned surface vehicle (USV) with servo dynamic characteristics, environmental disturbances and model’s uncertainties, and rudder saturation. Considering the characteristics of the rudder servo system (RSS), a nonlinear Norrbin model with second-order rudder is reconstructed, and proposes a finite time simple and practical course controller by the finite time dynamic surface control (FTDSC) technology, which achieve excellent finite time command filter. Then, the nonlinear disturbance observer (NDOB) is applied to estimate the lumped disturbances, which is easy to implement in engineering. Meanwhile, the bandwidth between the controller and the observer is studied, which affects the convergence speed of the observer. Besides, finite time dynamic auxiliary systems with smooth switching function (FTADS-SSF) is designed to compensate for rudder physical constraints with finite time convergence. Further practical finite time stability analysis indicates that the entire system is uniformly ultimately bounded (UUB). Finally, simulation comparison results have been demonstrated the proposed strategy.

Practical stability analysis of stochastic functional differential systems with G-Brownian motion and impulsive effects

This article is concerned with the practical stability performance of nonlinear impulsive stochastic functional differential systems driven by G-Brownian motion (G-ISFDSs). Comparing with traditional Lyapunov stability theory, practical stability can portray qualitative behavior and quantitative properties of suggested systems. By employing G-Itô formula, Lyapunov-Razumikhin approach and stochastic analysis theory, some novel conditions for pth moment practical exponential stability and quasi sure global practical uniform exponential stability of G-ISFDSs are established. The obtained results show that impulses may influence dynamic behavior of the addressed system. Two numerical examples are given to verify the validity of our developed results.

Input-to-state practical stability criteria of non-autonomous infinite-dimensional systems

We develop tools for the investigation of input-to-state practical stability (ISpS) and integral input-to-state practical stability (iISpS) of non-autonomous infinite-dimensional systems in Banach spaces. Sufficient conditions of ISpS and iISpS are given based on indefinite Lyapunov functions. The practical stability analysis is accomplished with the help of scalar practical stable functions. Then, a construction of ISpS Lyapunov function for a class of non-autonomous evolutions equations is provided in Hilbert spaces. We propose the ISpS Lyapunov methodology to make it suitable for the analysis of ISpS w.r.t. inputs from -spaces. Furthermore, we illustrate the theory with an example of a semi-linear reaction-diffusion equation.

A Time-Delay Approach to Extremum Seeking with Large Measurement Delays*

In this paper, we present a time-delay approach to gradient-based extremum seeking (ES) with known large distinct measurement delays, for N-dimensional (ND) static quadratic maps. We assume that the Hessian has a nominal known part and norm-bounded uncertainty, the extremum point belongs to a known ball, and the extremum value to a known interval. By using the orthogonal transformation, we first transform the original static quadratic map into a new one with the Hessian containing a nominal diagonal part. By applying a time-delay approach to the resulting ES system, we arrive at the neutral type system with a nominal linear time-delay system. We further present this system as a retarded one and employ variation of constants formula for practical stability analysis. To obtain tight bounds we exploit positivity of the fundamental matrix that corresponds to the nominal system with delays. Explicit conditions in terms of simple scalar inequalities depending on tuning parameters and delay bounds are established to guarantee the practical stability of the ES control systems. An example from the literature illustrates the efficiency of the new approach.

Input‐to‐state practical stability analysis and controller design of switched affine systems: An observer‐based approach

AbstractThis paper addresses the problems of the input‐to‐state practical stability (ISPS) analysis and output feedback controller design for switched affine systems (SASs) subject to external disturbances. First, a switched affine observer is developed to estimate unmeasurable states. Then by combining the sampled‐data control approach, a less conservative mode‐dependent dynamic event‐triggered mechanism (ETM) is established. The proposed dynamic ETM cannot only avoid Zeno behavior but also reduce the network transmission burden effectively. Further, based on time‐dependent Lyapunov‐Krasovskii functional and state‐dependent switching laws, a set of feasible ISPS conditions are presented in the LMI forms by means of singular value decomposition. The designed switching law depends upon the sampled‐data information of the estimated state and gets rid of the chattering phenomenon. Finally, an application example of the DC‐DC flyback converter is given to verify the efficacy of the proposed algorithm.

Practical Stability and Event-Triggered Load Frequency Control of Networked Power Systems

Practical stability analysis for delayed systems is discussed. Weak practical stability conditions are derived by using Halanay’s inequality and the Lyapunov method. The results are applied to address the problem of practical stability of a power system over a delay-induced communication network. An event-detection-based control scheme is proposed to reduce the communication burdens. Based on the obtained practical stability conditions and the proposed event-detection scheme, sufficient practical stability conditions for load frequency control of a networked power system are given. Furthermore, a new design approach to the event-detection-based controller is presented. Finally, a numerical simulation is given to show the effectiveness and advantage of the obtained results.

Averaged sub-gradient integral sliding mode control design for cueing end-effector acceleration of a two-link robotic arm

Acceleration tracking is a significant problem in aeronautics, automotive, and biomedical technical areas because its solution may yield effective simulation of motion cues. In the case of aeronautics, the proper solution for the tracking problem improves the in-flight simulations for the training of plane pilots. These simulators can be set up using robotic devices that develop controlled motions with the end-effector following the required three-dimensional reference accelerations robustly. Hence, the primary goal of this study is the effective application of the integral sliding mode controller to solve the acceleration tracking problem for the end-effector of a two-link robotic arm. The control design problem is formulated as an optimization of a convex (non-strict) performance functional depending on the difference between the acceleration of the robotic arm and the desired acceleration using the averaged sub-gradient (ASG) descendant method. A novel sliding surface considers the sensitiveness threshold for acceleration dynamics, inspired by the limit of detection in the pilot vestibular apparatus. The proposed controller was analyzed in terms of the finite-time convergence of the sliding surface and the practical stability analysis for the tracking error dynamics. Our main contribution is the design of the online averaged sub-gradient optimization controller based on integral SMCs. The controller solves the end-effector acceleration tracking for a two-link robotic arm, which implements a simplified version of a flight simulator that is considered to be operated under uncertain scenarios and assumes the presence of perturbations and modeling errors. The controller considers the case of incomplete knowledge of the robotic arm model, which adds an extra degree of robustness to the control design. The numerical evaluations demonstrate the attributes of the ASG formulation compared to traditional state feedback control, using the performance functional, the norm of the acceleration tracking error, and the control input variation

Dimensional Reduction-Based Moment Model for Probabilistic Slope Stability Analysis

Uncertainty is an inevitable factor that influences the function analysis, design, and safe operation in engineering systems. Due to the complexity property and unclear failure mechanism, uncertainty is an intrinsic property of slope engineering. Hence, stability analysis and design cannot meet the demands of slope engineering based on the traditional deterministic method, which cannot deal with uncertainty. In this study, a practical reliability approach was developed to consider the uncertainty factor in slope stability analysis by combining the multiplicative dimensional reduction method (MDRM) and first-order second moment (FOSM). MDRM was used to approximate the complex, nonlinear, high-dimensional, and implicit limit state function. The statistical moment of safety factor was estimated based on the moment method using MDRM. FOSM is adopted to compute the reliability index based on the statistical moment of the safety factor. The proposed method was illustrated and verified by an infinite slope with an analytical solution. The reliability index and failure probability were compared with Monte Carlo simulations (MCS) in various cases. Then, it was applied to a slope based on numerical solutions. The results show that the proposed method is feasible and effective for probabilistic slope stability analysis. The reliability index obtained from the proposed method shows high consensus with the traditional response surface method (RSM). It shows that the proposed method is effective, efficient, and accurate. MDRM provides a practical, simple, and efficient probabilistic slope stability analysis approach.

Adaptive Finite-Time Neural Constrained Control for Nonlinear Active Suspension Systems Based on the Command Filter

This article focuses on the adaptive finite-time command filter control problem for nonlinear quarter active suspension systems with actuator failure. In the previous designs of active suspension systems, a second-order system for the vehicle body movement is employed to achieve the controller design and a zero-dynamic analysis is needed, thus the designed controller only contains a part of system variables and there is a difficulty in selecting a proper Lyapunov function in the zero-dynamic analysis. In order to overcome the aforementioned problems, a novel active suspension system is shown based on the Butterworth low-pass filter. The neural networks (NNs) are used to identify the unknown functions of active suspension systems. Meanwhile, the command filter is proposed to handle the “explosion of complexity” problem caused by the adaptive backstepping technique. Then, the adaptive practical finite-time control scheme combined with the command filter and neural identify technique is constructed in a unified framework, which can handle the “singularity” problem. Through the practical finite-time stability analysis, it is easily to obtain that all signals of closed-loop systems are bounded in a finite time. Finally, simulation results for the nonlinear quarter active suspension systems are provided to verify the effectiveness of the NN control scheme.

Practical Stability Analysis and Switching Controller Synthesis for Discrete-time Switched Affine Systems via Linear Matrix Inequalities

This paper considers the practical asymptotic stabilization of adesired equilibrium point in discrete-time switched affine systems.The main purpose is to design a state feedback switching rule forthe discrete-time switched affine systems whose parameters can beextracted with less computational complexities. In this regard,using switched Lyapunov functions, a new set of sufficientconditions based on matrix inequalities are developed to solve thepractical stabilization problem. For any size of the switched affinesystem, the derived matrix inequalities contain only one bilinearterm as a multiplication of a positive scalar and a positivedefinite matrix. It is shown that the practical stabilizationproblem can be solved via a few convex optimization problems,including Linear Matrix Inequalities (LMIs) through gridding of ascalar variable interval between zero and one. The numericalexperiments on an academic example and a DC-DC buck-boost converter,as well as comparative studies with the existing works, prove thesatisfactory operation of the proposed method in achieving betterperformances and more tractable numerical solutions.

Discrete Bidirectional Associative Memory Neural Networks of the Cohen–Grossberg Type for Engineering Design Symmetry Related Problems: Practical Stability of Sets Analysis

In recent years, artificial intelligence techniques have become fundamental parts of various engineering research activities and practical realizations. The advantages of the neural networks, as one of the main artificial intelligence methods, make them very appropriate for different engineering design problems. However, the qualitative properties of the neural networks’ states are extremely important for their design and practical performance. In addition, the variety of neural network models requires the formulation of appropriate qualitative criteria. This paper studies a class of discrete Bidirectional Associative Memory (BAM) neural networks of the Cohen–Grossberg type that can be applied in engineering design. Due to the nature of the proposed models, they are very suitable for symmetry-related problems. The notion of the practical stability of the states with respect to sets is introduced. The practical stability analysis is conducted by the method of the Lyapunov functions. Examples are presented to verify the proposed criteria and demonstrate the efficiency of the results. Since engineering design is a constrained processes, the obtained stability of the sets’ results can be applied to numerous engineering design tasks of diverse interest.

Neural Networks in Engineering Design: Robust Practical Stability Analysis

Abstract In recent years, we are witnessing artificial intelligence being deployed on embedded platforms in our everyday life, including engineering design practice problems starting from early stage design ideas to the final decision. One of the most challenging problems is related to the design and implementation of neural networks in engineering design tasks. The successful design and practical applications of neural network models depend on their qualitative properties. Elaborating efficient stability is known to be of a high importance. Also, different stability notions are applied for differently behaving models. In addition, uncertainties are ubiquitous in neural network systems, and may result in performance degradation, hazards or system damage. Driven by practical needs and theoretical challenges, the rigorous handling of uncertainties in the neural network design stage is an essential research topic. In this research, the concept of robust practical stability is introduced for generalized discrete neural network models under uncertainties applied in engineering design. A robust practical stability analysis is offered using the Lyapunov function method. Since practical stability concept is more appropriate for engineering applications, the obtained results can be of a practical significance to numerous engineering design problems of diverse interest.

Practical stability analysis of perturbed fuzzy control system related to unperturbed fuzzy control system

Practical stability analysis of perturbed fuzzy control system related to unperturbed fuzzy control system

Local input‐to‐state stability analysis on compact set for disturbance observer‐based uncertain multivariable nonlinear control systems

AbstractThis article proposes a local input‐to‐state stability (LISS) analysis as a practical stability analysis approach. In existing LISS analysis approaches, a region including a state trajectory is not specified, and the decrement of a Lyapunov function must be guaranteed in the entire domain of the system state. This reduces the advantage of LISS by limiting the state region, and limits the class of systems for which stability can be guaranteed. To expand the class of systems for which stability can be guaranteed, the LISS Lyapunov function on a compact set (LISS LF CS) is proposed to guarantee LISS. By using the LISS LF CS, the region containing the state trajectory was revealed and the LISS condition was relaxed. In addition, the convergence rate and steady state error bound were determined for systems with LISS LF CS. The input‐to‐state stability (ISS) and LISS were analyzed for a multivariable disturbance observer‐based control system using the ISS and LISS LFs, respectively. The advantages of the proposed LISS analysis are demonstrated by comparing the ISS and LISS conditions. The analytical results were verified by conducting numerical simulations.

Trajectory planning and low-chattering fixed-time nonsingular terminal sliding mode control for a dual-arm free-floating space robot

AbstractThis paper addresses fixed-time trajectory tracking for a dual-arm free-floating space robot (FFSR) with the large initial errors and bounded uncertainty. A wrist-based trajectory planning method is improved by fixed-time stability to fast eliminate the error caused by singularity. Then, a novel low-chattering and global-nonsingular fixed-time terminal sliding mode control strategy is studied by state approaching angle and switching sliding mode; the practical fixed-reachable Lyapunov stability analysis is presented for a mechanical control system. In the end, the proposed trajectory planning method and controller are combined to improve the tracking accuracy of end-effector to the nanoscale. Simulation results validate the effectiveness of the proposed methodologies.