Stability Guarantees Research Articles

A novel smooth quaternion-based attitude tracking control

The fact that two antipodal points in the quaternion characterize the same physical attitude depicts that the design of the global attitude control system is uneasy. This study deals with a smooth quaternion-based attitude tracking control system that is composed of a differential equation known as the augmented dynamical system. The augmented dynamical system plays such an important role that it is possible to conduct a novel perspective on viewing the set containing all possible motions as not a manifold. Therefore, the topological obstruction does not exist. The designed attitude tracking control system has a guarantee of stability in the large within a set containing all possible motions. It is able to avoid the unwinding phenomenon, and it is noise-induced chattering-free since there is no discontinuity. Furthermore, we show that the smooth attitude tracking control system has an integral input-to-state stability (iISS) guarantee in the presence of uncertainties in the moment of inertia and environmental disturbance. Simulations carried out show the effectiveness of the designed attitude tracking control system.

A stable decoupled perfectly matched layer for the 3D wave equation using the nodal discontinuous Galerkin method

In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough for the sound waves to decay. The computational cost is lowered by strategically truncating the computational domain with an efficient boundary treatment. One commonly used boundary treatment is the perfectly matched layer (PML), which dampens outgoing waves without polluting the computed solution in the inner domain. The purpose of this study is to propose and assess a new perfectly matched layer formulation for the 3D acoustic wave equation, using the nodal discontinuous Galerkin finite element method. The formulation is based on an efficient PML formulation that can be decoupled to further increase the computational efficiency and guarantee stability without sacrificing accuracy. This decoupled PML formulation is demonstrated to be long-time stable, and an optimization procedure for the damping functions is proposed to enhance the performance of the formulation.

Model Predictive Control With Stability Guarantee for the Versatile Buck–Boost Converter

Model Predictive Control With Stability Guarantee for the Versatile Buck–Boost Converter

Dinamika Harga Beras di Kota Kendari: Analisis Fluktuasi 2015-2023

Food price stability is one of the essential issues in the direction of government policy. Price uncertainty at the farm level and the guarantee of food price stability at the consumer level are unresolved problems. This study aims to analyze rice price fluctuations in Kendari City from 2015 to 2024. The research was conducted in Kendari City in March - May 2024. The research used secondary data, namely time series data on rice prices in Kendari City from 2015 to 2023. The research data collection technique is a literature study, namely collecting time series data on rice prices in Kendari City sourced from the Central Bureau of Statistics and related agencies. The research variable is the price of rice in Kendari City from 2015 to 2023. Data analysis used to analyze rice price fluctuations in Kendari City is the Coefficient of Variation (CV). The results showed that rice price fluctuations in Kendari City from 2015 to 2023 were low, with a coefficient of variation (CV) of 3%. The highest rice price condition in Kendari City occurred in 2023, which amounted to IDR 13,321 per kilogram. At the same time, the lowest rice price condition occurred in 2015, which amounted to IDR 9,738 per kilogram. Therefore, government policy intervention is needed to stabilize food prices, especially rice in Kendari City.

Mixed H2/H-infinity Controller Design for Triple Inverted Pendulum System

The steady increase in reliance on robotic systems in industrial applications arises the need to ensure their reliability despite the presence of external disturbances in the environment they work in and their parameters variations due to several factors like: change of temperature, wear and tear effect, and payload variation. Traditional controllers usually fail to maintain the system's stability and performance in the presence of uncertainty, while robust controllers aim to guarantee stability and desired performance across a range of possible uncertainties in the system through incorporating these uncertainties into their design process. This paper investigates the robustness of three controllers namely, H2 controller, H-infinity controller, and mixed H2/H-infinity controller, applied to the triple inverted pendulum system which translates to robustly control legged robots and robotic arms. The results show that among the three controllers, only the mixed H2/H-infinity control system is robustly stable and maintains its performance with stability margin 1.1864 and performance margin 1.1662. Index Terms— H2, H-infinity, Mixed H2/H-infinity, Robust Control, triple inverted pendulum.

Legal Cooperation and Conflict Resolution Mechanism in Guangdong-Hong Kong-Macao Greater Bay Area

The Guangdong-Hong Kong-Macao Greater Bay Area (GBA) is an important strategic region for China's economic development. The coordination and integration of its legal system plays a key role in realizing the economic, social and cultural integration in the region. However, as Hong Kong, Macao and Guangdong belong to different legal systems and social systems respectively, the differences between the legal systems lead to frequent conflicts of laws and hinder the coordinated development in the region. Based on the constitutional and legal foundations, historical and cultural backgrounds of Guangdong, Hong Kong and Macao, as well as the practical experience of Guangdong, this paper analyzes in detail the main challenges facing the current legal collaboration and conflict resolution mechanism in the GBA. These challenges are mainly reflected in the imperfect legislative design, the inadequacy of legal protection, and the unclear legal remedies. Through in-depth discussion of these issues, this paper proposes specific ways to establish a legislative coordination mechanism, formulate a unified substantive law, develop diversified relief channels, and ensure the equal application of law by residents of the three places, with a view to optimizing the legal cooperation and conflict resolution mechanism of the GBA, so as to provide a solid legal guarantee for regional stability and prosperity. The research in this paper not only provides a new perspective for understanding the complexity of legal integration in the GBA, but also puts forward feasible suggestions for deepening regional legal cooperation in the future.

MECHANISM OF TAX CONSULTING IN THE MANAGEMENT OF THE TAX COMPONENT OF ENTERPRISE ECONOMIC SECURITY

The article considers the mechanism of tax consultancy as an important element of the management of the tax component of the economic security of an enterprise, which is particularly relevant in the context of constant changes in tax legislation and growing requirements for transparency of financial statements. Tax consultancy is a complex process of providing companies with qualified assistance in the field of tax planning, optimisation of tax liabilities and management of tax risks. It is substantiated that tax consulting not only helps to reduce the tax burden, but also ensures compliance of the company's tax policy with the requirements of current legislation, which, in turn, is a guarantee of long-term stability and financial sustainability of the company. The article examines the structural elements of the tax liability management mechanism, which include tax planning, ensuring conditions for timely and correct calculation of tax liabilities, as well as organisational and control components. Particular attention is paid to the analysis of the tax planning process as one of the key stages of tax consulting. It is determined that effective tax planning allows an enterprise to optimise the structure of income and expenses, thereby reducing the tax burden and ensuring the rational use of financial resources. This paper considers the methods of ensuring compliance with tax reporting requirements as an important factor in the process of tax consulting. The function of tax consultancy in the formulation and execution of strategies designed to mitigate tax risks and enhance the efficacy of enterprise financial management is established. The necessity of utilising contemporary information technologies in the domain of tax consulting is underscored, as this enables the enhancement of the precision and efficacy of managerial resolutions pertaining to taxation. It can be concluded that effective tax consulting plays a pivotal role in enhancing the economic resilience of an enterprise. It serves to fortify the enterprise against external and internal threats, including those posed by shifts in the tax environment and economic challenges.

Lateral and Longitudinal Integrated Emergency Collision Avoidance System With Handling Stability Guarantee

Lateral and Longitudinal Integrated Emergency Collision Avoidance System With Handling Stability Guarantee

Certificates of nonexistence for analyzing stability, stabilizability and detectability of LPV systems

By computing Lyapunov functions of a certain, convenient structure, Lyapunov-based methods guarantee stability properties of the system or, when performing synthesis, of the relevant closed-loop or error dynamics. In doing so, they provide conclusive affirmative answers to many analysis and design questions in systems and control. When these methods fail to produce a feasible solution, however, they often remain inconclusive due to (a) the method being conservative or (b) the fact that there may be multiple causes for infeasibility, such as ill-conditioning, solver tolerances or true infeasibility. To overcome this, we develop linear-matrix-inequality-based theorems of alternatives based upon which we can guarantee, by computing a so-called certificate of nonexistence, that no poly-quadratic Lyapunov function exists for a given linear parameter-varying system. We extend these ideas to also certify the nonexistence of controllers and observers for which the corresponding closed-loop/error dynamics admit a poly-quadratic Lyapunov function. Finally, we illustrate our results in some numerical case studies.

Novel generalized policy iteration for efficient evolving control of nonlinear systems

In this article, we construct a novel generalized policy iteration framework to address optimal regulation problems for discrete-time nonlinear systems in a more efficient way. Relevant properties are investigated for the framework, including monotonicity and convergence of the iterative value function sequence as well as the admissibility of the iterative control policy. Additionally, an innovative approach is developed to seek an initial admissible control policy for the framework with an adjustable searching speed. Based on these, an evolving control algorithm is presented with stability guarantee. This algorithm employs iterative control policies for system control during the computation of the optimal control policy, as opposed to waiting for the generation of the optimal control policy before implementing control. Eventually, two simulation experiments are conducted with real-world physical backgrounds, in order to illustrate the performance of the proposed strategy.

Lumenless and Stylet-Driven Leads for Left Bundle Branch Area Pacing: Materials, Techniques, Benefits, and Trade-Offs of the Two Approaches.

Left bundle branch area pacing (LBBPa) is an innovative technique for physiological pacing. Compared with His bundle pacing, LBBPa provides better pacing thresholds, lower rates of macrodislodgment, and a reliable strategy for cardiac resynchronization. LBBPa traditionally employs lumenless leads (LLL), which are characterized by small lead bodies and a fixed helix design. These features guarantee stability, avoid helix retraction, and facilitate easier septal penetration, all contributing to an advantageous learning curve. On the other hand, stylet-driven pacing leads (SDL) have shown comparable success rates related to lumenless pacing leads, although they carry risks of helix retraction and lead fracture. SDL have been increasingly employed with favorable results, as they provide good maneuverability and support during implantation with continuous monitoring of ECG-paced morphology. Different manufacturers are offering a variety of SDL, and new dedicated tools are being developed to simplify lead implantation. In this review, we examine the procedural techniques, advantages, and limitations of the most commonly used pacing leads and tools for LBBPa, and we summarize the complications associated with both lumenless leads (LLL) and stylet-driven leads (SDL).

Reinforcement Learning Control of Hypersonic Vehicles and Performance Evaluations

This work presents a new framework for model-based continuous-time reinforcement learning (CT-RL) control of hypersonic vehicles (HSVs). The predominant classes of CT-RL methods for general nonlinear systems in adaptive dynamic programming (ADP) and deep RL tend to either present substantial theoretical results but lack practical synthesis capability (ADP) or show empirical promise without offering theoretical guarantees (deep RL). Meanwhile, RL control frameworks developed directly for HSVs tend to require a simplified model and complicated control structure, and they lack the substantial numerical evaluations essential for real-world flight implementation. To directly address these challenges, we propose a new decentralized excitable integral reinforcement learning framework within which the reference input-based exploration improves persistence of excitation. Together with new insights on prescaling and established decentralized control structure for HSVs, we demonstrate the resulting controller for significant performance improvement over classical Linear Quadratic Regulator (LQR) and feedback linearization methods. Additionally, we provide convergence, optimality, and closed-loop stability guarantees of the proposed method. We demonstrate these performance guarantees over a set of substantial and systematic numerical evaluations on an unstable, nonminimum phase HSV model subject to varying modeling errors and initial conditions.

Neural Observer With Lyapunov Stability Guarantee for Uncertain Nonlinear Systems.

In this article, we propose a novel nonlinear observer based on neural networks (NNs), called neural observers, for observation tasks of linear time-invariant (LTI) systems and uncertain nonlinear systems. In particular, the neural observer designed for uncertain systems is inspired by the active disturbance rejection control, which can measure the uncertainty in real time. The stability analysis (e.g., exponential convergence rate) of LTI and uncertain nonlinear systems (involving neural observers) are presented and guaranteed, where it is shown that the observation problems can be solved only using the linear matrix inequalities (LMIs). Also, it is revealed that the observability and controllability of the system matrices are required to demonstrate the existence of solutions for LMIs. Finally, the effectiveness of neural observers is verified in three simulation cases, including the X-29A aircraft model, the nonlinear pendulum, and the four-wheel steering vehicle.

Closed‐loop stability analysis of deep reinforcement learning controlled systems with experimental validation

AbstractTrained deep reinforcement learning (DRL) based controllers can effectively control dynamic systems where classical controllers can be ineffective and difficult to tune. However, the lack of closed‐loop stability guarantees of systems controlled by trained DRL agents hinders their adoption in practical applications. This research study investigates the closed‐loop stability of dynamic systems controlled by trained DRL agents using Lyapunov analysis based on a linear‐quadratic polynomial approximation of the trained agent. In addition, this work develops an understanding of the system's stability margin to determine operational boundaries and critical thresholds of the system's physical parameters for effective operation. The proposed analysis is verified on a DRL‐controlled system for several simulated and experimental scenarios. The DRL agent is trained using a detailed dynamic model of a non‐linear system and then tested on the corresponding real‐world hardware platform without any fine‐tuning. Experiments are conducted on a wide range of system states and physical parameters and the results have confirmed the validity of the proposed stability analysis (https://youtu.be/QlpeD5sTlPU).

Unsupervised learning for equitable DER control

In the context of managing distributed energy resources (DERs) within distribution networks (DNs), this work focuses on the task of developing local controllers. We propose an unsupervised learning framework to train functions that can closely approximate optimal power flow (OPF) solutions. The primary aim is to establish specific conditions under which these learned functions can collectively guide the network towards desired configurations asymptotically, leveraging an incremental control approach. The flexibility of the proposed methodology allows to integrate fairness-driven components into the cost function associated with the OPF problem. This addition seeks to mitigate power curtailment disparities among DERs, thereby promoting equitable power injections across the network. To demonstrate the effectiveness of the proposed approach, power flow simulations are conducted using the IEEE 37-bus feeder. The findings not only showcase the guaranteed system stability but also underscore its improved overall performance.

Analysis of the spatial differentiation and driving force of arable land abandonment and non-grain in the hilly mountainous areas of Gannan

Food security has a bearing on national development and people's livelihoods and is an important guarantee of social stability for national development. The problems of arable land abandonment and non-grain are becoming more and more serious, and national food security is difficult to guarantee, which will seriously hinder the forward development of China's society and economy. Taking Ruijin City of Jiangxi Province as an example, this study calculated the abandonment level and non-grain level of arable land in Ruijin City respectively from two aspects, and explored the spatial differentiation law of farmland abandonment and non-grain level in the hilly and mountainous areas of southern Jiangxi Province by using spatial autocorrelation and cold and hot spot analysis methods, and the causes of arable land abandonment and non-grain spatial differentiation in the hilly mountainous areas of Gannan were revealed by the methods of Geodetector factor detection and interaction detection. Conclusions of the study: (1) Ruijin City, the abandoned area was 1216.73 hm2, the abandonment rate of each village ranged from 0.01 % to 50.62 %, and the comprehensive abandonment rate was 4.90 %; the area of non-grain was 2937.27 hm2, and the rate of non-grain of each village ranged from 0.01 % to 100.00 %, and the comprehensive non-grain rate was 11.83 %. The area of non-grain was 2937.27 hm2, and the rate of non-grain in each village ranged from 0.01 % to 100.00 %, and the comprehensive rate of non-grain was 11.83 %. (2) The phenomenon of abandonment of arable land and non-grain in Gannan hilly and mountainous areas has a certain clustering and driving effect in space. Globally, the phenomena of arable land abandonment and non-grain in Ruijin City are positively correlated, with the global Moran's I of arable land abandonment rate being 0.05, and the global Moran's I of arable land non-grain being 0.73. (3) Whether or not arable land in the hilly mountainous areas of Gannan is abandoned is affected by the combination of socioeconomics, natural resources, farming conditions, and economic location, with elevation, the degree of arable land contiguity, and population density being the dominant factors. The interaction of elevation, degree of concentration and contiguity, field regularity, and per capita arable land area increased the spatial variability of arable land abandonment in the hilly mountainous areas of Gannan. Whether the phenomenon of non-grain occurs or not is affected by socio-economic conditions, farming conditions and economic location, of which the proportion of paddy fields, land transfer price, arable land area, and urban-rural gradient are the dominant factors. The proportion of paddy land, the price of land transfer, the area of arable land, and the urban-rural gradient interact with each other, and the tendency of arable land to be planted with non-grain crops is more serious.

Stable predictive control of continuous stirred-tank reactors using deep learning

In this work, a Lyapunov-based predictive control method utilizing deep learning techniques is proposed for driving continuous-time nonlinear processes towards the desired equilibrium point. Initially, a neural ordinary differential equation model is developed to learn the continuous-time dynamics from discrete-time sampling data. Subsequently, the theoretical conditions that the control Lyapunov function (CLF) developed on the learned continuous-time system is feasible to act on the actual system through a zero-order-holder are analyzed. Building upon the theoretical analysis and the constructed continuous-time dynamics, a deep neural network control Lyapunov function (DNN-CLF) controller is developed. Importantly, the DNN-CLF is independent of the affine system formulation, effectively addressing the challenge of designing the CLF. Benefiting from the stability guarantee provided by the established DNN-CLF, it is integrated into the model predictive control (MPC) framework to develop Lyapunov-based MPC to further improve the control performance. To ensure safety, considering error propagation and associated risks with enlarging the feasible region of the CLF, tubes are constructed and integrated into the MPC scheme. Finally, a numerical simulation of a chemical process is conducted to validate the efficiency of the proposed method.

Method for testing the stability of an autoregressive model of the vocal tract and adjusting its parameters

Within the framework of the traditional direction of research in the field of acoustic measurements, an autoregressive model of the vocal tract as a key link in the human speech apparatus is considered. The acute problem of ensuring the stability of the autoregressive model in systems with adaptation of its parameters to the observed speech signal of short duration is pointed out. To overcome this problem, the task was set of testing the stability of the autoregressive model and adjusting its parameters based on the results of this testing. The study is based on the author’s method of formant analysis of vowel sounds of speech through the synthesis of a recursive shaping filter in the free oscillation mode. To solve sated task, a method is proposed for testing the stability and adjusting the parameters of the autoregressive model of the vocal tract based on a two-stage algorithm for its transformation. At the first stage of transformation, the stability of the autoregressive model is tested using the impulse response of the shaping filter. At the second stage, if the stability of the autoregressive model is violated, its impulse response is modified by element-by-element multiplication by a variable exponential value that asymptotically converges to zero. A regular algorithm has been developed for recalculating the modified impulse response into an adjusted vector of autoregressive parameters at the second stage of transformation. Based on the results of experimental testing of the proposed method, it was concluded that guaranteed stability of the autoregressive model of the vocal tract has been achieved with minimal distortion in the frequency domain. The results obtained are useful in the development and modernization of automatic speech recognition systems, digital speech communications, artificial intelligence and other information systems that use data compression and speech coding based on an autoregressive model of the vocal tract in automatic speech signal processing.

Advanced Optimal Tracking Control With Stability Guarantee via Novel Value Learning Formulation.

In this article, to solve the optimal tracking control problem (OTCP) for discrete-time (DT) nonlinear systems, general value iteration (GVI) scheme and online value iteration (VI) algorithms with novel value function are discussed. First, the disadvantage of the traditional value function for the OTCP is presented and the novel value function is introduced. Second, we analyze the monotonicity and convergence of GVI and establish the admissibility condition of GVI to evaluate the admissibility of the current iterative control. Note that a novel approach is introduced to analyze the admissibility. Third, based on the attraction domain, improved control policies with online VI can be obtained by judging the location of the current tracking error and reference point. Finally, the stability of the online VI-based control system is guaranteed. Besides, we provide two simulation examples to show the performance of the proposed methods.

Constructive synchronous observer design for inertial navigation with delayed GNSS measurements

Inertial Navigation Systems (INS) estimate a vehicle’s navigation states (attitude, velocity, and position) by combining measurements from an Inertial Measurement Unit (IMU) with other supporting sensors, typically including a Global Navigation Satellite System (GNSS) and a magnetometer. Recent nonlinear observer designs for INS provide powerful stability guarantees but do not account for some of the real-world challenges of INS. One of the key challenges is to account for the time-delay characteristic of GNSS measurements. This paper addresses this question by extending recent work on synchronous observer design for INS. The delayed GNSS measurements are related to the state at the current time using recursively-computable delay matrices, and this is used to design correction terms that leads to almost-globally asymptotic and locally exponential stability of the error. Simulation results verify the proposed observer and show that the compensation of time-delay is key to both transient and steady-state performance.