Stability Controller Design Research Articles

String stable control design for automated vehicles under cyberattacks

Emerging automated vehicle (AV) technologies open a door for cyberattacks, where a select number of AVs are compromised to drive in an adversarial manner, degrading the performance of transportation systems. Hence, designing stable controls for AVs that can mitigate the impact of attacks on traffic flow is important and necessary as AVs gradually become a reality. In this study, we first present a general framework for describing mixed-autonomy traffic involving AVs and human-driven vehicles (HVs) based on car-following dynamics. Under this framework, a class of malicious attacks on AV control commands (vehicle acceleration) is mathematically characterized. To deal with the lack of knowledge of the attacks, we model attacks as an unstructured process, allowing for the inclusion of both deterministic and stochastic attack behaviors, bounded by a known bound (to remain stealthy) without being subject to any specific statistical distribution. Moreover, we analytically derive a set of sufficient conditions for string stable control design of individual AVs which can help mitigate the disturbances to traffic flow caused by unknown attacks on AVs. Furthermore, for any given market penetration rate of AVs, a set of conditions is also derived for selecting appropriate feedback gains of AVs to ensure string stability of heterogeneous traffic, reducing the undesired impact of attacks on traffic flow. These sufficient conditions provide important criteria for string stable control design of AVs without requiring much knowledge of the attacks. A series of numerical results is presented to show effectiveness of the proposed approach on mitigating attack disruption.

On Observer and Controller Design for Nonlinear Hadamard Fractional-Order One-Sided Lipschitz Systems

This paper presents an extensive investigation into the state feedback stabilization, observer design, and observer-based controller design for a specific category of nonlinear Hadamard fractional-order systems. The research extends the conventional integer-order derivative to the Hadamard fractional-order derivative, offering a more universally applicable method for system analysis. Furthermore, the traditional Lipschitz condition is adapted to a one-sided Lipschitz condition, broadening the range of systems amenable to analysis using these techniques. The efficacy of the proposed theoretical findings is illustrated through several numerical examples. For instance, in Example 1, we select an order of derivative r = 0.8; in Example 2, r is set to 0.9; and in Example 3, r = 0.95. This study enhances the comprehension and regulation of nonlinear Hadamard fractional-order systems, setting the stage for future explorations in this domain.

Relaxed conditions for parameterized linear matrix inequality in the form of nested fuzzy summations

The aim of this study is to investigate less conservative conditions for parameterized linear matrix inequalities (PLMIs) that are formulated as nested fuzzy summations. Such PLMIs are commonly encountered in stability analysis and control design problems for Takagi-Sugeno (T-S) fuzzy systems. Utilizing the weighted inequality of arithmetic and geometric means (AM-GM inequality), we develop new, less conservative linear matrix inequalities for the PLMIs. This methodology enables us to efficiently handle the product of membership functions that have intersecting indices. Through empirical case studies, we demonstrate that our proposed conditions produce less conservative results compared to existing approaches in the literature.

Robust non-monotonic Lyapunov based stability and stabilization methods for continuous-time systems: Applied on bilateral teleoperation system

This study introduces a Non-monotonic Lyapunov (NML) framework aimed at stability evaluation and controller design for continuous-time systems, particularly under conditions of uncertainty. Conventional Lyapunov techniques often exhibit a conservative nature, particularly in the context of uncertain systems, which necessitates the development of less conservative alternatives like NML. The NML methodology distinguishes itself by not imposing strict monotonicity requirements for demonstrating the decrease of a Lyapunov functional. Consequently, this paper derives new stability and stabilization criteria framed as matrix inequalities applicable to a specific class of uncertain systems. The practical applicability of the introduced approach is illustrated through controller design for uncertain systems, exemplified by a nonlinear bilateral teleoperation model. Assorted demonstrative examples and simulation outcomes support the findings, underscoring the NML approach’s efficaciousness.

Stability analysis of random fractional-order nonlinear systems and its application

The research on stability analysis and control design for random nonlinear systems have been greatly popularized in recent ten years, but almost no literature focuses on the fractional-order case. This paper explores the stability problem for a class of random Caputo fractional-order nonlinear systems. As a prerequisite, under the globally and the locally Lipschitz conditions, it is shown that such systems have a global unique solution with the aid of the generalized Gronwall inequality and a Picard iterative technique. By resorting to Laplace transformation and Lyapunov stability theory, some feasible conditions are established such that the considered fractional-order nonlinear systems are respectively Mittag-Leffler noise-to-state stable, Mittag-Leffler globally asymptotically stable. Then, a tracking control strategy is established for a class of random Caputo fractional-order strict-feedback systems. The feasibility analysis is addressed according to the established stability criteria. Finally, a power system and a mass–spring-damper system modeled by the random fractional-order method are employed to demonstrate the efficiency of the established analysis approach. More critically, the deficiency in the existing literatures is covered up by the current work and a set of new theories and methods in studying random Caputo fractional-order nonlinear systems is built up.

Hierarchical attitude stabilization controller design and analysis for underactuated spacecraft on SO(3)

In this paper, the complete attitude stabilization of underactuated spacecraft with two parallel single gimbal control moment gyroscopes (SGCMGs) is explored on 3-dimensional special orthogonal group (SO(3)) and its corresponding Lie algebra (so(3)). Instead of assumption on zero total angular momentum in existing article, a less conservative criterion is adopted to ensure system controllability, which does not simplify system dynamics. On the kinematic level, an ideal controller is proposed to globally stabilize attitude without singular initial condition and stagnation behavior. Besides, the ideal kinematic controller is developed on so(3), which avoids singularity or unwinding phenomenon caused by other attitude parameters. On the dynamic level, a hierarchical controller consisting of two parts is proposed. The high-level sliding mode part enforces finite time stabilization of angular velocity about underactuated axis while the low-level part tracks ideal angular velocity commands about actuated axes. A rigorous proof of the whole dynamic-kinematic system that has not been explored before is given. Analysis of hierarchical control from the perspective of linear algebra provides a novel insight into controller design for underactuated systems. Furthermore, the paradigm of controller design which is applicable to other underactuated systems is derived. Simulation results validate the effectiveness of the proposed control logic.

Stress-dependent instantaneous cohesion and friction angle for the Mohr–Coulomb criterion

The strength criterion of rock is essential for stability control and safety design of geotechnical engineering constructions. Due to its widespread adoption, the Mohr–Coulomb (M-C) criterion is prominent among strength criteria. However, the M-C criterion is constrained by three significant limitations: it fails to capture the nonlinear strength response, overlooks the critical state, and disregards σ2. This study introduces a novel Stress-dependent Instantaneous Friction angle and Cohesion (SIFC) model for the M-C criterion to represent the convex strength envelope of intact rock, covering the spectrum from non-critical to critical states. In pursuit of this objective, an innovative approach for calculating these instantaneous shear parameters at each corresponding σ3 is initially introduced. By examining the confining pressure dependency of the instantaneous friction angle and cohesion, the SIFC model is derived and introduced to the M-C criterion. The SIFC-enhanced M-C criterion, utilizing parameters obtained from triaxial tests under lower σ3, delineates the complete non-linear strength envelope in (σ1, σ3) space, covering brittle to ductile behavior. This criterion is then extended to polyaxial stress conditions. Validation through triaxial test data confirms that the SIFC-enhanced M-C criterion accurately reflects the strength characteristics of the tested rocks.

Control design for beam stabilization with self-sensing piezoelectric actuators: managing presence and absence of hysteresis

Control design for beam stabilization with self-sensing piezoelectric actuators: managing presence and absence of hysteresis

Large-scale model test and numerical analysis of load-bearing arch characteristics of large cross-section tunnel under high geostress

Understanding the failure process and the load-bearing arch effect of the surrounding rock is crucial for the stability control and support design of tunnels under high geostresses. In this study, the progressive collapse behavior and the formation mechanism of the load-bearing arch of a soft rock tunnel under high geostress were investigated by a model test and numerical simulations. First, a large-scale model test was conducted to study the stress redistribution rules and the failure process of the soft rock under different overloads. According to the model test results, the formation of the final load-bearing arch was divided into four stages including initial local load-bearing arch formation, rock failure inside the local arch, overall load-bearing arch formation and load-bearing arch outward transition. Both the progressive failure and arch mechanism were related to the stress transfer effect. Then, numerical simulations were carried out to verify the stress response results from the model test. The determination method for the inner and outer boundaries of the load-bearing arch was put forward based on the circumferential stress distribution, which was validated by the model test results. Furthermore, the relationship between the radial displacement of the tunnel boundary and the arch position was illustrated. It was found that the load-bearing arch showed an oval shape with a big top and a small bottom. The arch position was linearly correlated with the radial displacement at the tunnel wall. This study provides a comprehensive understanding of the load-bearing arch characteristics of large cross-section tunnels in soft rocks under high geostress conditions, which can be referred to in construction control and support design during tunnel construction.

Trajectory tracking in linear complementarity systems with and without state jumps: A passivity approach

This work is largely concerned with trajectory tracking in linear complementarity systems (LCS). The main analytical tool for stability analysis and control design is passivity and the associated linear matrix inequalities (LMIs) for feedback passification. Cases with and without state-jumps, with and without parametric uncertainties, are analyzed. Theoretical findings are illustrated with examples from circuits with set-valued, nonsmooth electronic components, networks with unilateral interactions, and mechanical system with unilateral spring.

A novel finite-time stability criteria and controller design for nonlinear impulsive systems

The issue of a novel finite-time stability and stabilization design for a class of nonlinear impulsive systems is discussed in this paper. In previous finite-time control designs for impulsive systems, the convergence rate of these control strategies is even less rapid than the exponential convergence rate when the initial state is distant from the origin. To overcome this problem, two sufficient conditions for the novel finite-time stability of impulsive systems are presented, in which the stabilizing impulses and the destabilizing impulses are considered, respectively. Meanwhile, the upper bound of the settling-time is evaluated. In addition, combining Lyapunov functions theory with impulsive control, we design a controller for impulsive dynamical systems to satisfy the novel finite-time stability. Finally, two simulation examples are given, in which the first example demonstrates the superiority of the proposed finite-time stability criterion for nonlinear impulsive systems by comparing it with traditional finite-time stability, and the second example verifies the effectiveness of the presented controller.

High-Performance Multi-Level Inverter with Symmetry and Simplification.

This paper presents a high-performance, multilevel inverter with symmetry and simplification. This inverter is a single-phase, seven-level symmetric switched-capacitor inverter based on the concept of the double voltage clamping circuit connected to the half-bridge circuit. Above all, only a single DC power supply is used to achieve a single-phase inverter with seven levels and a voltage gain of three. In addition to analyzing the operating principle of the proposed switched-capacitor multilevel inverter in detail, the stability analysis and controller design are carried out by the state-space averaging method. The feasibility and effectiveness of the proposed structure are validated by some simulated results based on the PSIM simulation tool and by some experiments using FPGA as a control kernel, respectively. However, in this study, the switches were implemented by MOSFETs to meet a high switching frequency. These MOSFETs can be replaced by IGBTs in the motor drive applications so that the used switching frequency can be reduced.

A general matrix decomposition approach with application to stabilization of networked systems with stochastic sampling and two‐channel deception attacks

AbstractThis study is concerned with the stabilization analysis and controller design for networked systems with stochastic sampling and two‐channel deception attacks. First, we give a general matrix decomposition approach which is applicable to scenarios where the system matrix contains complex‐value eigenvalues. Then, a discrete stochastic framework is established for a class of networked systems which considers the joint effects of sampling errors and two‐channel deception attacks. Utilizing the matrix decomposition approach introduced in this study, it becomes feasible to decouple the expectation operations for specific coupling matrices characterized by substantial nonlinearity and randomness. Based on this, a stabilization controller is constructed that ensures the exponential mean‐square stability of the resulting discrete stochastic system. Finally, three simulation examples are provided to validate the effectiveness of the proposed approach.

Data‐driven adaptive control design for active stabilization of stratospheric airship imaging platform: A characteristic model approach

AbstractIn response to the problem of disturbance in the imaging equipment of stratospheric airships, this study designs a vibration isolation and stability system for carrying imaging equipment. The system mainly consists of microprocessor, gimbal, voice coil motor(VCM) and rubber ring. By using adaptive control law based on characteristic model to control the double closed control loop of the motor composed of position loop and speed loop, the camera deflection caused by disturbance is effectively eliminated. Furthermore, in vertical vibration suppression, the adaptive control law based on the characteristic model is also applied to the double closed control loop of the voice coil motor, which removes most of the vertical vibration and realizes active vibration isolation. The passive isolation of the system is completed by rubber rings. The experimental results show that the vibration isolation and stabilization system have good performance in complex disturbance environments, effectively stabilizing the imaging equipment.

Memory sampled-data control design for attitude stabilization of uncertain spacecraft with randomly missing measurements

This paper focuses on stabilizing the attitude of the rigid spacecraft under the sampled-data control design technique with constant communication delay. The system dynamics with model uncertainty (perturbation) and missing measurements are considered. The aim is to design a desirable attitude control that ensures the stabilization of the rigid spacecraft with an optimal H∞ performance level. A novel Lyapunov–Krasovskii functional is developed, incorporating looped characteristics, for the proposed study on the rigid spacecraft model by developing relevant new terms. Making use of the Lyapunov function as well as free-matrix-based integral inequality, sufficient stability criteria are established to assure the stability of the rigid spacecraft model. Furthermore, the desired sampled-data control gain matrices are acquired through the solution of linear matrix inequalities, which guarantees the asymptotic stability of the rigid spacecraft model. Finally, the numerical simulation demonstrates the efficacy of the theoretical study proposed for the rigid spacecraft model.

Fully distributed event-triggered formation-containment control for heterogeneous multi-agent systems with guaranteed positive MTI

In this work, we address the event-triggered output formation-containment control problem for heterogeneous multi-agent systems with multiple leaders. The aim is to achieve formation of follower agents and containment of multiple leaders by designing fully distributed event-triggered control strategy, while the minimum triggering interval (MTI) is guaranteed to be strictly positive, which is a stronger condition than simply excluding Zeno behavior. First, an output feedback fully distributed control law is proposed. Then, a novel event-triggering mechanism (ETM) is designed by introducing an auxiliary function with time-varying coefficients. By means of the auxiliary function, the time it takes for the auxiliary function to decrease from given initial condition to zero can be imposed to be the MTI. Moreover, a novel Lyapunov function depending on the auxiliary function and error term is constructed for stability analysis and control design. Finally, the effectiveness of the obtained results is illustrated by simulation results.

Stability analysis and control synthesis of hybrid time-varying linear systems using a discretization-based approach

A strategy for stability analysis and control design concerning a class of hybrid linear time-varying (LTV) systems is proposed in this paper. First, the transition matrix of the system is computed and then used to formulate the stability analysis condition, unifying both the flows and jumps into a single continuous-time framework and resulting in a straightforward methodology for hybrid dynamics. Such condition is then adapted to yield the proposed synthesis techniques, capable of generating a time-varying state-feedback gain to stabilize the hybrid LTV system. A discretization procedure is then proposed for both analysis and synthesis conditions, resulting on a numerically suitable approach that allows the adaptation of any LTV discrete-time synthesis technique to deal with the considered hybrid LTV systems. Finally, to highlight the possibilities of the methodology, the conditions are adapted for the stabilization of sampled-data time-varying systems. Numerical examples illustrate the validity and potentialities of the proposed techniques.

A novel adaptive control design for exponential stabilization of memristor‐based CVNNs with time‐varying delays using matrix measures

AbstractThe present study introduces a new adaptive control framework that aims to attain exponential stability in complex‐valued neural network systems utilizing memristors while accounting for time‐varying delays. The control issues in systems of this nature are mostly attributed to the presence of memristors and time‐varying latency. To overcome these challenges and achieve stabilization outcomes, a methodology is employed that integrates adaptive control approaches inside a matrix‐based framework. This study employs Lyapunov's stability theory to establish exponential stabilization conditions and conduct convergence analysis. The efficacy of the suggested control algorithm in achieving exponential stabilization and robustness under varied delays is demonstrated through numerical simulations.

Dissipativity-based control for networked control systems under bilateral Round-Robin protocols and denial-of-service attacks

A dissipativity-based control strategy adopting bilateral Round-Robin (RR) protocols for networked control systems (NCSs) suffering from denial-of-service (DoS) attacks is investigated in this work. To save limited network resources in multi-packet transmission scenarios, RR protocols are adopted for coordinating the node access on bilateral (i.e., sensor-to-controller and controller-to-actuator) channels. Subsequently, the NCSs integrating considerations of bilateral RR protocols and DoS attacks are further described as the switched time-delay model. The sufficient stability condition and controller design criterion are derived by using Lyapunov theory to ensure the closed-loop exponential mean-square stability and (Q,S,R) dissipative performance under fragile network environment. Furthermore, to maximize the tolerable system delay and reduce the conservativeness of proposed results effectively, an optimization algorithm is also proposed. Finally, the superiority and feasibility of the proposed methods are verified through two practical examples.

Optimal controller design for reactor core power stabilization in a pressurized water reactor: Applications of gold rush algorithm.

Nuclear energy (NE) is seen as a reliable choice for ensuring the security of the world's energy supply, and it has only lately begun to be advocated as a strategy for reducing climate change in order to meet low-carbon energy transition goals. To achieve flexible operation across a wide operating range when it participates in peak regulation in the power systems, the pressurised water reactor (PWR) NE systems must overcome the nonlinearity problem induced by the substantial variation. In light of this viewpoint, the objective of this work is to evaluate the reactor core (main component) of the NE system via different recent optimization techniques. The PWR, which is the most common form, is the reactor under investigation. For controlling the movement of control rods that correspond with reactivity for power regulation the PWR, PID controller is employed. This study presents a dynamic model of the PWR, which includes the reactor core, the upper and lower plenums, and the piping that connects the reactor core to the steam alternator is analyzed and investigated. The PWR dynamic model is controlled by a PID controller optimized by the gold rush optimizer (GRO) built on the integration of the time-weighted square error performance indicator. Additionally, to exhibit the efficacy of the presented GRO, the dragonfly approach, Arithmetic algorithm, and planet optimization algorithm are used to adjust the PID controller parameters. Furthermore, a comparison among the optimized PID gains with the applied algorithms shows great accuracy, efficacy, and effectiveness of the proposed GRO. MATLAB\ Simulink program is used to model and simulate the system components and the applied algorithms. The simulation findings demonstrate that the suggested optimized PID control strategy has superior efficiency and resilience in terms of less overshoot and settling time.