Proof Of Stability Research Articles

Fixed-time observer-based tracking controller for a hysteretic piezoelectric deformable mirror of an adaptive optic system.

Piezoelectric deformable mirrors (DM) are benefited from the high accuracy and swift dynamics. The hysteresis phenomenon, which inherently exists in piezoelectric materials, degrades the capability and precision of the adaptive optics (AO) systems. Also, the dynamics of piezoelectric DMs make the controller design more complicated. This research aims to design a fixed-time observer-based tracking controller (FTOTC), which estimates the dynamics, compensates the hysteresis, and ensures tracking to the actuator displacement reference, in the fixed time. Unlike the existing inverse hysteresis operator-based methods, the proposed observer-based controller overcomes the computational burdens and estimates the hysteresis in real-time. The proposed controller tracks the reference displacements, while the tracking error converges in the fixed time. The stability proof is presented by two consecutive theorems. Numerical simulations demonstrate superior tracking and hysteresis compensation by the presented method, from a comparison viewpoint.

A novel control strategy for Matrix Converters based on Transient Power Balance

The Matrix Converter is a power electronics topology that allows direct conversion of an alternating-current (AC) source to an AC load operating at a different frequency. The associated control problem is inherently difficult since it is both nonlinear and underactuated. This paper describes a novel control strategy for Matrix Converters based on Transient Power Balance. The scheme achieves the following design objectives: tracking of a desired load current, tracking of a desired supply (leading or lagging) power factor, rapid active damping of supply-current oscillations, arising from a supply-side resonant filter, without needing any additional resistance on the supply side, and mitigation of supply-current distortion arising from supply-voltage distortion. Achieving these goals simultaneously has hitherto been an open problem in this area. All of these goals are achieved in the face of significant errors in circuit component values. A proof of local asymptotic stability of the proposed algorithm is given and associated design constraints are addressed. The claims are illustrated by simulation studies.

Inverse Reinforcement Q-Learning Through Expert Imitation for Discrete-Time Systems.

In inverse reinforcement learning (RL), there are two agents. An expert target agent has a performance cost function and exhibits control and state behaviors to a learner. The learner agent does not know the expert's performance cost function but seeks to reconstruct it by observing the expert's behaviors and tries to imitate these behaviors optimally by its own response. In this article, we formulate an imitation problem where the optimal performance intent of a discrete-time (DT) expert target agent is unknown to a DT Learner agent. Using only the observed expert's behavior trajectory, the learner seeks to determine a cost function that yields the same optimal feedback gain as the expert's, and thus, imitates the optimal response of the expert. We develop an inverse RL approach with a new scheme to solve the behavior imitation problem. The approach consists of a cost function update based on an extension of RL policy iteration and inverse optimal control, and a control policy update based on optimal control. Then, under this scheme, we develop an inverse reinforcement Q-learning algorithm, which is an extension of RL Q-learning. This algorithm does not require any knowledge of agent dynamics. Proofs of stability, convergence, and optimality are given. A key property about the nonunique solution is also shown. Finally, simulation experiments are presented to show the effectiveness of the new approach.

Robust Discrete-Time Lateral Control of Racecars by Unknown Input Observers

This brief addresses the robust lateral control problem for self-driving racecars. It proposes a discrete-time estimation and control solution consisting of a delayed unknown input-state observer (UIO) and a robust tracking controller. Based on a nominal vehicle model, describing its motion with respect to a generic desired trajectory and requiring no information about the surrounding environment, the observer reconstructs the total force disturbance signal, resulting from imperfect knowledge of the time-varying tire-road interface characteristics, presence of other vehicles nearby, wind gusts, and other model uncertainty. Then, the controller actively compensates the estimated force and asymptotically steers the tracking error to zero. The brief also presents a closed-loop stability proof of the method, ensuring perfect asymptotic estimation and tracking by the controlled vehicle. The proposed solution advantageously needs no a-priori information about the total disturbance boundedness, additional variables to model uncertainty, or observer parameters to be tuned. Its effectiveness and superiority to existing methods are studied in theory and shown in simulations where a full racecar model, based on the vehicle dynamics blockset, is required to track aggressive maneuvers. Through a faster and more accurate disturbance estimation, the solution robustly ensures better dynamic responses even with measurement noise.

A Simple Learning Approach for Robust Tracking Control of a Class of Dynamical Systems

This paper studies the robust tracking control problem for a class of uncertain nonlinear dynamical systems subject to unknown disturbances. A robust trajectory tracking control law is designed via a simple learning-based control strategy. In the developed design, the cost function based on the desired closed-loop error dynamics is minimized by means of gradient descent technique. A stability proof for the closed-loop nonlinear system is provided based on the pseudo-linear system theory. The learning capability of the developed robust trajectory tracking control law allows the system to mitigate the adverse effects of the uncertainties and disturbances. The numerical simulation results for a planar PPR robot are included to illustrate the effectiveness of the developed control law.

Distributed output data-driven optimal robust synchronization of heterogeneous multi-agent systems

This work presents an output-feedback policy learning algorithm underlining input–output system data for distributed robust optimal synchronization of heterogeneous multi-agent systems. The output-feedback synchronization problem in the context of this work is formulated via robust output regulation and reinforcement learning modeling the interactions among agents by a zero-sum game. The proposed learning and control structure only requires the local system data for each agent and distributed output data among communicating neighbors. We utilize system-level synchysis for the continuous-time state reconstruction for the distributed learning with convergence and stability proofs under the proposed output-feedback policy for solving the zero-sum game. We further show that policy learning is assured under the proposed data criteria relating to input–output data only rather than any inter-immediate gains from policy iterations. Based on the cooperative robust output regulation, this work gains robustness after the learning is complete and establishes an output data-driven distributed optimal robust synchronization without knowing accurate system dynamics. A numerical example shows the effectiveness of the proposed learning algorithm.

Adaptive finite-time fault-tolerant control for nano-satellite attitude tracking under actuator constraints

In this paper, a finite-time fault-tolerant control method is developed for attitude tracking of a nano-satellite with three magnetorquers and one reaction wheel in the presence of actuator faults, inertia uncertainties, external distribution, and actuator constraints. For this purpose, the modified non-singular fast terminal sliding mode control is used due to the ability of robustness against uncertainties and finite-time convergence. In this approach, the modified sliding surface variable is constructed based on angular velocity and attitude error to converge the attitude error to zero in a finite time. In addition, three adaptive parameters are employed to reduce the adverse effect of uncertain expressions and to track the attitude commands with high control accuracy. The adaptive parameters and sliding surface variable are used in the reaching phase of the controller to decrease the chattering phenomenon. The dynamics of adaptive parameters, with regard to the angular velocities of the nano-satellite and reaction wheel and the sliding surface variable, are obtained during the stability proof of the closed-loop system. Also, the finite-time convergence of sliding surface and attitude variables are proved by the extended Lyapunov condition, and the convergence regions of attitude tracking errors are obtained. The simulations are accomplished and compared with an existing adaptive sliding mode control approach to evaluate the performance of the proposed controller. The results verify that the proposed controller performs better than the mentioned controller in terms of finite-time convergence, the accuracy of attitude tracking, and the reduction of the chattering phenomenon.

Neural Network and Dynamic Inversion Based Adaptive Control for an HALE-UAV against Icing Effects

In the past few decades, in-flight icing has become a common problem for many missions, potentially leading to a reduction in control effectiveness and flight stability, which would threaten flight safety. One of the most popular methods to address this problem is adaptive control. This paper establishes a dynamic model of an iced high-altitude long-endurance unmanned aerial vehicle (HALE-UAV) with disturbance and measurement noise. Then, by combining multilayer perceptrons (MLP) with a nonlinear dynamic inversion (NDI) controller, we propose an MLP-NDI controller to compensate for online inversion errors and provide a brief proof of control stability. Two experiments were conducted: on one hand, we compared the MLP-NDI controller with other typical controllers; on the other hand, we evaluated its robustness and adaptiveness under different icing conditions. Results indicate that the MLP-NDI controller outperforms other typical controllers with higher tracking accuracy and exhibits strong robustness in the presence of icing errors and measurement noise, which has huge potential to ensure flight safety.

Dynamic Control of Soft Robotic Arm: An Experimental Study

The objective of this letter is to investigate the dynamic control of a soft robotic arm. First, a modular soft robotic hardware and an affordable actuator-space encoder were presented. We then discussed the soft robot modeling, and adaptive passivity control strategy with stability proof. The proposed controller was tested in different operation scenarios, and compared to the standard PD feedback linearization control and passivity control. In all experimental settings, the adaptive passivity control scheme was able to achieve superior performance, even with significant modeling uncertainties and disturbances. The theoretical analysis and experimental validations of the proposed controller will pave the way toward the practical implementations of the soft robotic system in the dynamic scenarios.

Off-Policy Risk-Sensitive Reinforcement Learning-Based Constrained Robust Optimal Control

This article proposes an off-policy risk-sensitive reinforcement learning (RL)-based control framework to jointly optimize the task performance and constraint satisfaction in a disturbed environment. The risk-aware value function, constructed using the pseudo control and risk-sensitive input and state penalty terms, is introduced to convert the original constrained robust stabilization problem into an equivalent unconstrained optimal control problem. Then, an off-policy RL algorithm is developed to learn the approximate solution to the risk-aware value function. During the learning process, the associated approximate optimal control policy is able to satisfy both input and state constraints under disturbances. By replaying experience data to the off-policy weight update law of the critic neural network, the weight convergence is guaranteed. Moreover, online and offline algorithms are developed to serve as principled ways to record informative experience data to achieve a sufficient excitation required for the weight convergence. The proofs of system stability and weight convergence are provided. The Simulation results reveal the validity of the proposed control framework.

Homogeneous weighted motion planning for cooperated manipulator systems under position-torque constrained processing Environment

Real-time motion planning under position and torque constraints is a critical challenge for cooperative manipulator efficiency and safety operation. Real-time motion planning at the velocity level improves computation efficiency, eliminates the complex derivative calculation of the Jacobian matrix, and the velocity planning solution can be used directly for robotic kinematic control. However, little research attention has been attached to handling the position and torque constraints simultaneously at velocity level for cooperative manipulator systems. In this paper, we introduce a novel homogeneous weighted least-norm method (HWLN) for joint velocity redistribution of cooperated manipulators. Within the coupled kinematics-dynamics model of cooperated manipulators, joint position and torque constraints are simultaneously homogenized and taken into account by the constraint performance index. To avoid joint's constraint saturations, two real-time weight updating laws are designed for the joint position and driving torque respectively. The joint velocities of cooperated manipulators are then adaptively redistributed using the pseudo-kinetic-energy minimum optimization criteria. When compared to single manipulator regulation, this strategy takes greater advantage of cooperative redundancy and significantly enhances the position-torque planning performance. Mathematical stability proof is presented. In the meanwhile, numerical experiment results under various joint position and torque constraints demonstrate the effectiveness of the proposed HWLN method. The experimental results for motion planning and control of two 6R ABD-20Kg robotic manipulators are provided.

General proportional integral observer (GPIO) - based disturbance compensation for minimum variance time synchronization

Precise time synchronization is an enabling technology for mission-critical time-sensitive Industrial Internet of Things (IIoT). However, the crystal oscillator clock which is widely used in IIoT may suffer from periodic disturbances caused by repetitive motion or periodic vibration. To improve the time synchronization of distributed nodes subject to periodic disturbances, this paper proposes a novel disturbance rejection framework, General-Proportional-Integral-Observer-based Disturbance Compensation (GPIO-DC), with the proof of stability, and combined with a 2-freedom control design strategy to optimize both the disturbance rejection and clock tracking performance. And the GPIO’s unique feature of blocking zeros are fully exploited to reject the periodic disturbance at its frequencies and a zero-pole optimal design algorithm is given. With the disturbance being compensated, a disturbance-free minimum variance time synchronization protocol for a complex network is developed and optimized by using Linear Matrix Inequality (LMI) to minimize the variance of networked synchronization errors. The performance of the proposed method is devalued by intensive simulation. Comparing with recent relevant research, the proposed method achieves a better performance in disturbance rejection and minimum variance.

Global stability of a predator–prey model with generalist predator

Proof of the global stability for unique locally stable coexistence equilibrium points with the help of a suitable Lyapunov function is an interesting research problem for predator–prey type models. The proof of the global stability becomes challenging for the models which admit more than one coexistence equilibrium point. In this article, we prove the global stability of the coexistence equilibrium point for a predator–prey model with a generalist predator with the help of the Lyapunov function and the Bendixson–Dulac criteria under two different parametric restrictions. Further, we use a Lyapunov functional and apply LaSalle’s invariance principle to prove the global stability of the coexistence equilibrium point of the corresponding delayed model, with maturation delay.

The Evolutionary Principles of the Attractiveness of Symmetry and Their Possible Sustainability in the Context of Research Ambiguities

Symmetry belongs to one of the basic principles of the beauty of human and non-human objects since antiquity. Even though its significance has been verified by numerous theories and research studies, there is a number of papers suggesting that this principle may be false. The study identifies five major evolutionary principles, in the context of new approaches and research ambiguities based mainly on neuroscience and evolutionary psychology, that support the thesis that highlights the significance of symmetry in the perception and assessment of attractiveness: 1. symmetry as an honest signal of various health characteristics; 2. symmetry as proof of developmental stability; 3. effectiveness; 4. comprehensibility; 5. predictability. In the context of the mechanisms described above it also seeks possible explanations for the existence of contradictory research results related to the attractiveness of symmetry. The outcome of the study is the postulation of three hypotheses: 1. the naturalness hypothesis (symmetry is only attractive to the same degree that it naturally occurs in the subject); 2. the accent hypothesis (minor asymmetries do not disprove the principles of symmetry, they make them more visible); 3. the ecology hypothesis (the attractiveness of symmetry is conditioned by the situation and depends on the type of subject assessed) that allow us to integrate both past and contemporary (and putatively contradictory) research findings. The paper also provides proposals for the verification of the postulated hypotheses.

Implicit discretization of Lagrangian gas dynamics

We construct an original framework based on convex analysis to prove the existence and uniqueness of a solution to a class of implicit numerical schemes. We propose an application of this general framework in the case of a new non linear implicit scheme for the 1D Lagrangian gas dynamics equations. We provide numerical illustrations that corroborate our proof of unconditional stability for this non linear implicit scheme.

Flocks, Mobs, and Figure Eights: Swarming as a Lemniscatic Arch

Inspired by the natural mobbing behavior of birds, this work presents a novel, quasi-distributed swarming strategy called the Dynamic Lemniscatic Arch. It resolves the problem of producing globally-stable, evenly-spaced lemniscate (or, figure-eight) trajectories while relying on local interactions only. Such trajectories are advantageous in applications where energy consumption and mechanical strain must be minimized. Previous work in lemniscate curves has typically relied on predetermined trajectories, rather than on the emergent structure of the swarm. Furthermore, we enrich the traditional 2-dimensional lemniscate plane curve structure by forming an arch in the third dimension. This arch provides more consistent coverage in surveillance type tasks and, with minor variations in parameters, can be used to produce mobbing behavior. The technique relies on time-varying quaternion rotations linked to the positions of dynamically induced virtual agents. We provide a mathematical proof of stability, which demonstrates the swarm converges to the desired geometry. Simulations show that the strategy performs well with multiple agents and in numerous different configurations.

Supplemented with reinforcement learning to improve the detection of passive remote sensing devices

In this paper, a policy iterative algorithm based on reinforcement learning is proposed to improve the balanced detection quality of passive remote sensing equipment. Firstly, the basic structure of the policy iteration algorithm is given for nonlinear affine systems, and stability proof is given. The whole process of detection information of passive remote sensing equipment is equivalent to the absorption of electric energy by the explored object. A nonlinear affine model for the PI solution is established by using this equivalent model. The working quality based on various information sensors is equivalent to the discrete-time cost function. Finally, a simulation experiment is carried out for a class of passive remote sensing equipment with 8 kinds of characteristic information and a virtual self-powered device is considered. The effectiveness of the algorithm is proven.

Analytical Design of the Regulator for Ensuring the Optimality and Stability of the Reserve of Innovative Industrial Products

Demanded by the formation of the knowledge economy and the digitalization of its industrial sphere, the development of science-intensive industries requires the analytical design of the regulator and economic and mathematical modeling of dynamic processes of saturation of the market segment with innovative industrial products. In this context, two tasks are being formalized: the first is the regulation of the reserve of these products in order to stabilize it in conjunction with the indicators of the rate of change in the volume of its production and demand for it, and the second is the analytical design of the optimal regulator of the reserve of innovative products with the achievement of a minimum of its content and losses arising from due to the shortage of this product with an increased demand for it, with the proof of the asymptotic stability in general of the obtained solutions of both problems. The construction of corresponding models deepens the understanding of investment and innovation processes and equips analytical tools for adaptive management of the efficiency and stability of industrial enterprises in a turbulent economic environment.

Power-Based Velocity-Domain Variable Structure Passivity Signature Control for Physical Human-(Tele)Robot Interaction

The excess of passivity (EoP) of the human biomechanics plays an imperative role in absorbing the interaction energy during physical human–(tele)robot interaction and can be exploited by controllers used for stabilization of human-centered (tele)robotic systems. However, the first generation of nonlinear EoP-based stabilizers loaded the force reflection channel resulting in degradation of the force profile. This will challenge applications that are heavily dependent on the quality of force reflection, such as telerobotic rehabilitation. This article explores the possibility of developing a nonlinear stabilizer that modifies the reflected velocity to the follower-side operator based on the corresponding EoP map. As an applied benefit in the context of telerehabilitation, the proposed stabilizer does not require information about the EoP of all patients; instead, it would require that for the individual therapist who works with the group of patients. The article provides the mathematical derivation and stability proof of the nonlinear design of the stabilizer named “power-based velocity-domain variable structure passivity signature control (PV-VSPSC).” The proposed nonlinear stabilizer is evaluated through systematic experiments and systematic grid simulation studies in this paper.

The subdivision-based IGA-EIEQ numerical scheme for the binary surfactant Cahn–Hilliard phase-field model on complex curved surfaces

In this paper, we consider numerical approximations of the binary surfactant phase-field model on complex surfaces. Consisting of two nonlinearly coupled Cahn–Hilliard type equations, the system is solved by a fully discrete numerical scheme with the properties of linearity, decoupling, unconditional energy stability, and second-order time accuracy. The IGA approach based on Loop subdivision is used for the spatial discretizations, where the basis functions consist of the quartic box-splines corresponding to the hierarchic subdivided surface control meshes. The time discretization is based on the so-called explicit-IEQ method, which enables one to solve a few decoupled elliptic constant-coefficient equations at each time step. We then provide a detailed proof of unconditional energy stability along with implementation details, and successfully demonstrate the advantages of this hybrid strategy by implementing various numerical experiments on complex surfaces.