Feedback Stabilization Research Articles

Stability analysis of LTV systems via gain and phase

Abstract This paper considers the feedback stability analysis of infinite-dimensional discrete-time linear time-varying systems with combined gain and phase information. The framework considers a system to be a causal linear operator described by a lower triangular infinite-dimensional complex matrix. For $r$-sectorial operators, we first derive a sufficient condition for the invertibility of $I+AB$ using the gain and phase information. Finally, we use this invertibility criterion to give a sufficient condition for feedback stability of $r$-sectorial systems.

Flow Field Analysis on Critical Feedback Information for UAV Autonomous High Speed Descent in Power Line Scenario

Abstract To improve the UAV efficiency in power line inspection, it must autonomously and rapidly descend to a specific height to complete the charging or landing task. This task requires the UAV to contain a stable control loop to face the specific airflow during autonomous and rapid descent: the vortex ring problem, and this specific airflow will reduce the UAV controllability. To implement the UAV autonomous high-speed descent, a control method must provide feedback information on the affected airflow and output a stable rotational speed. Hence, this paper designs a UAV autonomous high-speed descent control loop and proposes a variable rotor speed method to solve the feedback information in the control loop. This method reveals the relationship between the air movement caused by the rotor rotation and the controllability of the UAV high-speed descent. Therefore, with this method, the UAV control loop can obtain stable feedback on the air movement and achieve autonomous high-speed descent. To solve the UAV feedback information, we built the model to calculate the rotor speed in the autonomous high-speed descent UAV control loop and verified it by the CFD. The verification results showed that the model could reflect the actual fly condition. The proposed method solves the problem of UAV autonomous high-speed descent feedback information, improving the work efficiency of UAVs in power line inspection operations.

Bounded output feedback stabilization for nonlinear planar systems with unknown structures and measurements

Bounded output feedback stabilization for nonlinear planar systems with unknown structures and measurements

A note on boundary feedback stabilization for degenerate parabolic equations in multi-dimensional domains

Abstract In this paper, we are concerned with the problem of stabilization of a degenerate parabolic equation with a Dirichlet control, evolving in bounded domain 𝓞 ⊂ ℝ d , d ≥ 2. We apply the proportional control design technique based on the spectrum of the linear operator which governs the evolution equation. The stabilizing feedback control, we design here, is linear, of finite-dimensional structure, easily manageable from the computational point of view.

AI-Assisted Insole Sensing System for Multifunctional Plantar-Healthcare Applications.

The pervasive global issue of population aging has led to a growing demand for health monitoring, while the advent of electronic wearable devices has greatly alleviated the strain on the industry. However, these devices come with inherent limitations, such as electromagnetic radiation, complex structures, and high prices. Herein, a Solaris silicone rubber-integrated PMMA polymer optical fiber (S-POF) intelligent insole sensing system has been developed for remote, portable, cost-effective, and real-time gait monitoring. The system is capable of sensitively converting the pressure of key points on the sole into changes in light intensity with correlation coefficients of 0.995, 0.952, and 0.910. The S-POF sensing structure demonstrates excellent durability with a 4.8% variation in output after 10,000 cycles and provides stable feedback for bending angles. It also exhibits water resistance and temperature resistance within a certain range. Its multichannel multiplexing framework allows a smartphone to monitor multiple S-POF channels simultaneously, meeting the requirements of convenience for daily care. Also, the system can efficiently and accurately provide parameters such as pressure, step cadence, and pressure distribution, enabling the analysis of gait phases and patterns with errors of only 4.16% and 6.25% for the stance phase (STP) and the swing phase (SWP), respectively. Likewise, after comparing various AI models, an S-POF channel-based gait pattern recognition technique has been proposed with a high accuracy of up to 96.87%. Such experimental results demonstrate that the system is promising to further promote the development of rehabilitation and healthcare.

Regional Static Output Feedback Stabilization Based on Polynomial Lyapunov Functions for a Class of Nonlinear Systems

Regional Static Output Feedback Stabilization Based on Polynomial Lyapunov Functions for a Class of Nonlinear Systems

Robust Output Feedback Stabilization and Tracking for an Uncertain Nonholonomic Systems with Application to a Mobile Robot.

This paper presents a novel robust output feedback control that simultaneously performs both stabilization and trajectory tracking for a class of underactuated nonholonomic systems despite model uncertainties, external disturbance, and the absence of velocity measurement. To solve this challenging problem, a generalized normal form has been successfully created by employing an input-output feedback linearization approach and a change in coordinates (diffeomorphism). This research mainly focuses on the stabilization problem of nonholonomic systems that can be transformed to a normal form and pose several challenges, including (i) a nontriangular normal form, (ii) the internal dynamics of the system are non-affine in control, and (iii) the zero dynamics of the system are not in minimum phase. The proposed scheme utilizes combined backstepping and sliding mode control (SMC) techniques. Furthermore, the full-order high gain observer (HGO) has been developed to estimate the derivative of output functions and internal dynamics. Then, full-order HGO and the backstepping SMC have been integrated to synthesize a robust output feedback controller. A differential-drive type (2,0) the wheeled mobile robot has been considered as an example to support the theoretical results. The simulation results demonstrate that the backstepping SMC exhibits robustness against bounded uncertainties.

MILD combustion stabilization issues through the analysis of hysteresis behaviors: The case of new energy carriers

MILD combustion processes are renewed to reveal a strong resilience to extinction phenomena and/or instabilities, whereas the oxidation process is stabilized trough ignition phenomena. Under MILD conditions, igni-diffusive and/or perfectly mixed kernels, forming during the mixing process between hot products and fresh reactants, are so much diluted and pre-heated to escape classical feed-back flammable flames stabilization mechanisms, while ignition and extinction events merge in a unique condition through “anhysteretic” behaviors. So far, considering methane as reference fuel, it has been largely demonstrated the mentioned “anhysteretic” condition is very conservative and defines a sub-domain of MILD combustion processes, following Cavaliere and de Joannon's definition. Furthermore, the coincidence of ignition and extinction phenomena can occur also preserving hysteresis phenomena. In turns, this condition strongly enlarges the stabilization domain of MILD combustion processes, starting from the upper branch of the hysteresis behaviors to the real extinction, with characteristic unstable loci to consider as further/last opportunity to promote stable operative conditions through the formation of local thermo-kinetic conditions in the combustion chamber during hot products/fresh reactants mixing process (injection configuration/burner design), or by forced ignition events. The hysteresis behaviors of renewable/alternative fuels, relevant within the decarbonization policies of several energy sectors, are thoroughly discussed under MILD conditions through numerical studies in model reactors in order to shed light on common and/or different features, and outline practical rules towards the definition of stable MILD combustion domains. Results show that, as MILD combustion is a chemical kinetics-driven processes, stability issues have to be discussed in relation to fuel nature, albeit with common behavior can be derived. The coincidence between extinction/ignition phenomena is reached for extremely diluted conditions, already ascribable to MILD combustion conditions, thus defining a small sub-domain of the process. This condition can be reached through “hysteretic” or “anhysteretic” behaviors.

Asymptotic adaptive output-feedback stabilisation of nonlinear systems with unknown growth rate and sensor uncertainty

For a class of nonlinear systems with sensor uncertainty, the problem of adaptive output feedback stabilisation is investigated in this paper. It is assumed that only the output is available for feedback control, which suffers from sensor uncertainty. At the same time, the nonlinear function in the system model has an unknown growth rate. To solve this problem, a set of state observers is designed to estimate the unknown system states based on the uncertain output, and an adaptive output-feedback control is designed based on this. By using the corollary of Barbalet's Lemma, it is shown that the equilibrium of the closed-loop system is asymptotically stable. Finally, simulation results verify the effectiveness of the control scheme

Adaptive output feedback stabilisation control for cascaded systems with output constraints and disturbance

The system under consideration is a cascaded system composed of integral input-to-state stable inverse dynamics and a non-holonomic system. An adaptive output feedback stabilisation control is proposed for the system with disturbance and output constraints. The dynamic uncertainty is eliminated using the technique that changes the supply rate. An extended state observer is proposed by defining the non-vanishing disturbance as a new state variable of the system. The asymmetric time-varying output constraint is solved by utilising the tan-type barrier Lyapunov function. The result shows that the adaptive output feedback controller guarantees the stability of the closed-loop system without violating the asymmetric time-varying output constraints under the backstepping technique. Simulation results are given to verify the effectiveness of the control method.

Feedback Stabilization of Quasi-One-Sided Lipschitz Nonlinear Discrete-Time Systems with Reduced-Order Observer

The feedback stabilization problem for nonlinear discrete-time systems with a reduced-order observer is investigated, in which the nonlinear terms of the systems satisfy the quasi-one-sided Lipschitz condition. First, a discrete-time reduced-order observer for nonlinear systems is designed. Then, a feedback controller with a reduced-order observer is designed for realizing the stabilization of nonlinear discrete-time systems. We prove that the design of a feedback controller and reduced-order observer of systems can be carried out independently in the case of discrete-time with nonlinear terms, which largely reduces the computational complexity of the observer and controller. The introduction of the quasi-one-sided Lipschitz condition simultaneously enhances the robustness and stability of nonlinear control systems. Finally, the feasibility and effectiveness of the proposed design approach is verified by a numerical simulation.

Output feedback stabilization of stochastic high‐order nonlinear time‐delay systems with unknown output function

AbstractThis article considers the problem of output feedback stabilization for a class of stochastic high‐order nonlinear time‐delay systems with unknown output function. For stochastic high‐order nonlinear time‐delay systems, based on the Lyapunov stability theorem, by combining the addition of one power integrator and homogeneous domination method, the maximal open sector of output function is given. As long as output function belongs to any closed sector included in , an output feedback controller can be developed to guarantee the closed‐loop system globally asymptotically stable in probability.

Feedback stabilization of probabilistic finite state machines based on deep Q-network.

As an important mathematical model, the finite state machine (FSM) has been used in many fields, such as manufacturing system, health care, and so on. This paper analyzes the current development status of FSMs. It is pointed out that the traditional methods are often inconvenient for analysis and design, or encounter high computational complexity problems when studying FSMs. The deep Q-network (DQN) technique, which is a model-free optimization method, is introduced to solve the stabilization problem of probabilistic finite state machines (PFSMs). In order to better understand the technique, some preliminaries, including Markov decision process, ϵ-greedy strategy, DQN, and so on, are recalled. First, a necessary and sufficient stabilizability condition for PFSMs is derived. Next, the feedback stabilization problem of PFSMs is transformed into an optimization problem. Finally, by using the stabilizability condition and deep Q-network, an algorithm for solving the optimization problem (equivalently, computing a state feedback stabilizer) is provided. Compared with the traditional Q learning, DQN avoids the limited capacity problem. So our method can deal with high-dimensional complex systems efficiently. The effectiveness of our method is further demonstrated through an illustrative example.

Small-Gain and Small-Angle Conditions for Feedback Stability Analysis of Linear Stochastic Systems

Small-Gain and Small-Angle Conditions for Feedback Stability Analysis of Linear Stochastic Systems

Saturated Boundary Feedback Stabilization for a Nonuniform Timoshenko Beam With Disturbances and Uncertainties

Saturated Boundary Feedback Stabilization for a Nonuniform Timoshenko Beam With Disturbances and Uncertainties

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

In this paper, the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities is investigated. By constructing the new Lyapunov-Krasovskii functional and reduced-order observer, based on homogeneous domination theory together with the adding a power integrator method, an output feedback controller is developed to guarantee the equilibrium of the closed system globally uniformly asymptotically stable.

Bioenzyme-free dual-mode sensing for organophosphorus pesticides based on UiO-66-NH2 MOFs encapsulated tris(2,2′-bipyridyl) ruthenium(II)

Herein, we proposed a novel bioenzyme-free dual-mode sensing strategy for the rapid and accurate monitoring of organophosphorus pesticides (OPs) by preparing tris(2,2′-bipyridyl) ruthenium(II) (Ru(bpy)32+) encapsulated with UiO-66-NH2 MOFs as nanozyme (Ru@Zr-MOFs). The as-prepared Ru@Zr-MOFs nanozyme not only exhibits superior peroxidase-like activity which can catalyze O-phenylenediamine (OPD) oxidation to generate yellow 2,3-diaminophenazinc, but also exhibits dual-fluorescence feature (at 442 and 612 nm respectively) and specific interaction capacity with OPs. However, in the existence of OPs, the peroxidase-like activity of Ru@Zr-MOFs nanozyme is restricted and the oxidation process of OPD is stopped; meanwhile, the fluorescence of Ru@Zr-MOFs at 442 nm increases rapidly (< 10 s) while that at 612 nm is apathetic, thus a colorimetric and ratiometric fluorescent sensing strategy was first designed to detect OPs by using glyphosate (Gly) as a typical model of OPs. Then, in consideration of the benefits of smartphone which can make the sensing process more convenient, stable, rapid and sensitive feedback, a smartphone coupled with hydrogel detection platform was proposed also for OPs determination. In addition, the designed sensing strategy offers superior selectivity, stability and real application capabilities. It’s thus expected the as-designed Ru@Zr-MOFs nanozyme based dual-mode sensing strategy possesses important real application for the low-cost, rapid, sensitive and accurate determination of OPs.

Exponential stability of non-conformable fractional-order systems

Abstract Recently, the authors Guzman et al. (2018) introduced a new simple well-behaved definition of the fractional derivative called non-conformable fractional derivative. In this paper we study the exponential stability of non-conformable fractional-order systems by using the Lyapunov function and Gronwall inequality. These inequalities can be used as handy tools to research stability problems of nonlinear systems. Sufficient conditions for exponential stability are given using the Lyapunov theory. Further, deals with the state feedback stabilization problems for a family of nonlinear systems satisfying a Lipschitz continuity condition. The stability of the controller is proved by means of the new Lyapunov stability theorem given in this paper. A numerical example is given to illustrate the efficiency of the obtained result.

Active feedback stabilization of super-efficient microcombs in photonic molecules.

Dissipative Kerr soliton (DKS) frequency combs, when generated within coupled cavities, exhibit exceptional performance concerning controlled initiation and power conversion efficiency. Nevertheless, to fully exploit these enhanced capabilities, it is necessary to maintain the frequency comb in a low-noise state over an extended duration. In this study, we demonstrate the control and stabilization of super-efficient microcombs in a photonic molecule. Our findings demonstrate that there is a direct relation between effective detuning and soliton power, allowing the latter to be used as a setpoint in a feedback control loop. Employing this method, we achieve the stabilization of a highly efficient microcomb indefinitely, paving the way for its practical deployment in optical communications and dual-comb spectroscopy applications.

Design stabilisers for multi-input affine control stochastic systems via stochastic control Lyapunov functions

This paper studies the problem of state feedback stabilisation, in the sense of a weak solution, for a class of multi-input affine control stochastic systems whose drift and diffusion terms are dependent on the control and for which classical methods are not applicable. Based on the generalised stochastic Lyapunov theorem and on the technique of stochastic control Lyapunov functions, sufficient conditions for the existence of a continuous stabilising feedback control are proposed, and a state feedback controller can be developed to guarantee the closed-loop system globally asymptotically stable in probability. This work generalises previous results on the stabilisation of single-input affine control stochastic systems. The obtained results are illustrated by a numerical example.