Lyapunov-based Approach Research Articles

Semi-decentralized Lyapunov-based formation control of multiple omnidirectional mobile robots

<p>This paper introduces an advanced formation control algorithm based on a Lyapunov approach for coordinating multiple omnidirectional mobile robots in collaborative object transport tasks. The semi-decentralized strategy ensures that the robots maintain a predefined geometric formation, crucial for stability during material transportation, and dynamically adapt to avoid collisions using onboard sensors. Experimental with a physical robot simulator demonstrates successful maintenance of line and triangle formations achieving an average side length maintenance of 1.00 meters with minimal deviation. Quantitative analysis across 30 experimental runs reveals consistent performance, with a maximum side length fluctuation of only 2 centimeters, validating the effectiveness of maintaining formation within a multi-robot system (MRS) framework. The Lyapunov-based approach proves to be an efficient method for cooperative object transport, achieving consistent performance with minimal deviation.</p>

A Lyapunov-Based Approach to Joint Optimization of Resource Allocation and 3-D Trajectory for Solar-Powered UAV MEC Systems

A Lyapunov-Based Approach to Joint Optimization of Resource Allocation and 3-D Trajectory for Solar-Powered UAV MEC Systems

Adaptive Hierarchical Fractional-Order Sliding Mode Control Strategy for Multi-terminal VSC-HVDC System with Wind Farm

In this paper, an adaptive hierarchical fractional-order sliding mode controller (AHFSMC) for a multi-terminal Voltage Source Converter (VSC) based High Voltage Direct Current (HVDC) Integrated with a wind farm (WF) system is designed. Multi-terminal VSC-HVDC (MtVDC) connected to wind farms has received several attentions in the power sector because of its numerous benefits. The effectiveness of MtVDC, on the other hand, is dependent on the control scheme used. To achieve this goal, a hierarchical sliding mode control method by fractional-order calculus is used. The controller parameters are adjusted according to a suitable adaptation method to enhance the proposed controller's robustness compared to the system uncertainties coefficient. An appropriate Lyapunov-based approach is used to achieve the adaptation rule. This paper discusses a scheme to design additional controllers in MtVDC systems to damp electromechanical oscillations, one of several features of HVDC presently under active study. Numerical simulations validate the proposed control strategy's feasibility and efficiency. This novel approach is employed for the upgrading of system stability with the dynamic properties of the MtVDC in a variety of operative conditions.

Model-based impending lithium battery terminal voltage collapse detection via data-driven and machine learning approaches

Lithium battery is an important power source of an electrical vehicle (EV). Practically, when a battery is about to fail, it needs to be removed from the load because keeping it connected can lead to permanent damage. Hence, it is important to detect battery failure to sustain the lifespan of the battery and avoid safety issues which will contribute to the sustainability of the EV. However, determining the effective disconnecting or discharging moment of the battery remains a challenging issue in EV applications. In order to solve the abovementioned problem, a control framework and maximum likelihood estimation are proposed to estimate the parameters of a battery model. In addition, both the sparse representation and dynamic mode decomposition (DMD) approaches are applied to protect the physical battery unit from a failure scenario. For comparison purposes, the proposed framework is compared to a Lyapunov-based detection approach along with neural network (NN) and linear discriminant analysis (LDA). Moreover, several state estimation algorithms are applied to estimate battery state of charge (SOC) at each time step: extended Kalman filter, extended Kalman smooth variable structure filter, and cubature Kalman filter. Finally, the experimental results showed that the proposed DMD approach outperforms the sparse representation, NN, LDA, and Lyapunov-based approaches in terms of detection accuracy. Moreover, the proposed DMD strategy is more robust towards the inaccuracy of the estimated SOC. Besides that, the proposed battery model parameter estimation approach exhibited fast processing time; therefore, it is a reliable choice for recomputing the model parameters from time to time to compensate aging effect. An autonomous unmanned aerial vehicle (UAV) was simulated as a proof-of-concept in a MATLAB environment to verify the detection performance of the proposed methods. Both actual and UAV results showed that the DMD demonstrated more robust detection performance than other methods in terms of processing time and detection accuracy.

Periodic and Dynamic Periodic Event-Triggered Control for Nonlinear Cyber-Physical Systems Under DoS Attacks via a Hybrid System Approach

This paper is focused on the problem of periodic and dynamic periodic event-triggered control for nonlinear cyber-physical systems (CPSs) under denial-of-service (DoS) attacks and exogenous disturbances. The analysis relies on a new model to design periodic event-triggered control and dynamic periodic event-triggered control schemes such that the nonlinear CPSs are resilient to a class of malicious attacks which can be characterized by attacking frequency and attacking duration. By developing an average dwell-time automaton and a time-ratio monitor to describe frequency and duration of the DoS attacks, general hybrid dynamical frameworks are firstly proposed for event-triggered nonlinear CPSs. Based on the established models, novel Lyapunov functions are constructed. Furthermore, thanks to the Lyapunov-based approach, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> -gain performance of the considered nonlinear CPSs under DoS attacks is analyzed. Finally, the feasibility of the theoretical findings is demonstrated by a numerical example.

Lyapunov-based approach to event-triggered control with self-triggered sampling

In this paper, a Lyapunov-based design method for event-triggered control with self-triggered sampling is proposed. In the proposed method, update of the control input and sampling of the state are individually determined based on two kinds of upper bounds of the Lyapunov function. By the proposed method, a non-monotonic Lyapunov function can be constructed. By non-monotonic decrease of a Lyapunov function, the number of communications can be reduced. In the neighborhood of the origin, we consider a control method such that the state stays in a certain set. As a result, it is guaranteed that the closed-loop system is uniformly ultimately bounded. Through a numerical example, we demonstrate the effectiveness of the proposed method.

Discrete-Time Adaptive Control for Uncertain Scalar Multiagent Systems with Coupled Dynamics: A Lyapunov-Based Approach

Discrete-time architectures offer a distinct advantage over their continuous counterparts, as they can be seamlessly implemented on embedded hardware without the necessity for discretization processes. Yet, because of the difficulty of ensuring Lyapunov difference expressions, their designs, which are based on quadratic Lyapunov-based frameworks, are highly complex. As a result, various existing continuous-time results using adaptive control methods to deal with system uncertainties and coupled dynamics in agents of a multiagent system cannot be directly applied to the discrete-time context. Furthermore, compared to their continuous-time equivalent, discrete-time information exchange based on periodic time intervals is more practical in the control of multiagent systems. Motivated by these standpoints, in this paper, we first introduce a discrete-time adaptive control architecture designed for uncertain scalar multiagent systems without coupled dynamics as a preliminary result. We then introduce another discrete-time adaptive control approach for uncertain multiagent systems in the presence of coupled dynamics. Our approach incorporates observer dynamics to manage unmeasurable coupled dynamics, along with a user-assigned Laplacian matrix to induce cooperative behaviors among multiple agents. Our solution includes Lyapunov analysis with logarithmic and quadratic Lyapunov functions for guaranteeing asymptotic stability with both controllers. To demonstrate the effectiveness of the proposed control architectures, we provide an illustrative example. The illustrative numerical example shows that the standard discrete-time adaptive control in the absence of observer dynamics cannot guarantee the reference state vector tracking, while the proposed discrete-time adaptive control can ensure the tracking objective.

COOPERATIVE CONTROL OF TEAMS OF CATAMARAN SURFACE VESSELS WITH NOISY DYNAMICS*

This work investigates the cooperative control of teams of unmanned water surface vehicles (USVs) affected by maritime disturbances like water waves, currents, and wind encapsulated as stochastic noise. A distributed control strategy using local team communication is introduced to navigate the USVs through waypoints, maintaining desired formations and avoiding collisions. The control's bounded convergence is assessed using a Lyapunov-based approach adapted to stochastic systems. Numerical simulations are used to confirm the effectiveness of the control scheme, highlighting the balance between control parameters and noise intensity. Notably, the stochastic process is pivotal in replicating the noise observed in the USV kinematic variables while avoiding singularities caused by the collision avoidance forces.

A novel model reference adaptive control approach investigation for power electronic converter applications

This paper demonstrates the viability and effectiveness of a novel adaptive control approach applied to power electronic converters. A methodology based on the formulation of a Lyapunov-based approach is showcased to represent the operation of a new adaptive controller for the regulation of two power converter topologies (Buck and Boost). The models of the Buck and Boost converter topologies include the parasitic parameters that represent the non-ideal components. The basic idea of the control approach is to demonstrate adaptive stabilization for the proposed non-linear system. The most important design specification to stabilize the system is to track the reference trajectory in such a way that the error on the output variable converges asymptotically to zero. This adaptation mechanism is explicitly designed so that the asymptotic stability of the equilibrium condition is guaranteed according to the Lyapunov theorem and sensitivity theory. The details of the design algorithm are explained in the paper. The proposed control approach has been compared to other Lyapunov-based control techniques proposed in literature for the same non-ideal converters. The results show that the proposed controller provides better level of robustness and performance than the other well-established Lyapunov based controllers. To verify the effectiveness of the controller in real time, a test bench has been set up with prototypes of both converters and the controller has been implemented using the Arduino microcontroller and the control system driven through the Matlab/Simulink platform.

Interval Bipartite Synchronization of Multiple Neural Networks in Signed Graphs.

Interval bipartite consensus of multiagents described by signed graphs has received extensive concern recently, and the rooted cycles play a critical role in stabilization, while the structurally balanced graphs are essential to achieve bipartite consensus. However, the gauge transformation used in the linear system is no longer feasible in the nonlinear case. This article addresses interval bipartite synchronization of multiple neural networks (NNs) in a signed graph via a Lyapunov-based approach, extending the existing work to a more practical but complicated case. A general matrix M in signed graphs is introduced to construct the novel Lyapunov functions, and sufficient conditions are obtained. We find that the rooted cycles and the structurally balanced graphs are essential to stabilize and achieve bipartite synchronization. More importantly, we discover that the nonrooted cycles are crucial in reaching interval bipartite synchronization, not previously mentioned. Several examples are presented to illustrate interval bipartite synchronization of multiple NNs with signed graphs.

Avoidence Strategies for Fractional Order Systems with Caputo Derivative

Abstract A control strategy is derived for fractional-order dynamic systems with Caputo derivative to guarantee collision-free trajectories for two agents. To guarantee that one agent keeps the state of the system out of a given set regardless of the other agent’s actions a Lyapunov-based approach is adopted. As a special case showing that the given approach to choosing proposed strategy is constructive for a fractional-order system with the Caputo derivative, a linear system as an example is discussed. Obtained results extend to the fractional order case the avoidance problem Leitman’s and Skowronski’s approach.

On scaling robust feedback control and state estimation problems in power networks

Many mainstream robust control/estimation algorithms for power networks are designed using the Lyapunov theory as it provides performance guarantees for linear/nonlinear models of uncertain power networks but comes at the expense of scalability and sensitivity. In particular, Lyapunov-based approaches rely on forming semi-definite programs (SDPs) that are (i) not scalable and (ii) extremely sensitive to the choice of the bounding scalar that ensures the strict feasibility of the linear matrix inequalities (LMIs). This paper addresses these two issues by employing a celebrated non-Lyapunov approach (NLA) from the control theory literature. In lieu of linearized models of power grids, we focus on (the more representative) nonlinear differential algebraic equation (DAE) models and showcase the simplicity, scalability, and parameter-resiliency of NLA. For some power systems, the approach is nearly fifty times faster than solving SDPs via standard solvers with almost no impact on the performance. The case studies also demonstrate that NLA can be applied to more realistic scenarios in which (i) only partial state data is available and (ii) sparsity structures are imposed on the feedback gain. The paper also showcases that virtually no degradation in state estimation quality is experienced when applying NLA.

Position-attitude coupling guidance and control for asteroid landing with a flexible lander

Landing on an asteroid is a highly valuable endeavor accompanied by significant challenges, making it a promising area for further research. This paper aims to present a flexible lander specifically designed for asteroid landing missions while also studying the guidance and control techniques involved in its descent phase. Firstly, the paper briefly introduces the mission simulation model and asteroid environment from previous work. It then provides a detailed exposition on the guidance model which facilitates trajectory planning and the attitude control model used for managing the lander's attitude. The parametric trajectory is subsequently applied to obtain the position-attitude coupling trajectory that allows for the flexible lander's trajectory planning. The generating set search method is used to optimize the parametric trajectory under the appropriate constraints, ensuring high efficiency. In tracking the proposed trajectory, an open-loop control is applied for position tracking, while a closed-loop attitude controller is proposed for attitude control. An attitude control technique involving a combination of the nonsingular sliding mode control method with RBF to capture perturbations and unmodeled dynamics is adopted, and its global stability is proven using a Lyapunov-based approach. Monte Carlo simulation is conducted to test the performance of the proposed trajectory planning technique with results showing that real-time trajectory generation and refreshing are achieved. The feasibility and accuracy of the proposed guidance and control technique are further verified with another set of Monte Carlo simulation. Finally, the paper highlights one successful scenario including the descent and touching phases of asteroid landing with the flexible lander, illustrating its feasibility further.

A Novel Fast Fixed-Time Backstepping Control of DC Microgrids Feeding Constant Power Loads

Nonlinear behavior of constant power loads (CPLs) and their negative incremental impedance, which impose adverse effects on system damping and stability margins, necessitate developing proper strategies for efficient implementation framework of DC microgrid. In this paper, a fixed-time sliding mode disturbance observer (SMDO) is first addressed to provide an estimation of the instantaneous power flow moving along the uncertain CPLs with time-varying nature within a fixed time. It not only expedites the estimation rate but also improves the robustness against physical parameter variation. The fast fixed-time backstepping technique is then developed based on the estimated load power to control the duty cycle of the boost converter such that the entire power grid becomes stable and the desired voltage of the DC bus is tracked within a fixed time irrespective of the initial conditions. A rigorous Lyapunov-based approach is represented to guarantee the fixed-time stability of the proposed scheme. Finally, to validate the merits and implementation feasibility of the proposed methodology, the experimental realization is represented under various operating case studies.

A Lyapunov approach to stability of positive semigroups: an overview with illustrations

The stability analysis of possibly time varying positive semigroups on non-necessarily compact state spaces, including Neumann and Dirichlet boundary conditions is a notoriously difficult subject. These crucial questions arise in a variety of areas of applied mathematics, including nonlinear filtering, rare event analysis, branching processes, physics and molecular chemistry. This article presents an overview of some recent Lyapunov-based approaches, focusing principally on practical and powerful tools for designing Lyapunov functions. These techniques include semigroup comparisons as well as conjugacy principles on non-necessarily bounded manifolds with locally Lipschitz boundaries. All the Lyapunov methodologies discussed in the article are illustrated in a variety of situations, ranging from conventional Markov semigroups on general state spaces to more sophisticated conditional stochastic processes possibly restricted to some non-necessarily bounded domains, including locally Lipschitz and smooth hypersurface boundaries, Langevin diffusions as well as coupled harmonic oscillators.

Lyapunov-based sampled-data set stabilisation of boolean control networks with time delay and state constraint

Lyapunov-based approach to sampled-data set stabilisation of constrained delayed Boolean control networks (DBCNs) is investigated in this paper. The main mathematical tool is semi-tensor product (STP) of matrices. Since the sampling interval is selected from a finite set, the STP method is adopted to convert the dynamics of constrained DBCNs under nonuniform sampled-data control into a switched Boolean network (SBN). It is worth noting that the switches can only occur at the sampling instant. Using the techniques of Lyapunov function and average dwell time, several sufficient conditions are proposed for the global stability of SBN. Moreover, by virtue of reachable set approach, a procedure is established to design state feedback sampled-data stabilisers for constrained DBCNs. The obtained results are applied to the cell survival regulation of apoptosis networks.

Distributed Economic MPC for Dynamically Coupled Linear Systems: A Lyapunov-Based Approach

This article develops a distributed economic model predictive control (EMPC) method which is applied in a group of interconnected linear subsystems subject to unknown bounded disturbances. Multiple subsystems are coupled through the dynamics, and the control objective is to optimize some general performance criteria of the whole system which may take economic considerations into account. First, a two operation modes EMPC optimization problem is formulated, which incorporates the constraints derived from the Lyapunov technique. In the first mode, each subsystem focuses on the optimization of the economic performance while maintaining the state in a certain region. In the second mode, the system states are steered to a neighborhood of a steady state by making use of the Lyapunov-based constraints. Furthermore, a consensus alternating direction method of multipliers (ADMM) is adopted to solve the model predictive control optimization problems with a coupled predicted model constraint in a distributed way. By introducing consensus constraints, the resulting local optimization problem does not depend on real-time optimal solutions from neighboring subsystems and allows subsystems to solve it in parallel. Moreover, the closed-loop system is ensured to be input-to-state stable (ISS) with respect to the disturbances. To demonstrate the effectiveness of the algorithm, we conduct numerical simulations on a thermal power interconnected system.

Stochastic time-varying extremum seeking and its applications

We investigate a stochastic time-varying extremum seeking method based on new stochastic averaging theorems for time-varying systems and its application to distributed source seeking with switching topology. Firstly, we present sufficient conditions for the approximation of the time-varying averaging system to the time-varying original system with stochastic perturbations and obtain the solution property of the original system under the stability of invariant sets of the average system. Then, by using our developed stochastic averaging theory, we prove that the proposed stochastic time-varying extremum seeking algorithm converges to the time-varying optimal solution. Furthermore, based on the method of stochastic time-varying extremum seeking, we propose a distributed stochastic source seeking algorithm which navigates multiple vehicles to seek the source of aggregated multiple signal fields under a switching topology. We can prove the exponential convergence of such a distributed algorithm by our stochastic averaging theorems and a Lyapunov-based approach. Finally, we present detailed simulation results to illustrate the effectiveness of our method.

LMI-based [formula omitted] boundary practical consensus control for nonlinear multi-agent systems with actuator saturation

This paper mainly addresses the practical consensus problem of nonlinear multi-agent systems modeled by reaction–diffusion equations subject to the bounded external disturbances. Different from the existing consensus control methods associated with spatiotemporal dynamics, the proposed H∞ Neumann boundary controller based on distributed measurement data can guarantee the optimal disturbance attenuation performance under the actuator saturation. Initially, a consensus spatiotemporal error model is constructed by introducing the Kronecker product and equivalent directed graph. Subsequently, a linear matrix inequalities (LMIs)-based sufficient condition is derived by combining the improved Lyapunov-based approach and H∞ norm. Then, an optimization problem is proposed by applying invariant set, such that the consensus errors can converge to a minimized bounded region in the presence of actuator saturation. Finally, comparison simulations on the synchronization of FitzHugh–Nagumo (FHN) model are given to demonstrate the effectiveness of proposed methodology.

Adaptive Neural-Network-Based Nonsingular Fast Terminal Sliding Mode Control for a Quadrotor with Dynamic Uncertainty

This paper proposes an adaptive neural-network-based nonsingular fast terminal sliding mode (NN-NFTSMC) approach to address the trajectory tracking control problem of a quadrotor in the presence of model uncertainties and external disturbances. First, the dynamic model of the quadrotor with uncertainty is derived. Then, a control scheme using nonsingular fast terminal sliding mode control (NFTSMC) is proposed to guarantee the finite-time convergence of the quadrotor to its desired trajectory. NFTSMC is firstly formulated for the case that the upper bound of the lumped uncertainty is known in advance. Under this framework, a disturbance observer by using the hyperbolic tangent nonlinear tracking differentiator (TANH-NTD) is designed to estimate the external interference, and a neural network (NN) approximator is used to develop an online estimate of the model uncertainty. Subsequently, adaptive algorithms are designed to compensate the approximation error and update the NN weight matrix. An NN-NFTSMC algorithm is formulated to provide the system with robustness to the model uncertainty and external disturbance. Moreover, Lyapunov-based approach is employed to prove the global stability of the closed-loop system and the finite-time convergence of the trajectory tracking errors. The results of a comparative simulation study with other recent methods illustrate the proposed control method reduces the chattering effectively and has remarkable performance.