Control Lyapunov Research Articles

Advanced Sliding Mode Design for Optimal Automatic Generation Control in Multi-Area Multi-Source Power System Considering HVDC Link

The multi-area multi-source power system (MAMSPS), which uses a variety of power sources including gas, hydro, thermal, and renewable energy, has recently been implemented to balance the growing demand for electricity and the overall capacity for power generation. In this paper, an integral sliding mode control with a single-phase technique (ISMCSP) is applied to two areas, with each area including gas–wind–thermal power systems with HVDC system. Firstly, a two-area gas–wind–thermal power system with HVDC (TAGWTPSH) is the first model in this scheme to consider the parameter uncertainties of a MAMSPS. Secondly, sliding mode design law with a single-phase technique is introduced to alleviate chattering and oscillation problems. Then, power system stability is ensured by the Lyapunov control theory based on the new LMIs technique. Thirdly, the ISMCSP’s effectiveness in a MAMSPS is also assessed under random load patterns and parameter variations regarding settling time and over-/undershoot. The ISMCSP was created to alter the fundamental sliding mode control, and therefore the suggested approach performs better than recently published approaches. This is demonstrated by the frequency overshoot deviation value in frequency deviations: 0.7 × 10−3 to 2.8 × 10−3 for the TAGWTPSH with the suggested ISMCSP. In the last case, for random changes in load from −0.4 to +0.5 p. u, the proposed ISMCSP method still stabilizes the frequency of the areas meeting the standard requirements for AGC.

Feedback-based quantum algorithm inspired by counterdiabatic driving

In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to iteratively construct quantum circuits. Here, we propose a substantial enhancement by implementing a protocol that uses ideas from quantum Lyapunov control and the counterdiabatic driving protocol, a key concept from quantum adiabaticity. Our approach introduces an additional control field inspired by counterdiabatic driving. We apply our algorithm to prepare ground states in one-dimensional quantum Ising spin chains. Comprehensive simulations demonstrate a remarkable acceleration in population transfer to low-energy states within a significantly reduced time frame compared to conventional feedback-based quantum algorithms. This acceleration translates to a reduced quantum circuit depth, a critical metric for potential quantum computer implementation. We validate our algorithm on the IBM cloud computer, highlighting its efficacy in expediting quantum computations for many-body systems and combinatorial optimization problems. Published by the American Physical Society 2024

Stable Levitation of Single-point Levitation Systems for Maglev Trains by Improved Cascade Control

The stable levitation of single-point levitation systems for electromagnetic suspension (EMS) maglev trains, which belongs to the control task of nonlinear and unstable systems, is investigated in this paper. Considering the simplicity and convenience of the control application, we dedicate ourselves to combining and applying common control methods to achieve the stable levitation rather than designing complex controls or using advanced control methods. For this goal, the single-point levitation system is divided into an electromagnetic system and a motion system first. On this basis, we design the Lyapunov controller and sliding mode controller as Controller I, while another Lyapunov controller and the standard Proportional Integral Derivative (PID) controller are designed as Controller II, which are used to control the electromagnetic system and motion system respectively and constitute the improved cascade control to achieve the stable levitation. Furthermore, the switching controller consisting of the standard PID controller and the designed Lyapunov controller is used as Controller II for the improvement of both stability and robustness.

Enhanced Visual SLAM for Collision-Free Driving with Lightweight Autonomous Cars.

The paper presents a vision-based obstacle avoidance strategy for lightweight self-driving cars that can be run on a CPU-only device using a single RGB-D camera. The method consists of two steps: visual perception and path planning. The visual perception part uses ORBSLAM3 enhanced with optical flow to estimate the car's poses and extract rich texture information from the scene. In the path planning phase, the proposed method employs a method combining a control Lyapunov function and control barrier function in the form of a quadratic program (CLF-CBF-QP) together with an obstacle shape reconstruction process (SRP) to plan safe and stable trajectories. To validate the performance and robustness of the proposed method, simulation experiments were conducted with a car in various complex indoor environments using the Gazebo simulation environment. The proposed method can effectively avoid obstacles in the scenes. The proposed algorithm outperforms benchmark algorithms in achieving more stable and shorter trajectories across multiple simulated scenes.

Feedback-based quantum algorithms for ground state preparation

The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states can have broad impacts. Variational quantum algorithms are one class of ground state algorithms that has received significant attention in recent years. These algorithms utilize a hybrid quantum-classical computing framework to prepare ground states on quantum computers. However, this requires solving a classical optimization problem that can become prohibitively expensive in high dimensions. Here, we develop formulations of feedback-based quantum algorithms for ground state preparation that can be used to address this challenge for two broad classes of Hamiltonians: Fermi-Hubbard Hamiltonians, and molecular Hamiltonians represented in second quantization. Feedback-based quantum algorithms are optimization-free; in place of classical optimization, quantum circuit parameters are set according to a deterministic feedback law derived from quantum Lyapunov control principles. This feedback law guarantees a monotonic improvement in solution quality with respect to the depth of the quantum circuit. A variety of numerical illustrations are provided that analyze the convergence and robustness of feedback-based quantum algorithms for these problem classes. Published by the American Physical Society 2024

Lyapunov control strategy for low-frequency offshore wind power based on hexagonal converters

Lyapunov control strategy for low-frequency offshore wind power based on hexagonal converters

Lyapunov-based prescribed-time stabilisation control of quantum systems

This paper addresses the prescribed-time stabilisation control problem for quantum systems characterised by a single control input. A control law based on the relative state distance is formulated. Through the application of prescribed-time Lyapunov control techniques, the stabilisation of the quantum system to one of the eigenstates of the internal Hamiltonian within a prescribed-time is established. Notably, in contrast to existing quantum system control methods, our proposed approach ensures stabilisation within a specified time, allowing for the flexible selection of the settling-time upper bound according to preference, independent of the initial conditions.

Reinforced Lyapunov controllers for low-thrust lunar transfers

Future missions to the Moon and beyond are likely to involve low-thrust propulsion technologies due to their propellant efficiency. However, these still present a difficult trajectory design problem, owing to the near continuous thrust, lack of control authority and chaotic dynamics. Lyapunov control laws can generate sub-optimal trajectories for such missions with minimal computational cost and are suitable for feasibility studies and as initial guesses for optimisation methods. In this work a Reinforced Lyapunov Controller is used to design optimal low-thrust transfers from geostationary transfer orbit towards lunar polar orbit. Within the reinforcement learning (RL) framework, a dual-actor network setup is used, one in each of the Earth- and Moon-centred inertial frames respectively. A key contribution of this paper is the demonstration of a forwards propagated trajectory, removing the need to define a patch point a priori. This is enabled by an adaptive patch distance and extensive initial geometry exploration during the RL training. Results for both time- and fuel-optimal transfers are presented, along with a Monte Carlo analysis of the robustness to disturbances for such transfers. Phasing is introduced where necessary to aid rendezvous with the Moon. The results demonstrate the potential for such techniques to provide a basis for the design and guidance of low-thrust lunar transfers.

Closed-loop designed open-loop control of quantum systems: An error analysis

Quantum Lyapunov control, an important class of quantum control methods, aims at generating converging dynamics guided by Lyapunov-based theoretical tools. However, unlike the case of classical systems, disturbance caused by quantum measurement hinders direct and exact realization of the theoretical feedback dynamics designed with Lyapunov theory. Regarding this issue, the idea of closed-loop designed open-loop control has been mentioned in literature, which means to design the closed-loop dynamics theoretically, simulate the closed-loop system, generate control pulses based on simulation and apply them to the real plant in an open-loop fashion. Based on bilinear quantum control model, we analyze in this article the error, i.e., difference between the theoretical and real systems’ time-evolved states, incurred by the procedures of closed-loop designed open-loop control. It is proved that the error at an arbitrary time converges to a unitary transformation of initialization error as the number of simulation grids between 0 and that time tends to infinity. Moreover, it is found that once the simulation accuracy reaches a certain level, adopting more accurate (thus possibly more expensive) numerical simulation methods does not efficiently improve convergence. We also present an upper bound on the error norm and an example to illustrate our results.

Proposing a novel nonlinear integrated control technique for an electric power steering system to improve automotive dynamic stability

This article proposes a new control solution for an electric power steering (EPS) system to ensure the stability of car's dynamic behaviours. This work provides two new contributions which differ from previously existing publications. Firstly, a novel control method for the steering system is designed in this article based on a combination of proportional-integral-derivative (PID) and backstepping control techniques. The input to the backstepping algorithm is the output of the PID controller, whose parameters are tuned by a complex fuzzy algorithm with two inputs. Secondly, values of road reaction torque and other dynamic effects are calculated using a complex automotive dynamics model based on a nonlinear motion model and a spatial oscillation model. The stability of the control system is evaluated through the Lyapunov control function and the error between the output signals, while the dynamic stability is evaluated through the changes in car's dynamic behaviours. According to the simulation results, output values always closely follow ideal values with negligible errors if and only when the steering system is controlled by the proposed algorithm. In some conditions, the steering motor angle error achieved by the proposed controller does not exceed 0.022 rad, much lower than the fault scenario. In addition, the vehicle's roll angle and motion trajectory always follow the desired value with minimal errors. In conclusion, if the EPS system is controlled by the new control technique shown in this article, car dynamic stability will be guaranteed under all investigated conditions.

Parameter-dependent conditions for H ∞ stabilisation of polynomial parameter-varying system with delay

This paper considers the problems of achieving exponential stability and H ∞ stabilisation for polynomial parameter-varying system with time-varying delay. Unlike some existing linear parameter-varying results that treat system parameters as time invariant factors, this paper makes full use of the nonlinearity and time-varying characteristics of system through introducing a novel delay-and-parameter-dependent Lyapunov function. The main conclusions are discussed in three cases (system without input, system with disturbance input, system with disturbance input and control input). And the H ∞ stabilisation problem is solved by constructing a controller which is inserted with system parameters and their derivatives. The structures of Lyapunov function and controller lead to that the derived criteria for exponential stabilisation are expressed by state-and-parameter-dependent linear matrix inequalities, which are efficiently solved by sum-of-squares program. The effectiveness and superiority are verified through two numerical examples.

Autonomous multiple‐trolley collection system with nonholonomic robots: Design, control, and implementation

AbstractThe task of collecting and transporting luggage trolleys in airports, characterized by its complexity within dynamic public environments, presents both an ongoing challenge and a promising opportunity for automated service robots. Previous research has primarily developed on universal platforms with robot arms or focused on handling a single trolley, creating a gap in providing cost‐effective and efficient solutions for practical scenarios. In this paper, we propose a low‐cost mobile manipulation robot incorporated with an autonomy framework for the collection and transportation of multiple trolleys that can significantly enhance operational efficiency. The method involves a novel design of the mechanical system and a vision‐based control strategy. We design a lightweight manipulator and the docking mechanism, optimized for the sequential stacking and transportation of trolleys. On the basis of the Control Lyapunov Function and Control Barrier Function, we propose a vision‐based controller with online Quadratic Programming, which improves the docking accuracy. The practical application of our system is demonstrated in real‐world scenarios, where it successfully executes the multiple‐trolley collection task.

A complete control structure based backstepping controller design for stacked multi-cell multi-level SPWM VSC STATCOM

Currently, the installation of FACTS (Flexible Alternative Current Transmission System) devices such as synchronous static compensators (STATCOM) represent a very useful solution to improve both network stability and power quality. The effectiveness of these devices is principally determined by the used static converter (topology and the switching strategy) and the adopted dynamic law characterizing the controller structure. This paper illustrates the stacked five-level, multi-cell STATCOM compensator performances governed by a Backstepping controller technique compared to the use of the conventional PI controller (SPWM) for controlling voltage variation (sags or overshoots) affecting a given network point. The interest in using stacked multi-cell converters topology is to increase the number of voltage levels in order to ensure a good quality voltage waveform at the specified connection point. Therefore, the proposed backstepping controller based on the use of Lyapunov control functions presents a simplified structure and a reduced computational load compared to many others advanced control approaches. The proposed system is verified by running a simulation analysis with Matlab Simulink environment. The simulation results obtained show that the proposed STATCOM configuration ensures good voltage regulation at the common connection point (PCC), correction of the unity power factor on the grid side and good response time via reactive power compensation under variable load conditions.

Synchronization analysis of fuzzy inertial neural networks with time‐varying delays via non‐reduced order method

SummaryIn this article, the asymptotic synchronization of a class of fuzzy inertial neural networks (FINNs) with time‐varying delays is investigated. First, the direct analysis approach is applied to replace the accustomed variable transformation and the reduced‐order method for addressing the inertial term. Second, a suitable Lyapunov function and control scheme are devised to obtain several new sufficient conditions to guarantee the asymptotic synchronization of the class of FINNs with time‐varying delays. It turns out that the obtained criteria are simpler and more effective. Meanwhile, some numerical examples demonstrate the effectiveness of the proposed strategies and verify the theoretical results.

Global exponential synchronization of BAM memristive neural networks with mixed delays and reaction–diffusion terms

Based on m-norm, this paper investigates global exponential synchronization (GES) for BAM memristive neural networks (BAMMNNs) with mixed delays and reaction–diffusion (RD) terms. Different from the existing literatures, this paper discusses the GES of the NNs based on a new integral inequality with infinite distributed delay. This method is based on inequality technique and comparison principle, which makes the form of Lyapunov function and controller more simple. Next, by introducing two different control strategies and the concept of driven response, two sufficient conditions are got to ensure GES of the proposed system. It is noteworthy that the results obtained by algebraic inequality are extension of the previous conclusions. Finally, two instances verify the correctness of the conclusions.

Trajectory Tracking Nonlinear Hybrid Control of Automated Guided Vehicles

Automated guided vehicles (AGVs), so necessary in industrial environments, require precise control of trajectory tracking to make accurate stops at logistics stations, such as loading stations, or to pick up or drop off trolleys, pallets, or racks. This paper proposes a hybrid control architecture for trajectory tracking of a hybrid tricycle-differential AGV. The control strategy combines conventional proportional integral derivative (PID) control with advanced nonlinear Lyapunov control (LPC). The LPC is used for trajectory tracking while the PID is used for speed control of the robot. The stability of the controller is demonstrated for any differentiable trajectory. When a PID optimized with genetic algorithms is compared with the proposed controller for several trajectories, the LPC outperforms it in all cases.

Rotary inverted pendulum control using neuro-adaptive robust generalized dynamic inversion

The objective of this research is to design a robust control system for trajectory tracking of the under-actuated Rotary Inverted Pendulum (RIP). The focus is on achieving semi-global asymptotic stability in the absence of knowledge about the RIP geometric and inertia parameters. The control design commences by formulating differential servo constraint dynamics (VCD) that encapsulates the control objectives for the RIP. The baseline generalized dynamic inversion (GDI) control law is derived by inverting the VCD for the control voltage input using the Moore–Penrose generalized inverse. To enhance robustness against modeling uncertainties and exogenous disturbances, a sliding mode control (SMC) element is integrated within the GDI control system, resulting in the robust GDI (RGDI) control system. Furthermore, an adaptive estimator that is based on Radial Basis Function Neural Networks (RBF-NN) is adopted to eliminate the dependency of the RGDI control system on the RIP mathematical model. The weighting matrices of the RBF-NN are updated with the aid of a Lyapunov control function. The proposed control system offers robust solution and guarantees semi-global asymptotic stability to the unstable equilibria of the RIP dynamics in the absence of a mathematical model. The proposed control system’s performance is evaluated through computer simulations and experimental tests on a real RIP system. Comparative analyses with traditional SMC and linear quadratic control methodologies are conducted to show the effectiveness of the proposed approach.

Stability Guaranteed Model Predictive Control With Adaptive Lyapunov Constraint

This paper aims to design a stabilized Adaptive Model Predictive Control (MPC) for nonlinear continuous systems with unknown dynamics at the start time. The proposed method is based on the Lyapunov MPC (LMPC) where the derivative of the Lyapunov function of the closed-loop system is limited to be less than that under an auxiliary Lyapunov controller. Different from the existing LMPC methods, this paper provides an online constraint updating strategy, which gradually reduces the conservation of the constraint. Specifically, the piece-wise linear (PWL) model updated by the Set-Membership (SM) identification method is adopted in the constraint and the auxiliary controller design, which can result in a non-increasing boundary of the model error. Then, a sufficient condition that guarantees the stabilization of the closed-loop system is deduced, which takes the effect of sample-and-hold implementation and the error boundary of the PWL model into account. By this condition, an optimization problem to update the Lyapunov controller for relaxing the constraints of MPC is proposed. We prove that, by the proposed method, the states will eventually converge to a small region around the equilibrium, both this small region and the conservatism of MPC decrease with the increasing of the accuracy of the PWL model. The application of the proposed method to a chemical process demonstrates the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The control problem of nonlinear continuous systems with unknown dynamics has attracted the attention of researchers. This article develops an Adaptive MPC for this kind of system, which updates the boundary of uncertainties according to the measurement, and updates the constraints of MPC according to the updated uncertainty boundary. It provides a guaranteed stabilization and continuously relaxed constraint design for MPC where machine learning-based models are employed to predict the future trajectory. In the process of implementation, the method solves two optimization problems: one is to get the parameters of constraints which is based on the PWL model, and the other is used to optimize the future trajectory with the updated constraints. To proceed, the initial boundary of the uncertainty should be given at the initial instant, the initialization of PWL models and constraints can be configured based on it. The proposed method can be used for tracking control of chemical processes, power systems, robots, etc., where the accurate dynamics are not provided in advance and an improved performance is required.

Actor–Critic Physics-Informed Neural Lyapunov Control

Actor–Critic Physics-Informed Neural Lyapunov Control

Implicit Lyapunov control of multi-control Hamiltonian systems in degenerate cases

In closed quantum systems, if controlled systems are not strongly regular or there exists at least one eigenstate that is directly uncoupled to the target state, then such systems control will become degenerate cases. This paper proposes a quantum control method designed by an implicit Lyapunov function to transfer states of the quantum systems in these two degenerate cases, especially the method proposed is suitable for multi-control Hamiltonian systems. The state distance is selected as the Lyapunov function in this paper. Numerical simulation experiments on a 4-level system are done, and the experiment results indicate the effectiveness of the implicit Lyapunov control method proposed for degenerate cases and multi-control Hamiltonians.