Lyapunov Function-based Control Research Articles

Adaptive tracking control-based Nussbaum gain for a class of multi-input and multi-output nonlinear systems with time-varying state constraints

This article studies an adaptive backstepping barrier Lyapunov function-based control scheme for a class of multi-input and multi-output nonlinear systems in the presence of time-varying asymmetric full-state constraints and external disturbances. Simultaneously, a prominent feature of these systems is the unknown time-varying control direction. To stabilize such systems, Nussbaum gain technique is constructively framed to overcome the unknown control direction problem. To prevent that the constraints are overstepped, the time-varying asymmetric barrier Lyapunov functions are employed in each step of the backstepping design. The design involves an adaptive-based online approximator to cope with unknown dynamics of the system. A simulation example on aircraft skin inspection robot with three-dimensional trajectory is given to show the effectiveness of the proposed control scheme.

Composite Switched Lyapunov Function-Based Control of DC–DC Converters for Renewable Energy Applications

Renewable energy sources play a pivotal role in the pursuit of sustainable and eco-friendly power solutions. While offering environmental benefits, they present inherent challenges. Photovoltaic systems rely on surrounding conditions, wind systems contend with variable wind speeds, and fuel cells are both costly and inefficient. Furthermore, the energy injected by renewable energy sources (RES) exhibits unpredictable behavior. To tackle these problems, researchers employ diverse power electronic devices and converters like inverters, power quality filters, and DC–DC choppers. Among these, DC–DC converters stand out for effectively regulating DC voltage and enhancing the efficiency of RESs. The meticulous selection of a suitable DC–DC converter, coupled with the integration of an efficient control technique, significantly influences overall power system performance. This paper introduces a novel approach to the design of switching controllers for DC–DC converters, specifically tailored for application in renewable energy systems. The proposed controller leverages the power of composite switched Lyapunov functions (CSLF) to enhance the efficiency and performance of DC–DC converters, addressing the unique challenges posed by renewable energy sources. Through comprehensive analysis and simulation, this study demonstrates the efficacy of the controller in optimizing power transfer, improving stability, and ensuring reliable operation in diverse renewable energy environments. Moreover, the small-scale DC–DC converter experiment’s findings are presented to confirm and validate the proposed scheme’s practical applicability.

Reinforcement learning control for a flapping-wing micro aerial vehicle with output constraint

Purpose This paper aims to study the application of reinforcement learning (RL) in the control of an output-constrained flapping-wing micro aerial vehicle (FWMAV) with system uncertainty. Design/methodology/approach A six-degrees-of-freedom hummingbird model is used without consideration of the inertial effects of the wings. A RL algorithm based on actor–critic framework is applied, which consists of an actor network with unknown policy gradient and a critic network with unknown value function. Considering the good performance of neural network (NN) in fitting nonlinearity and its optimum characteristics, an actor–critic NN optimization algorithm is designed, in which the actor and critic NNs are used to generate a policy and approximate the cost functions, respectively. In addition, to ensure the safe and stable flight of the FWMAV, a barrier Lyapunov function is used to make the flight states constrained in predefined regions. Based on the Lyapunov stability theory, the stability of the system is analyzed, and finally, the feasibility of RL in the control of a FWMAV is verified through simulation. Findings The proposed RL control scheme works well in ensuring the trajectory tracking of the FWMAV in the presence of output constraint and system uncertainty. Originality/value A novel RL algorithm based on actor–critic framework is applied to the control of a FWMAV with system uncertainty. For the stable and safe flight of the FWMAV, the output constraint problem is considered and solved by barrier Lyapunov function-based control.

Bounded distance control for Multi-UAV formation safety and preservation in target-tracking applications

The notion of safety in multi-agent systems assumes great significance in many emerging collaborative multi-robot applications. In this paper, we present a multi-UAV collaborative target-tracking application by defining bounded inter-UAV distances in the formation in order to ensure safe operation. In doing so, we address the problem of prioritizing specific objectives over others in a multi-objective control framework. We propose a barrier Lyapunov function-based distributed control law to enforce the bounds on the distances and assess its Lyapunov stability using a kinematic model. The theoretical analysis is supported by numerical results, which account for measurement noise and moving targets. Straight-line and circular motion of the target are considered, and results for quadratic Lyapunov function-based control, often used in multi-agent multi-objective problems, are also presented. A comparison of the two control approaches elucidates the advantages of our proposed safe-control in bounding the inter-agent distances in a formation. A concluding evaluation using Robot Operating System simulations illustrates the practical applicability of the proposed control to a pair of multi-rotors visually estimating and maintaining their mutual separation within specified bounds, as they track a moving target.

A New Neural Network Based Sliding Mode Adaptive Controller for Tracking Control of Robot Manipulator

In this paper a New RBF Neural Network based Sliding Mode Adaptive Controller (NNNSMAC) for Robot Manipulator trajectory tracking in the presence of uncertainties and disturbances is introduced. The research offers a learning with minimal parameter (LMP) technique for robotic manipulator trajectory tracking. The technique decreases the online adaptive parameters number in the RBF Neural Network to only one, lowering computational costs and boosting real-time performance. The RBFNN analyses the system's hidden non-linearities, and its weight value parameters are updated online using adaptive laws to control the nonlinear system's output to track a specific trajectory. The RBF model is used to create a Lyapunov function-based adaptive control law. The effectiveness of the designed NNNSMAC is demonstrated by simulation results of trajectory tracking control of a 2 dof Robotic Manipulator. The chattering effect has been significantly reduced.

Sliding Mode with Adaptive Control of Robot Manipulator Trajectory Tracking using Neural Network Approximation

This paper briefly discusses about the Robust Controller based on Adaptive Sliding Mode Technique with RBF Neural Network (ASMCNN) for Robotic Manipulator tracking control in presence of uncertainities and disturbances. The aim is to design an effective trajectory tracking controller without any modelling information. The ASMCNN is designed to have robust trajectory tracking of Robot Manipulator, which combines Neural Network Estimation with Adaptive Sliding Mode Control. The RBF model is utilised to construct a Lyapunov function-based adaptive control approach. Simulation of the tracking control of a 2dof Robotic Manipulator in the presence of unpredictability and external disruption demonstrates the usefulness of the planned ASMCNN.

Command Filtering and Barrier Lyapunov Function-Based Adaptive Control for PMSMs with Core Losses and All-State Restrictions

With the troubles of core losses and all-state confined to certain limitations which are the innate traits of permanent magnet synchronous motors (PMSMs), this article develops a command filtered adaptive backstepping approach to follow the track of PMSM’s desired rotor position. To begin with, the RBF neural network technique is utilized to get close to the uncharted nonlinear terms which existed in PMSM’s mathematical model. Meanwhile, an advanced adaptive command filter control methodology is constructed to avoid the computing explosion during the process of backstepping design. Furthermore, to make sure that all the state variables are confined into certain ranges, we employed the barrier Lyapunov function (BLF) at every step of the controllers construction. In addition, an error compensating mechanism is proposed to neutralize filtering errors and only one adaptive law is required. At last, simulation results bear out the superiority of the aforementioned control scheme.

Command filtered robust control of nonlinear systems with full-state time-varying constraints and disturbances rejection

For the barrier Lyapunov function-based control of full-state time-varying constrained systems via the traditional backstepping technology, due to repeated differentiations of virtual control functions involving time-varying barriers, the adverse effects of “explosion of complexity” caused by the backstepping iteration are more serious, which even makes it impossible to implement for high-order systems. In order to eliminate this negative influence, we take advantage of the command filtered backstepping approach which introduces a command filter to approximate the constructed virtual control law in each procedure of the backstepping design. More importantly, the approximate errors arising from the introduced filters will be removed by constructing a series of compensating signals. Meanwhile, some relatively conservative assumptions will be released compared with existing control strategies. Furthermore, largely unknown external disturbances that may exist in the system will be estimated in real-time via high-gain disturbance observers and then compensated feedforwardly in designing the controller. Specially, the scheme of the resulting control algorithm is simple and online computation time is saved. Finally, the stability of the whole closed-loop system and the control performance is strictly certificated, respectively.

Removing feasibility conditions on practical preassigned finite-time tracking for state-constrained high-order nonlinear systems

This paper investigates practical preassigned finite-time tracking control for state-constrained high-order nonlinear systems. Fuzzy systems are utilised to remove frequently used growth assumptions on completely unknown nonlinearities. By integrating nonlinear transformed functions with a key coordinate transformation into control design, full-state constraints can be handled without imposing feasibility conditions in traditional barrier Lyapunov function-based control methods. It is rigorously proved that the states of fuzzy systems remain within a specific compact set, on which fuzzy approximation is valid. Besides, asymmetric full-state constraints aren't violated for all time, and the tracking error converges to the prescribed small region around zero in a preassigned finite-time. Two simulation examples show the effectiveness and advantages of this control scheme.

Multiple Lyapunov function-based longitudinal maneuver control of air-breathing hypersonic vehicles

For the longitudinal maneuver mission of air-breathing hypersonic vehicles, this paper develops an adaptive control strategy based on multiple Lyapunov function method. A switched model is applied to describe vehicle dynamics within the admissible range of velocity and altitude, as well as to make a proper tradeoff between modelling accuracy and design complexity. In comparison to the existing common Lyapunov function-based control, the proposed control is less conservative and requires relatively small input by directly identifying uncertain parameters in the switched model. Moreover, the tedious analytical differentiations in back-stepping are bypassed by the integration of dynamic surface control and online differentiator technique. A simulation study is provided to verify the proposed control.

On Output Feedback Trajectory Tracking Control of an Omni-Mobile Robot

Abstract This paper presents the solution to the trajectory tracking control problem of an omnidirectional mobile robot without velocity measurements. Lyapunov function-based control design strategy is developed via an application of a quasi-invariance principle for non-autonomous systems of differential equations. The global uniform asymptotic stability property of the set of all equilibrium points of the closed-loop system has been proved by constructing a saturated position output feedback controller.

Constrained control Lyapunov function-based control of nonlinear systems

In this paper, we present an algorithm to address the problem of guaranteed stabilization of nonlinear systems from the largest set of initial conditions from where stabilization is possible, the so-called null controllable region (NCR), while also handling state constraints and partial unboundedness of the NCR. The controller uses the geometry of the NCR to inform a constrained control Lyapunov function which in turn provides feasibility and stability guarantees. The NCR is produced from a novel iterative growth algorithm that exploits a certain invariance property. The new controller implementation is illustrated using a chemical reactor system and compared to a conventional nonlinear model predictive control (MPC) implementation.

Comparative study on Lyapunov‐function‐based control schemes for single‐phase grid‐connected voltage‐source inverter with LCL filter

This study deals with various Lyapunov-function-based control (LFBC) schemes proposed for a single-phase grid-connected voltage source inverter with LCL filter. Use of LCL filter causes resonance which may adversely affect the controller's stability. The conventional (CLFBC) scheme employing the inverter-side current guarantees the asymptotic global stability, but it is not able to damp the resonance. As a remedy to the poor resonance damping, the adoption of grid-current and capacitor-voltage feedback schemes have been investigated. Although the former offers a globally asymptotically stable system, it cannot improve the poor resonance damping. However, the CLFBC with capacitor-voltage feedback scheme not only preserves the global stability, but also improves the resonance damping substantially. The analytical equations of the closed-loop poles for each control scheme are provided which can be used to compute the pole positions and the damping ratio needed for a desired response. Furthermore, the effect of changing controller gains on the loci of closed-loop poles is also studied. Simulation and experimental results obtained from 3.3 kW system demonstrate that the CLFBC with capacitor-voltage feedback scheme not only offers a global stability, but also leads to good quality sinusoidal grid current with reasonable total harmonic distortion and fast dynamic response.

Sliding-mode and Lyapunov function-based control for battery/supercapacitor hybrid energy storage system used in electric vehicles

In this paper, the control strategy of a fully-active hybrid energy storage system, which uses two bi-directional DC/DC converters to decouple supercapacitor and battery pack from the DC bus, is proposed based on a 5th-order averaged model. Three control objectives, the battery and supercapacitor currents as well as the DC bus voltage, are regulated by using the two DC/DC converters. A Lyapunov-function-based controller is proposed to regulate the DC bus voltage to its reference value. In addition, a sliding-mode controller is designed to control the battery and supercapacitor currents to their reference values. The battery current reference is generated by the energy management strategy, while the supercapacitor current reference is generated by the Lyapunov controller to ensure DC bus voltage regulation. Simulation and experimental results show that the proposed control method has satisfactory performance, including robust tracking and a smooth transition when the load power varies in the large range.

Lyapunov Function and Sliding Mode Control Approach for the Solar-PV Grid Interface System

This paper deals with control of a solar-photovoltaic (PV) power-generating system interfaced with the grid. A sliding mode control approach is used for achieving maximum power tracking control of a solar-PV array. The Lyapunov function-based control approach is designed and modeled for the dc–ac inverter to serve the functions of an active power injection to the grid, balanced grid currents at unity power factor and load currents harmonics compensation. The proposed approaches eliminate the need of adjustment of system parameters under changing loads and generation scenario. The effectiveness of the proposed control strategies is established using its stability analyses. The performance of the solar-PV power-generating system with the proposed control algorithms is demonstrated using simulation and experimental studies under various operating conditions.

H ∞ output-feedback LPV control for systems with input saturation

This paper investigates the problem of designing a dynamic H∞ output-feedback controller under an L∞ performance representing componentwise input constraints. In order to derive a less conservative stabilization condition therein, this paper introduces a Lyapunov function-based polytopic control law and proposes a method capable of applying the information on interpolation parameters appearing in the procedure of representing saturation nonlinearity as convex polytope. Through this paper, the resultant H∞/L∞ problem is efficiently solved based on the set invariance condition formulated in terms of linear matrix inequalities (LMIs).

Lyapunov-based bilateral teleoperation for surgical robotic forceps system with time varying delay

This paper addresses a new approach of bilateral control for a class of teleoperation systems with time-varying delay and its applications to bilateral teleoperation of robotic surgical device for minimally invasive surgery (MIS). A Lyapunov function-based bilateral control law for one-DOF teleoperation system that is capable of motion scaling in both position and force tracking is proposed so as to guarantee stability of the teleoperation system in the presence of time-varying delay. The proposed bilateral control law is adopted in vertical direction and horizontal direction for bending direction of the multi-DOF robotic forceps, respectively. Then, together with change of coordinates, the proposed bilateral control scheme is extended so that it may become applicable to bilateral control of omnidirectional bending of the multi-DOF robotic forceps manipulator incorporating a new screw-drive mechanism termed double-screw-drive mechanism. Thus, a scalable surgical device for MIS that can provide force feedback to surgeon is presented in this paper. In order to verify the effectiveness of the proposed bilateral control scheme, experimental works were carried out for the developed robotic forceps teleoperation test-bed for MIS.

CLF-Based Control Design for Unknown Multiinput Nonlinear Systems With Good Transient Performance

This technical note tackles the problem of constructing state-feedback stabilizers that guarantee good transient closed-loop performance when applied to general unknown nonlinear multiinput state-feedback stabilizable systems. An adaptive Control Lyapunov Function-based control scheme is proposed in order to address this problem. Mathematical analysis establishes that the proposed control scheme guarantees good closed-loop transient performance outside the regions where the system is uncontrollable, provided the controlled system admits a controllability-like property.

Globally Stable Control of Three-phase Three-wire Shunt Active Power Filters

This paper proposes a new control strategy for three-phase three-wire shunt active power filters. The idea in this strategy is to form an energy-like Lyapunov function in terms of the active filter states and then determine the control law that makes the time derivative of the Lyapunov function always negative for all values of the states. It is shown analytically that a globally stable control is possible. The references for the active filter currents are obtained by subtracting the measured load currents from the generated source current references. The amplitude of the source currents is adjusted by employing a proportional-integral regulator in the voltage control loop. Matlab simulations are performed for a nonlinear load drawing quasi-square-wave currents from the mains. Simulation results show that the Lyapunov function-based control strategy not only eliminates the load current harmonics successfully, but also exhibits excellent transient response during large load variations.

Lyapunov function-based control laws for revolute robot arms: tracking control, robustness, and adaptive control

A new class of joint level control laws for all-revolute robot arms is introduced. The analysis is similar to an energy-like Lyapunov function approach, except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. This approach gives way to a much simpler analysis and leads to a new class of control designs which guarantee both global asymptotic stability and local exponential stability. When Coulomb and viscous friction and parameter uncertainty are present as model perturbations, a sliding mode-like modification of the control law results in a robustness-enhancing outer loop. Adaptive control is formulated within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by simply replacing unknown model parameters by their estimates.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>