Lyapunov Redesign Method Research Articles

Anti-disturbance control strategy in capture stage for AUV dynamic base docking with optical guided constraints

This article investigates the challenge of potential optical guidance failure at the end of the underwater docking process due to relative attitude deviation between the Autonomous Underwater Vehicle (AUV) and the recovery platform, especially in the context of a moving base. A novel anti-disturbance control strategy is presented, accounting for environmental dynamics and optical guidance limitations. Firstly, we establish constraint models such as the effective field of view and the guidance beam associated with the optical guidance method. We then divide the recovery control strategy area based on the constraint model and propose the Line-of-sight Considering Visual Constraints (LOSCVC) docking control strategy. This strategy utilizes the line-of-sight method and the virtual leader method to make motion decisions based on the relative attitude offset and completes the docking operation by tracking the motion of the virtual leader. Furthermore, we consider the effect of ocean currents on the docking process of the moving base and design a disturbance compensation control law based on the Lyapunov redesign method. This strategy ensures the AUV maintains effective and continuous optical guidance during the capture phase, thereby achieving precise, safe, and rapid docking control. Simulation results validate the effectiveness and robustness of the proposed docking control strategy.

Three-Dimensional Optimal Guidance with Lyapunov Redesign for UAV Interception

Three-dimensional guidance laws are designed to intercept non-maneuvering targets and maneuvering targets in this paper. An optimal control approach with constant or time-variant feedback gain is proposed for interception. The cost function is designed with considerations on energy-efficiency and time-efficiency in the transient process. Lyapunov redesign method is applied to treat the target acceleration, where the precise information of target accelerations is not necessarily required. Efficacy of the proposed guidance laws is proved theoretically and verified by simulation results.

Moving sensors for improved estimation of dynamic structures: Experimental validation

In the monitoring of structural systems, the use of multiple high-end sensors may prove to be economically prohibitive. The alternative approach would be to use fewer devices capable of moving across the span of the structural system. In the proposed approach, a velocity sensor that is able to move across the spatial domain and obtain point-wise velocity measurements is combined to a novel dynamic observer. Based on the measured velocities, a state estimator is developed, the gain of which depends on the motion of the sensor. The motion of the sensor is defined using Lyapunov redesign methods and depends only on the estimation error at the current sensor position. The guidance policy is performance based and steers the sensor to spatial regions of the structure with larger estimation errors. The proposed approach is validated with a one-dimensional flexible structure, mathematically described by an Euler–Bernoulli partial differential equation. The moving sensor is realized through the use of a laser scanning vibrometer that provides both the moving measurements and additional measurements against which the proposed approach will be validated. Once measurements over a large number of locations are acquired, the experimental results are fed to the algorithm that selects the instantaneous sensor location. Experimental results for linear and nonlinear beam cases are presented to show the feasibility and robustness of the proposed approach.

A robust phase oscillator design for wearable robotic systems

The design of a phase-based robust oscillator for wearable robots, that could assist humans performing periodic or repetitive tasks, is presented in this paper. The bounds on perturbations, that guaranteed the stability of the output for the phase oscillator controller, were identified and the Lyapunov redesign method was applied to construct a robust controller using a bounding function. The robust controller produced a bounded control signal to modify the amplitude and frequency of the resulting second-order oscillator to modulate the stiffness and damping properties. In this paper, the focus is on the mathematical modeling of the controller, its dynamic stability and robustness for human–robot application. The proposed approach was verified through a simple pendulum experiment. The results provided evidence that a better limit cycle, with a controlled radial spread of the steady state, was obtained with Lyapunov redesigned phase oscillator. Finally, the potential of the proposed approach for hip assistance in a healthy subject wearing HeSa (Hip Exoskeleton for Superior Assistance) during periodic activities are discussed with preliminary results.

Vibration Control of an Axially Moving System with Restricted Input

In this study, we consider the global stabilization of an axially moving system under the condition of input saturation nonlinearity and external perturbation. Based on Lyapunov redesign method, observer backstepping, and high‐gain observers, an output feedback control strategy with an auxiliary system is constructed to eliminate the input saturation constraint effect and suppress the string system vibration, and a boundary disturbance observer is exploited to cope with the external disturbance. The stability of the controlled system is analyzed and proven based on Lyapunov stability without simplifying or discretizing the infinite dimensional dynamics. The presented simulation results show the effectiveness of the derived control.

Design of a robust path tracking controller for an unmanned bicycle with guaranteed stability of roll dynamics

ABSTRACTController design for a riderless bicycle is a difficult task due to its non-holonomic constraint and its complex dynamic. The problem will be more complex, when path tracking and stabilizing the roll angle of the bicycle are considered simultaneously. This paper proposes an analytical approach to stabilize the roll angle of an unmanned bicycle, in the meanwhile a desirable path is tracked by the bicycle. These two objectives are achieved due to the existing relation between the roll angle and the steering variable of the bicycle. In this paper, a multi-loop control structure is proposed to track a predetermined path. In the inner loop, the roll angle tracks a time-varying reference signal using the back-stepping method. This reference signal is manipulated in the outer loops to track the desired path. Moreover, the robustness of the system with respect to external disturbances is guaranteed by the Lyapunov redesign method. Finally, the efficiency of the proposed method is illustrated through computer simulations.

Design of a robust tracking controller for a nonholonomic mobile robot with side slipping based on Lyapunov Redesign and nonlinear H∞ methods

ABSTRACTIn this paper, robust control of nonholonomic mobile robots is considered which is more complex with respect to holonomic types, due to fewer degrees of freedom in their model. In addition, side slipping is considered which disturbs the nonholonomic constraint adversely. In previous researches, the slip is either estimated by an estimator or is measured using additional sensors. In this paper, the Kanayama transformation is modified such that the model of the robot only includes matched disturbances. Then, a robust tracking controller is designed using the Lyapunov redesign method when only the upper bound of the side slip is known. Moreover, in order to compare the performance of the proposed controller, the nonlinear H∞ control is also developed for this robot. Finally, the performance of these two controllers is compared and the simulation results show the appropriate efficiency of the proposed controllers.

Generation of stable oscillations in uncertain nonlinear systems with matched and unmatched uncertainties

ABSTRACTIn this paper, a robust limit cycle control technique is proposed for generation of stable oscillations in a class of uncertain nonlinear systems with both matched and unmatched uncertainties. For this purpose, first, the modified Lyapunov function is introduced which is appropriate for stability analysis of invariant sets (instead of equilibrium points). The structure of the proposed Lyapunov function is related to the shape of the desirable limit cycle. Next, in order to design the robust limit cycle control input, the backstepping and Lyapunov redesign methods are employed, simultaneously. The The classical Lyapunov redesign controller is discontinuous and robust with respect to matched uncertainties. To overcome unmatched uncertainties, a modified version of the Lyapunov redesign controller is suggested in each step of backstepping which results in a continuous robust control law. Furthermore, the convergence of the phase trajectories of the uncertain closed-loop system to the target limit cycle is proved using the extended Lyapunov stability theorem. Finally, computer simulations are performed to show the applicability of the given approach. In this regard, two uncertain nonlinear practical systems are considered and robust stable oscillations are generated in these systems via the proposed controller. Simulation results confirm the effectiveness of the proposed technique.

Adaptive Sliding Mode Control of Cooperative Spacecraft Rendezvous with Coupled Uncertain Dynamics

Pose tracking control of cooperative spacecraft rendezvous and docking systems subject to coupled and uncertain dynamics is studied in this paper. An adaptive sliding mode trajectory tracking controller is proposed to ensure asymptotic convergence of pose tracking errors and adaptive estimations in Lyapunov framework. An adaptation scheme of the controller gain is derived via Lyapunov redesign method to improve the control performance of the closed-loop system. Sliding mode control guarantees the robustness for dealing with parametric uncertainty and external disturbance. The boundary-layer technique is employed to overcome control chattering phenomenon. A numerical example demonstrates the effectiveness of the proposed controller.

Sufficient LMI conditions and Lyapunov redesign for the robust stability of a class of feedback linearized dynamical systems

The robust stability of a class of feedback linearizable minimum-phase nonlinear system, having parametric uncertainties, is investigated in this study. The system in new coordinates is represented to an equivalent formulation after the attempt of feedback linearization. Due to the parametric uncertainties the approximately linearized system entails a norm bounded input nonlinearity such that the equilibrium point condition in error dynamics can not be satisfied. Accordingly, to guarantee the regional asymptotic stability a control synthesis problem is proposed by means of sufficient Linear Matrix Inequalities (LMIs) together with an amended nonlinear control term, derived from the Lyapunov redesign method, which tackles zero steady-state error condition. The numerical examples of a general aviation aircraft's longitudinal dynamics and inverted pendulum are simulated to show the proficiency of the proposed control technique.

Flexible Structure Control of Unmatched Uncertain Nonlinear Systems via Passivity-based Sliding Mode Technique

This paper considers the problem of passivity-based sliding mode control of uncertain nonlinear systems. For this purpose, two cases are studied. In the first case, it is assumed that only the matched uncertainties exist in the system dynamics. In this case, the passivity-based control approach is used to design an appropriate sliding manifold with a flexible structure such that the asymptotic stability of the reduced-order model (i.e., the motion equations on the proposed sliding manifold) is guaranteed. In the second case, both matched and unmatched uncertainties are considered in the system dynamics and thus the reduced-order model has uncertain terms. In this case, the modified Lyapunov redesign technique is combined with the passivity-based control method for design of robust sliding manifold. The function that is basically used in the classical Lyapunov redesign method is the signum function, which is not differentiable. Since, for evaluating the derivative of the sliding manifold its equation must be differentiable, a new additional continuous control term is suggested. In addition, the robust practical stabilization of the motion equations is guaranteed without considering any limitation on the upper bound of the unmatched uncertainties. Finally, computer simulations are performed for a practical example (flexible spacecraft) and also a numerical example to demonstrate the ability of the proposed controller in robust stabilization of uncertain nonlinear dynamical systems.

Optimisation and adaptation of synchronisation controllers for networked second-order infinite-dimensional systems

ABSTRACTThe adaptation and optimisation of synchronisation control for networked second-order distributed parameter systems are considered. The objective is to design output feedback controllers guaranteeing agreement between the states of the N systems that individually track a reference model. The controller structure involves feedback terms consisting of the pairwise difference of the measurements of the second-order systems as well as coupling terms that enforce consensus. Placing the closed-loop networked systems in aggregate form allows for further optimisation of the synchronisation gains. Using the aggregate systems ‘closed-loop energy’ as a suitable optimisation measure, the search for the synchronisation gains reduces to the minimisation of the optimisation index, which eventually is described by the trace of the solution to a parameterised Lyapunov operator equation. Considering the adaptation of the synchronisation gains offers an alternative to optimisation. The adaptation is based on Lyapunov redesign-methods and utilises a parameter-dependent Lyapunov functional to extract them. Due to its structure, all network topology information is handled at the local level, thereby relaxing the graph topology conditions in the adaptive case. Numerical studies are included to provide an insight on the effects of synchronisation control of networked second-order distributed parameter systems.

Estimation of Gaseous Plume Concentration with an Unmanned Aerial Vehicle

The approach presented in this paper provides real-time estimation of a gaseous plume concentration using an unmanned aerial vehicle with sensors. The plume is generated by a moving aerial source and is modeled by the unsteady three-dimensional advection–diffusion equation with ambient winds and eddy diffusivities. The approach couples the unmanned aerial vehicle guidance with the performance of the concentration estimator and is implemented with efficient computational methods for real-time estimation. The unmanned aerial vehicle is modeled as a point-mass fixed-wing aircraft resulting in a sixth-order nonlinear dynamical system. The unmanned aerial vehicle is guided toward the region of maximum state-estimation error via a Lyapunov-redesign method. The estimation scheme provides the desired Cartesian velocities of the unmanned aerial vehicle, and a lower-level controller provides the control signals to the unmanned aerial vehicle. The finite volume discretization of the estimator incorporates a second-order total-variation-diminishing scheme for the advection term and dynamic grid adaptation with local grid-refinement centered at the unmanned aerial vehicle location. The approach is applied to a stationary source and a moving aerial source using realistic unmanned aerial vehicle specifications. The estimated plumes are compared with simulated plume data and show the effectiveness of the approach.

Boundary adaptive synchronization of networked PDEs with adaptive parameter estimators

This work considers the synchronization control of networked PDEs that have boundary observation and control. The PDEs are assumed identical, with information exchange dictated by a complete directed graph. Parametric uncertainties entering in the boundary, result in structured perturbation terms that may render the open loop system unstable. Additionally constant disturbance terms entering at the boundary are impeding state regulation. To address these parametric uncertainties, a precompensator is utilized to stabilize each networked PDE. Another component of the controller provides an on-line cancellation of the parametric uncertainties by attempting to cancel them through their adaptive estimate, and to attenuate the effects of boundary disturbances, their adaptive estimates are utilized in the controller. To provide a robustness in the adaptive estimation of the parametric uncertainties and the boundary disturbances, the standard adaptive laws are complemented with a consensus protocol term that penalizes the pairwise disagreement of the adaptive estimates. Finally, to enforce synchronization of all networked PDEs, a synchronization controller is included which utilizes only the outputs of all communicating PDE systems weighted by adaptive synchronization gains. These gains, derived from Lyapunov redesign methods, include a consensus term for added robustness and to enforce convergence. Simulation studies of five networked diffusion PDEs with boundary observation and control are included.

Estimation of a gaseous release into the atmosphere using a formation of UAVs

Abstract: The real-time estimation of a gaseous plume that results from gas released into the atmosphere by a moving aerial source is presented. The approach is utilizing a group of UAVs equipped with gas concentration sensors onboard and the concentration measurements are used in an estimation scheme in the form of a Luenberger observer. The estimator is modeled as the advection-diffusion equation, which is solved numerically in real-time using a finite volume method on a dynamically adapted computational grid. The UAVs maintain a rigid flying formation, with the control signals for the leader being provided by the Lyapunov-redesign method, which couples the UAV dynamics to the performance of the estimator. The follower UAVs provide plant information to the estimator and also compute the spatial gradients necessary for the implementation of the guidance scheme. Numerical examples illustrate the performance of the proposed approach.

Adaptation and Optimization of Synchronization Gains in the Regulation Control of Networked Distributed Parameter Systems

This work is concerned with the design and effects of the synchronization gains on the synchronization problem for a class of networked distributed parameter systems. The networked systems, assumed to be described by the same evolution equation in a Hilbert space, differ in their initial conditions. To address the synchronization problem, a coupling term containing the pairwise state differences of all the networked systems weighted by the synchronization gains is included in the controller of each networked system. By considering the aggregate closed-loop systems, an optimization scheme for the synchronization gains is proposed by minimizing an appropriate measure of synchronization. The integrated control and synchronization design is subsequently cast as an optimal control problem, the solution of which is found via the solution of parameterized operator Lyapunov equations. An alternative to the optimization of the synchronization gains is also proposed in which the adaptation of synchronization gains is derived from Lyapunov redesign methods. Both choices of the proposed synchronization controllers aim at achieving both the control and the synchronization objectives. An extensive numerical study examines the various aspects of the optimization and adaptation of the gains on the control and synchronization of networked 1D parabolic differential equations.

Robust control for robotic manipulators with non-smooth strategy

In this paper, a novel non-smooth robust control approach is presented for robotic manipulators. By using decimal power rule in Lyapunov redesign methods, the conventional robust control for robot is improved. Our approach can achieve higher control precision with faster convergence speed. The formulations of estimating residual set and settling time have been initially established. The practical stability property is analysed. An illustrative example is bench tested to validate the effectiveness of the proposed approach.

Lyapunov 재설계 방법을 이용한 무인 수상정의 군집 제어

In this paper, a practical controller for a group of USVs is proposed in order to avoid matrix inversion problems in computation. Using nonlinear mapping, a formation composed of nonholonomic agents can be stabilized even when the formation is stationary. Since there is no matrix inversion in computing the control law, the computation complexity can be resolved. A controller for stabilizing the formation errors in the presence of model uncertainty is considered using the Lyapunov redesign method. The asymptotic stability of the formation errors is shown. It is also shown that the proposed controller can be applied to guide a formation to a different shape without modification.

Robust stabilization of uncertain nonlinear slowly-varying systems: Application in a time-varying inertia pendulum

This paper considers the problem of robust stabilization of nonlinear slowly-varying systems, in the presence of model uncertainties and external disturbances. The main contribution of this paper is an extension of the Slowly-Varying Control Lyapunov Function (SVCLF) technique to design a robust stabilizing controller for nonlinear slowly-varying systems with matched uncertainties. In the proposed strategy, the Lyapunov redesign method is utilized to design a robust control law. This method, originally, leads to a discontinuous controller which suffers from chattering. In this paper, this problem is removed by using a saturation function with a high slope, as an approximation of the signum function. Since, using the saturation function leads to loss of asymptotic stability and, instead, guarantees only the boundedness of the system's states; therefore, some sufficient conditions are proposed to guarantee the asymptotic stability of the closed-loop uncertain nonlinear slowly-varying system (without chattering). Also, in order to show the applicability of the proposed method, it is applied to a time-varying inertia pendulum. The efficiency of the designed controller is demonstrated through analysis and simulations.

Adaptive control of uncertain nonlinear systems using mixed backstepping and Lyapunov redesign techniques

In this paper, a robust adaptive control law for a class of uncertain nonlinear systems is proposed. The proposed controller guarantees asymptotic output tracking of systems in the strict-feedback form with unknown static parameters, and matched and unmatched dynamic uncertainties. This controller takes advantages of a robust stability property of the Lyapunov redesign method and a systematic design procedure of the backstepping technique. In fact, the backstepping technique is employed to enrich the Lyapunov redesign method to compensate for not only matched – but also unmatched-uncertainties. On the other hand, using the Lyapunov redesign method in each step of the conventional backstepping technique makes backstepping robust. The suggested controller is designed through repeatedly utilizing the Lyapunov redesign method in each step of the backstepping technique. Simulation results reveal the efficiency of the Lyapunov redesign-based backstepping controller.