Stabilizing Control Law Research Articles

Adaptive anti-unwinding attitude stabilisation with predefined time for rigid spacecraft

In this paper, the problem of attitude stabilisation without unwinding is investigated for rigid spacecraft. To guarantee predefined-time convergence and unwinding-free performance of the closed-loop system, a predefined-time sliding mode function with adjustable parameters is proposed. This sliding mode function contains two equilibrium points. When the states of the closed-loop system are on the sliding mode surface, they converge to the equilibrium point near the initial states. Based on this sliding mode function, an adaptive attitude stabilising control law with tuning parameters is designed to compensate the external disturbances and inertia uncertainty. The presented control law guarantees that the settling time of the closed-loop system and the bounds of the system states can be explicitly determined in advance by adjusting parameters of the sliding mode function and the control law. Finally, numerical simulations are carried out to demonstrate the effectiveness of the presented control law. The simulation results illustrate that the predefined-time convergence and unwinding-free property of the closed-loop system are guaranteed by adopting the presented control law.

State Responses of Several Classes of Linear Systems Based on Fundamental Matrices.

State responses for several classes of linear systems are investigated in this article. The involved systems include state-delayed linear systems, and high-order linear systems. At first, the single-fundamental-matrix-based approach is extended to these systems, and their state responses are expressed by their fundamental matrices (FMs). In addition, the multiple-FMs-based approach is presented for these systems. Based on a group of FMs, the state responses for the considered time-invariant systems are derived. For the considered time-variant systems, their state responses are explicitly expressed by their transition matrices. As an application of the fundamental-matrix-based approach, a stabilizing control law is designed for a class of high-order fully actuated continuous-time linear systems with a single input-delay.

Fault-Tolerant Control of Stochastic High-Order Fully Actuated Systems.

In recent years, high-order fully actuated (HOFA) systems, founded by Prof. GR Duan, have recorded rapid progress for deterministic systems. However, the control issue of stochastic fully actuated systems is still an open problem. This study develops a novel stochastic HOFA system model that complements the existing HOFA methodology. Notably, stochastic signals can be considered in the proposed model, different from the case in the deterministic model. By adopting a high-order operator, equivalent control and stabilization control laws are realized to guarantee the global asymptotic stability in probability of the closed-loop system. For the system with sensor gain faults, an observer-based fault-tolerant control law is designed. Finally, the simulation results validate the effectiveness of the proposed control schemes.

Saturated stabilization of feed‐forward systems subject to lower‐order perturbations

AbstractThis article revisits saturated stabilization of the feed‐forward systems that are subject to lower‐order perturbations, with the purpose of providing new analysis approaches. To carry out the saturation reduction analysis, we do not use the existing time‐interval based contradiction approach, but propose a Lyapunov function method; to deal with the reduced system (the closed‐loop system that does not contain saturation any longer), we do not use the “adding a power integrator” backstepping scheme, but propose an approach which is established by jointly using the vector Lyapunov function theory, a matrix measure stability theory and the switching systems theory. As a result, a quite number of inequality computations can be avoided, and the stability conditions summarized in two analysis procedures can be expressed by directly using the system parameters. This article also shows that the established approaches are applicable to the uncertain feedforward systems subject to linear input perturbation and consequently, allows to present new stabilizing control laws for several intractable under‐actuated systems.

An Extension of the Feedback Linearization Method in the Control Problem of an Inverted Pendulum on a Wheel

This paper continues previous studies on designing stabilizing control laws for a mechanical system consisting of a wheel and a pendulum suspended on its axis. The control objective is to simultaneously stabilize the vertical position of the pendulum and a given position of the wheel. The difficulty of this problem is that the same control is used to achieve two targets, i.e., stabilize the pendulum angle and the wheel rotation angle. Previously, the output feedback linearization method was applied to this problem. The sum of the pendulum angle and the wheel rotation angle was taken as the output. For the closed loop system to be not only asymptotically stable in the output but also to have asymptotically stable zero dynamics, a dissipative term was added to the output-stabilizing control law. Below, a two-parameter modification of this law is described. Along with the dissipative term, we introduce a positive factor. The more general parameterization allows stabilizing this system in the cases where the control law proposed previously appeared ineffective. The properties of the new control law are investigated, and the attraction domain is estimated. The estimation procedure is reduced to checking the feasibility of linear matrix inequalities.

Modeling Control of Supercoiling Dynamics and Transcription Using DNA-Binding Proteins.

Nearly all natural and synthetic gene networks rely on the fundamental process of transcription to enact biological feedback, genetic programs, and living circuitry. In this work, we investigate the efficacy of controlling transcription using a new biophysical mechanism, control of localized supercoiling near a gene of interest. We postulate a basic reaction network model for describing the general phenomenon of transcription and introduce a separate set of equations to describe the dynamics of supercoiling. We show that supercoiling and transcription introduce a shared reaction flux term in the model dynamics and illustrate how the modulation of supercoiling can be used to control transcription rates. We show the supercoiling-transcription model can be written as a nonlinear state-space model, with a radial basis function nonlinearity to capture the empirical relationship between supercoiling and transcription rates. We show the system admits a single, globally exponentially stable equilibrium point. Notably, we show that mRNA steady-state levels can be controlled directly by increasing a length-scale parameter for genetic spacing. Finally, we build a mathematical model to explore the use of a DNA binding protein, to define programmable boundary conditions on supercoiling propagation, which we show can be used to control transcriptional bursting or pulsatile transcriptional response. We show there exists a stabilizing control law for mRNA tracking, using the method of control Lyapunov functions and illustrate these results with numerical simulations.

Event‐triggered control of Itô stochastic nonlinear delayed systems with state quantization

AbstractThe problem of event‐triggered control (ETC) of stochastic nonlinear delayed systems with state quantization is investigated. In order to reduce the communication burden and computational cost, an ETC mechanism and state quantization are introduced in the control scheme. Two configurations are considered to investigate their interaction: quantization before event‐trigger (QE) and quantization after event‐trigger (EQ), respectively. Based on this, a static event‐triggered mechanism (ETM) is designed while avoiding the Zeno phenomenon. The system allows known input‐to‐state stability (ISS) control law, followed by utilizing the Halanay inequality to achieve stabilization. In both configurations, the stabilization of the closed‐loop system is guaranteed. We show that communication times can be reduced by adjusting parameters and selecting the suitable configuration. Moreover, to further enhance resource conservation, we illustrate the feasibility of dynamic ETMs in this framework. Numerical simulation results validate the effectiveness of the proposed ETC schemes.

The Design of Phugoid Mode Stabilization in Angle of Attack Protection Control Law

To achieve the requirement of maintaining the angle of attack, the design of the angle of attack (AOA) protection control law often causes instability in the pitch attitude and generates phugoid mode oscillations. Conversely, adding a damping ratio of phugoid to suppress the oscillations would reduce the stability of the angle of attack and the maneuverability of the aircraft. Therefore, when designing the AOA protection control law, it is necessary to choose the appropriate damping ratio to allow the aircraft to have a certain balance between maneuverability and stability. At present, people do not pay enough attention to this, but the resulting aviation accidents make this problem urgent to be solved. In this paper, based on the general modeling process, the linear model of a sample aircraft is established. Different gain values are designed according to the different needs of different flight phases for aircraft maneuverability and stability. The simulation shows that in the flight phase, the phugoid mode stabilization control law designed by the eigenstate assignment method (EA) can reduce the phugoid oscillation effectively, while in the landing flare phase when maneuverability is more important, it provides a greater degree of maneuverability.

Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion

Transportation in warehouses and production workshops is a matter of urgency today. Most warehouses arrange routes for circulation along the shelves, transportation vehicles will move on this road to perform the task of exporting or importing goods. Routes will be arranged to move in one direction because vehicles do not have enough space to turn around in cramped warehouses. This causes many difficulties in planning the trajectory for transportation vehicles, especially self-propelled vehicles. In order to have an appropriate transportation plan, it is necessary to solve many problems, including: reasonable transport equipment, sufficient number of devices, optimal route layout, algorithm of operation center for Positioning and Navigation of transportation equipment,... This study proposes a method for transportation using an omnidirectional automated guided vehicle (AGV). The AGV's omnidirectional mobility is supported by the mecanum wheels. This study consists of two parts, the first part focuses on kinematic modeling for mecanum wheels and extends to robot’s platform using four mecanum wheels. Part two proposes a diagram to calculate the errors of the robot compared to a reference tracking line, design a control law based on the Lyapunov stability criterion. The stability of the control law is verified and confirmed by simulation on MATLAB environment.

Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion

Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion

A Unified Framework for Data-Driven Optimal Control of Connected Vehicles in Mixed Traffic

This paper presents a unified approach to the problem of learning-based optimal control of connected human-driven and autonomous vehicles in mixed-traffic environments including both the freeway and ring road settings. The stabilizability of a string of connected vehicles including multiple autonomous vehicles (AVs) and heterogeneous human-driven vehicles (HDVs) is studied by a model reduction technique and the Popov-Belevitch-Hautus (PBH) test. For this problem setup, a linear quadratic regulator (LQR) problem is formulated and a solution based on adaptive dynamic programming (ADP) techniques is proposed without a priori knowledge on model parameters. To start the learning process, an initial stabilizing control law is obtained using the small-gain theorem for the ring road case. It is shown that the obtained stabilizing control law can achieve general <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_{p}$</tex-math></inline-formula> string stability under appropriate conditions. Besides, to minimize the impact of external disturbance, a linear quadratic zero-sum game is introduced and solved by an iterative learning-based algorithm. Finally, the simulation results verify the theoretical analysis and the proposed methods achieve desirable performance for control of a mixed-vehicular network.

PTESO based robust stabilization control and its application to 3-DOF ship-borne parallel platform

In this paper, a prescribed-time extended state observer (PTESO) is constructed for a three degree-of-freedom (3-DOF) parallel ship-borne platform to estimate the platform’s total disturbances, including dynamic uncertainties, unknown time-varying external disturbances and coupling between the platform motion state variables. The constructed PTESO offers the advantages of converging within a prescribed time, suppressing initial peaking phenomenon and easy implementation. Furthermore, a PTESO based PD-like robust stabilization control law is designed, which maintains the support surface of the platform at a given horizontal position and orientation in the inertial space. Theoretical analyses show that the resulting closed-loop stabilization control system is stable. Simulation results with comparisons are presented to verify the effectiveness of our proposed robust stabilization control strategy.

Closed-Loop Guidance for Asteroid Landing Using Stability-Related Control and Three-Dimensional Convex Curvature Constraints

For asteroid landing missions in uncertain environments, the thrust commands determined by a feedback control and a fuel-optimal landing trajectory may exceed the allowable thrust magnitude, which affects the stability of the controller. In contrast to the traditional method that designs the nominal trajectory and feedback control law separately, a novel closed-loop guidance method that generates an optimal trajectory while designing a stable feedback control law within the thrust limit is proposed. The method incorporates the feedback control design into the nominal trajectory optimization by shaping controlled trajectory bundles into a contractive invariant set centered on the nominal trajectory. To shape the trajectory bundles, the contractive invariant criterion is derived and augmented into the optimization with the feedback gain as an optimization variable. Then, the corresponding feedback control, expressed by the feedback gain and contractive invariant set, is introduced to form a stability-related control constraint, which keeps closed-loop thrust within the limit and ensures control stability. In addition, to improve the collision avoidance capability in uncertain terrains, a three-dimensional convex curvature constraint is proposed by constraining the geometric relationship between position and velocity vectors, and used as a soft constraint in the optimization. Finally, the proposed method is simulated using a landing mission on asteroid 433 Eros, which validates the superiority in the tracking performance and the collision avoidance capability.

Global Finite-Time Stabilization of Spacecraft Attitude With Disturbances via Continuous Nonlinear Controller

In this paper, a robust continuous controller is investigated to solve the global finite-time attitude stabilization problem of rigid spacecraft system subject to multiple disturbances. The system order is firstly increased by derivation and the derivative of the actual torque is regarded as the virtual control law to be designed. Then, a super-twisting differentiator is constructed to provide finite-time angular acceleration estimations. Finally, based on the estimated angular accelerations, a discontinuous set stabilization control law is designed as the virtual controller. The actual continuous controller is obtained by integrating the discontinuous one. Rigorous proof and stability analysis are presented based on Lyapunov analysis. Compared with most of the existing finite-time control approaches in spacecraft systems, the proposed continuous control scheme guarantees the finite-time set stability of the closed-loop system. Moreover, the system states can converge to the equilibria even in the presence of derivative-bounded disturbances. Simulation studies of the proposed controller are illustrated to demonstrate the strong disturbance rejection ability, fast convergence rate, and high steady-state precision.

Analytical Synthesis of an Aircraft’s Lateral Motion Control by Output at the Lack of Measurements of Slip and Roll Angles

For a linearized fourth-order model describing the lateral motion of an aircraft with two controls, the stabilizing control laws analytical expressions are obtained at the lack of measurements of slip and roll angles. Analytical synthesis is based on a new approach of solving the problem of control by output. In contrast to the traditional Van der Woude approach using multilevel decomposition, the proposed approach is applicable to a wide class of systems with total dimension of control and observation vectors not exceeding the dimension of state vector. A compact formula is presented that determines the matrix of controller by output for a fourth-order dynamic system with two inputs and two outputs, provided that the indices of controllability and observability are not equal to each other. The results of simulation of control processes are given on the example of stabilization of the lateral motion of a hypothetical aircraft.

Composite anti-unwinding attitude control of spacecraft under actuator saturation and angular velocity limits

Spacecraft attitude control employs quaternion representation to avoid singularity issues and obtain global maneuver stability. However, it has redundancy associated, resulting in dual equilibrium points. The attitude control may confront the unwinding phenomenon due to the presence of the equilibria. In this paper, an anti-unwinding controller for spacecraft stabilization in the presence of external disturbances and inertial uncertainties, angular velocity limit, actuator saturation and faults is presented. Specifically, a modified extended state observer (ESO) is designed to obtain total disturbance estimates of the rigid-body spacecraft. Auxiliary parameters are added in the design to avoid initial high estimates in the proposed ESO design resulting in faster convergence. The proposed disturbance observer is to release the assumption that requires the estimated disturbance to be constant or varying at slow rates. Using the ESO estimates, a particular back-stepping-SMC (ESO-BTSMC) controller is devised to formulate anti-unwinding control law for spacecraft stabilization. Lyapunov stability theory is employed to prove closed-loop stability of system and estimation error convergence. Comparative simulations are performed to demonstrate the performance of the proposed control scheme. It is found that the proposed control scheme gives smooth and precise control performance along with faster transient response. Additionally, it also alleviates the chattering phenomenon.

MPC-Based Cooperative Enclosing for Nonholonomic Mobile Agents Under Input Constraint and Unknown Disturbance.

In this article, a model predictive control (MPC)-based cooperative target enclosing control approach is investigated for multiple nonholonomic mobile agents with input constraints and unknown disturbances. The agents are required to move along a desired circular orbit centered at a stationary target and maintain an even distribution on the orbit. Based on a dual-mode MPC strategy, a cooperative target enclosing control law is designed by only using the local sensing information. When the agents are inside a terminal region, a locally cooperative stabilizing control law is designed with a signal function defined componentwise part compensating for the unknown disturbances. A robust MPC algorithm is designed for the agents to enter the terminal region in finite time. Global asymptotic stability is guaranteed for multiple nonholonomic mobile agents with input constraints and unknown disturbances. Simulation results illustrate the effectiveness of the proposed approach.

A Passivity based Approach to Predefined-Time Stabilization

Passivity theory is an efficacious framework in designing control laws, in particular, predefined-time stabilizing control laws. To that end, this paper discusses a predefined-time variant of passivity, associated Lyapunov tools, and basic analysis of this property through feedback interconnection. In particular, a series of predefined-time passivity definitions are discussed which allow to establish a relationship between the passivity framework and predefined-time stability. These definitions are exploited for designing control laws that render a passive system predefined-time stable about an equilibrium point. Moreover, several negative feedback interconnections of these systems are discussed to investigate the predefined-time passivity properties and predefined-time stability of an equilibrium point (when external inputs are zero). The efficacy of the proposed results is illustrated through academic and realistic examples, and comparison is also done with other existing methods.

Simultaneous stabilization of nonlinear systems with different and multiple time‐varying delays

AbstractThe simultaneous stabilization is addressed for a collection of nonlinear systems with multiple time‐varying delays. The time delays vary not only from one system to the other but even from one state to another within a system. The nonlinear functions may also be different for each system of the collection. A delay‐independent simultaneously stabilizing control law is presented by developing a Control Lyapunov‐Krasovskii Functional (CLKF) method. This controller has a unified structure for all the systems and, despite differences in nonlinearities and delays, leads to the stabilization of all the systems, simultaneously. During the design procedure, first, a systematic approach is provided to construct a CLKF of a particular form for each system. Second, a simultaneously stabilizing control law is defined based on the constructed CLKFs. Finally, a practical example is given to verify the efficiency and applicability of the given method.

Robust model reference tracking for uncertain second‐order nonlinear systems with application to robot manipulator

AbstractIn this article, robust model reference control for uncertain second‐order nonlinear systems is investigated by applying fully actuated system approaches. A robust stabilizing control law is constructed for the uncertain systems based on the Lyapunov stability theory. With the obtained robust control results, a robust model reference tracking (RMRT) control scheme is proposed to ensure the tracking error finally converges globally into a bounded ellipsoid. The established RMRT controller is composed of three parts, the basic part cancels the known nonlinearities in the system and simultaneously assigns the linear dominant term in the closed‐loop system, the robustness part overcomes the effects of the nonlinear uncertainties in the system, the compensator part compensates the effect of the reference model state and reference control input to the tracking error. Furthermore, based on a general parametric solution to the type of Sylvester matrix equations, simple and complete parameterization of the RMRT control designs is provided. An application to robot manipulator indicates satisfactory control system performances with the proposed RMRT control scheme.