Saturated Control Law Research Articles

Adaptive Projection and Fuzzy Tracking Design for Unknown Control Coefficients and References.

This article addresses the tracking control problem of nonlinear pure-feedback systems, where the control coefficients and the dynamics of the references are unknown. Fuzzy-logic systems (FLSs) are used to approximate the unknown control coefficients and at the same time the adaptive projection law is designed to allow each fuzzy approximation to cross zero, which yields that the proposed method avoids the assumption of using Nussbaum function, that is, the unknown control coefficients never cross zeros. Another adaptive law is designed to estimate the unknown reference and then it is intergraded into the saturated tracking control law to achieve the uniformly ultimately bounded (UUB) performance of the resulting closed-loop system. Simulations show the feasibility and effectiveness of the proposed scheme.

OPTIMAL TRACKING CONTROL FOR ROBOT MANIPULATORS WITH INPUT CONSTRAINT BASED REINFORCEMENT LEARNING

This paper introduces an optimal tracking controller for robot manipulators with saturation torques. The robot model is presented as a strict-feedback nonlinear system. Firstly, the position tracking control problem is transformed into the optimal tracking control problem. Subsequently, the saturated optimal control law is designed. The optimal control law is determined through the solution of the Hamilton-Jacobi-Bellman (HJB) equation. We use a reinforcement learning algorithm with only one neural network (NN) to approximate the solution of the equation HJB. The technique of experience replay is used to relax a persistent citation condition. By Lyapunov analysis, the tracking and the approximation errors are uniformly ultimately bounded (UUB). Finally, the simulation on a robot manipulator with saturation torques is performed to verify the efficiency of the proposed controller.

Input-to-State Stability of Nonlinear Impulsive Systems Subjects to Actuator Saturation and External Disturbance.

This article mainly explores the local input-to-state stability (LISS) property of a class of nonlinear systems via a saturated control strategy, where both the external disturbance and impulsive disturbance being fully considered. In terms of the Lyapunov method and inequality techniques, some sufficient conditions under which the system can be made LISS are proposed, and the elastic constraint relationship among saturated control gain, rate coefficients, external disturbance, and domain of initial value is revealed. Moreover, the optimization design procedures are provided with the hope of obtaining the estimates of admissible external disturbance and domain of initial value as large as possible, where the corresponding saturated control law can be designed by solving LMI -based conditions. In the absence of an external disturbance, the locally exponential stability (LES) property can also be presented with a set of more relaxed conditions. Finally, two examples are presented to reveal the validity of the obtained results.

Distributed finite-time performance-prescribed time-varying formation control of autonomous surface vehicles with saturated inputs

This paper studies a time-varying formation control problem of a swarm of autonomous surface vehicles (ASVs) with prescribed constraints. Every ASV suffers from unavailable velocities, saturated inputs, internal uncertainties, and external disturbances. A distributed finite-time performance-prescribed time-varying formation control method is proposed for ASVs. Specifically, an adaptive fuzzy state observer (AFSO) is firstly proposed to recover the unavailable velocity by using saturated inputs and estimated disturbances from the fuzzy logic system. Secondly, a tunnel prescribed performance (TPP) function is designed to limit tracking errors with a concise form and smaller overshoot. At the kinematic level, with TPP-based error transformation, a C1 finite-time time-varying guidance law is proposed by using the smooth switch functions and recovered velocities. Next, a finite-time command filter based on Levant differentiator is presented to smooth the guidance signals. At the kinetic level, a C1 finite-time saturated control law is developed with the estimated velocities and disturbances. Then, it proves that tracking errors of the proposed closed-loop system converge into a small neighborhood around the equilibrium within finite time while evolving under TPP constraints regardless of saturated inputs. Finally, comparison results are provided to demonstrate the effectiveness of the proposed distributed finite-time performance-prescribed time-varying formation control method.

Saturated attitude control for rigid body under input delay and pointing constraints

This paper designs the saturated attitude control law for the rigid body with constant input delay and pointing constraints. Specifically, a quaternion-based artificial potential function (APF) is proposed to encode the scalar fields about the desired attitude and pointing constraints. A time-delay-compensation-based controller is further developed and shows the uniform ultimate boundedness of system responses. Benefiting from the properties of the proposed APF and its gradient, the designer can assign the bound on the control a priori. Moreover, the local minima problem is excluded by the convergence of the Lyapunov-Krasovskii (LK) functionals rather than merely the convergence of gradient. The unwinding phenomenon associated with unit quaternion is avoided as well. Finally, numerical examples are furnished to show the effectiveness of the proposed method.

Stabilization of asymmetric underactuated ships with input saturation: From underactuated to nonholonomic configuration

A stabilization controller is addressed for an asymmetric underactuated surface ship subject to input saturation in this work. Prior to control design, the considered ship system is converted into a cascade nonlinear system with a minimum phase by applying state and input transformations. And by introducing a circular trajectory, the investigated stabilization problem is successfully expressed into a tracking issue. Under these preparatory works, finite-time and saturated tracking control laws are proposed by converting the obtained tracking error system into an augmented new system and applying Nussbaum function. It has been demonstrated in stability analysis that the designed controllers can enable system states to converge to zero by choosing a sufficiently small radius of the circle, and meanwhile can also achieve the desired input saturation. The simulation results illustrate the validity of the presented control algorithm.

Observer-based robust fuzzy control of nonlinear networked systems with actuator saturation

In this article, the aim is to study the observer-based robust fuzzy control of nonlinear systems subject to actuator saturation via network communication. Unlike most existing results, system outputs are sufficiently processed by an adaptive event-triggered mechanism in an aperiodic sampling manner. By utilizing Takagi–Sugeno (T–S) fuzzy description, a fuzzy observer is established based on the sampled outputs suffering from network-induced delays. A saturated fuzzy control law is then derived from the estimated states of the observer. Moreover, by using ℒ∞ performance index, the adverse effect of persistent bounded disturbance is substantially attenuated. A novel Lyapunov functional, fully considering the characteristics of aperiodic event-triggered scheme and transmission delays, is investigated to analyze system stability and synthesize the desired controller. In view of the imperfect premise matching, the knowledge of asynchronous membership functions is imported into the derivation of a novel set of sufficient conditions for controller synthesis. Finally, the proposed observer-based control algorithm is verified by an illustrative example and simulation results.

Optimal Tracking Control for PMSM With Partially Unknown Dynamics, Saturation Voltages, Torque, and Voltage Disturbances

This article proposes a novel optimal tracking control scheme for permanent magnet synchronous motors (PMSMs) with partially unknown dynamics, saturation voltages, and disturbances in both speed and current dynamics. The strict-feedback nonlinear system is employed to present the PMSM model. Augmented feedforward control inputs are proposed to transform a speed and current tracking control problem of conventional cascade structures to an optimal control problem of a new structure. Consequently, the saturated adaptive optimal control law is designed for the problem. The optimal solution of Hamilton–Jacobi–Issac equation, which provides the value to the control law, is approximated by a simple online approximator. An integral reinforcement learning technique is used to tune the approximator without observing unknown dynamics. It is proven that the optimal value function, the control law, and the worst disturbance law converge to the near-optimal values. The simulation and experiment on a PMSM prototype model of a load drive application with a digital signal processing board TMS320F28379D of Texas Instrument are conducted to justify the effectiveness of the proposed scheme.

Neuroadaptive saturated control for relative motion based noncooperative spacecraft proximity with prescribed performance

This paper investigates the control issue of the noncooperative spacecraft proximity with prescribed performance by exploiting only relative motion information. To accommodate the direct use of relative measurement, the 6-degree-of-freedom (6DOF) relative dynamics is formulated in the body frame of the pursuer. Based on the smooth Gauss error function, a new asymmetric saturation function is developed to satisfy the practical control limitations. To maintain the relative attitude and position within specified constrained ranges, a novel performance function in possession of the preassigned settling time and convergence set of steady state error is proposed. Based on the backstepping framework, the relative attitude and position controllers are surveyed in sequence. In particular, a state constrained virtual control is first developed for each relative dynamics by introducing a nonlinear transformation. Then a neuroadaptive saturated control law is designed by implementing a Nussbaum function based adaptive control coefficient. Stability analysis indicates that the closed-loop 6DOF relative dynamics are asymptotically stable with prescribed performance. Numerical simulations further verify the proposed control strategy.

Stabilizing Control for a Ball and Beam System Considering Restricted Beam Angle

This paper develops for a ball and beam system a design method of control system transferring the ball to a target position considering restricted beam angle. First, we compensate the beam drive system as a second-order delay system to reduce the beam angle constraint to an input one. Using modal decomposition methods, we decompose the plant into the stable and unstable subsystems, and derive a nested saturating control law globally asymptotically stabilizing the unstable one. The control system using this control law has the property that when the ball is transferred, its speed is mostly limited less than a specified value. To reduce the steady-state error of the ball position as well as to alleviate the reset windup, a new type of IMC controller is introduced where a saturated output error between the actual plant stabilized by the saturating control law and the model is fed back. The effectiveness of the control law is demonstrated numerically and experimentally.

Neural Dynamics Variations Observer Designed for Robot Manipulator Control Using a Novel Saturated Control Technique

This work presents a novel controller for the dynamics of robots using a dynamic variations observer. The proposed controller uses a saturated control law based on sintg−1. function instead of tanh.. Besides, this function is an alternative to the use of tanh. in saturation control, since it reaches its maximum value more gradually than the hyperbolic tangent function. Using this characteristic, the transition between states is smoother, with similar accuracy to tanh.. The controller is designed using a saturated SMC (sliding mode controller) and a dynamic variations observer based on GRNN (general regression neural network). The originality of this work is the use of a combination of adaptive GRNN with a sliding mode controller (SMC) including a new saturation function. Finally, experiments based on trajectory tracking demonstrate the robustness and simplicity of this method.

LMI-based synthesis of a robust saturated controller for an underactuated mechanical system subject to motion constraints

In this paper, we suggest a control synthesis approach for the robust stabilization of an underactuated mechanical system, the Inertial Wheel Inverted Pendulum (IWIP), with norm-bounded parametric uncertainties and subject to both motion constraints and actuator saturation. A state-feedback controller is adopted to achieve such robust stabilization of the IWIP at its upright position, while the problem of the motion constraints is addressed by considering the saturation effect of the control input. Our design methodology of the robust saturated state-feedback control law is realized within the framework of Linear Matrix Inequalities (LMIs). We show first that the synthesis problem of such controller is written in terms of Bilinear Matrix Inequalities (BMIs), which are hardly tractable numerically. Then, in order to overcome this obstacle, we use some judicious mathematical tools to convert these BMIs into LMIs. Moreover, we consider the problem of enlarging the domain of attraction by computing the largest attractive invariant ellipsoid for the uncertain constrained nonlinear dynamics of the underactuated IWIP under the saturated state-feedback control law. Simulation results demonstrate the effectiveness and the robustness of the proposed robust saturated state-feedback controller towards norm-bounded parametric uncertainties while constraints on the system motion and the control input are respected.

Interpolation based predictive control by ellipsoidal invariant sets

A new interpolating control scheme for uncertain linear systems is developed. The interpolation is done between two saturated control laws, each given with its associated invariant set. A linear search is performed to compute a sub-optimal interpolation coefficient. Two algorithms are suggested — each incorporating a different optimization objective. The method guarantees robust stability and recursive feasibility, also in presence of persistent disturbances.

Logic-Based Switching Control for Stabilization of Stochastic Feedforward Nonlinear Systems

This article addresses the stabilization problem for a class of stochastic feedforward systems with unknown nonlinearities. Due to the unknown nonlinearities, a nested saturation control law is designed with a priori unknown saturation bounds. Then, a group of logic-based switching conditions are provided for tuning the saturation bounds adaptively. Global asymptotical stability in the probability of the system states is proven. The key features of the control approach lie in that both explicit bounds and specific forms of the nonlinearities could be unknown for designing and deploying the controller.

Constrained attitude maneuvers on [formula omitted]: Rotation space sampling, planning and low-level control

In this paper, we propose a novel framework that provides a systematic strategy to regulate the rigid body attitude on SO(3) within a generic constrained attitude zone. The proposed control scheme consists of three components: sampling, planning and low-level control. Specifically, an overlapping cell-like sampling for the attitude configuration space SO(3) is built and further reformulated to a graph model. Based on this abstraction, a complete graph search algorithm is utilized to generate a feasible path in the graph model. Both sufficient and necessary conditions on finding a feasible path are presented. Furthermore, to facilitate the control design, the point-to-point path is transformed into a smooth reference trajectory along the geodesics. Finally, a saturated low-level control law is formulated to robustly track the desired trajectory. Simulations demonstrate the effectiveness of the proposed control approach.

Low-Complexity Adaptive Saturated Control of a Class of Nonlinear Systems with Its Application

This paper investigates a low-complexity saturated control law for a class of nonlinear systems with consideration of the time-varying output constraint, control constraint, and external disturbance. First, a dead-zone model is employed to transform the control saturation nonlinearity into a linear one with respect to the real input signal. Then, the original system with time-varying output constraint is transformed into a constraint-free one, based on which a novel adaptive saturated control law is devised along the filtered error manifold. By employing minimum learning parameter technique and virtual error concept, only two adaptive parameters are needed to update online, which reduces the computational burdens dramatically. Finally, the applications to Duffing-Holmes chaotic system are organized to validate the effectiveness of the proposed control law.

Control of non-cooperative spacecraft in final phase proximity operations under input constraints

This paper addresses the approaching trajectory control problem for the final phase of non-cooperative spacecraft proximity operations in the presence of disturbances and even input saturation. As a stepping stone, a novel line-of-sight tracking model is developed to describe attitude maneuver towards the target in the proximity. Then, a two-stage artificial potential function is employed to enable the pursuer spacecraft to comply the safety trajectory during approaching the target. In each stage, gradients of potential function are analyzed and the local minimum problem associated with potential function can be addressed. Furthermore, a saturated control law is proposed to ensure a reliable real-time tracking measurement of the target, and the controller rigorously enforces safe path and actuator magnitude constraints. The associated stability proof is accomplished through Lyapunov method. Simulations are carried out to evaluate the effectiveness of the proposed method.

Faster Positioning of One Degree-of-Freedom Mechanical Systems With Friction and Actuator Saturation

This paper concerns with faster positioning of one degree-of-freedom (1DOF) mechanical systems with friction and actuator saturation. A very simple but quite effective saturated relay proportional-derivative (PD) control is proposed. The proposed control is conceived within the framework of nonlinear PD methodology. It is accomplished by adding a relay position error for friction compensation to the saturated PD control law. For faster transient with bounded input, a saturated nonlinear function is introduced. Lyapunov's direct method is employed to prove global asymptotic positioning. The appealing advantages of the proposed control are that it is fairly easy to construct without involvement of any modeling parameter and has the ability to avoid the actuator saturation. Numerical example and experiments demonstrate the effectiveness and improved performance of the proposed approach.

Saturated Boundary Feedback Stabilization of a Linear Wave Equation

In this paper, we study boundary feedback stabilization of a linear wave equation by saturated linear or nonlinear Neumann control laws. Firstly we prove asymptotic stabilization of the closed-loop system when the feedback control law has a linear growth rate around zero. In particular, we study the effect of spatial dimension on the decay rate of the closed loop system. More precisely, we prove that in the one-dimensional (1D) case the smooth solutions of the closed-loop system decay exponentially to zero as $t\rightarrow\infty$; in the two-dimensional case the smooth solutions decay asymptotically to zero faster than any polynomial $(1/t)^\alpha$ $\forall\;\alpha>0$; and in the three-dimensional case the smooth solutions decay to zero like $(1/t)^2$ as $t\rightarrow\infty$. Secondly we study robustness of the stabilization faced with the boundary disturbances. We show that, in the 1D case, every solution of the closed-loop system decays asymptotically to zero provided that the unknown disturbance is in ...

Integrated Visual Servoing Solution to Quadrotor Stabilization and Attitude Estimation Using a Pan and Tilt Camera

This paper presents an integrated visual servoing solution to the problem of quadrotor attitude estimation and stabilization based solely on image feedback from a pan and tilt camera and biased rate gyros. The solution comprises a control law for the quadrotor position and attitude, a control law for the pan and tilt camera platform, and an estimator for the vehicle attitude, whose interconnection stabilizes the quadrotor in hover above certain terrain landmarks. Lateral-longitudinal stabilization is achieved with a nested saturation control law by feedback of the image measurements, estimated attitude, and corrected angular velocity measurements and the vehicle is stabilized vertically by means of image feedback. Resorting to the input-to-state stability properties of the controllers, the quadrotor’s position and attitude are shown to converge to the desired equilibrium point and, in the end, the interconnected system’s closed loop is proven robust to observer estimation errors. Additionally, the pan and tilt camera is actively actuated to keep the relevant features visible in the image field of view for most operating conditions. The robustness and performance of the proposed control and estimation architecture is illustrated through both simulation and experimental results.