Input Saturation Research Articles

Analytic optimal control for multi-satellite assembly using linearized twistor-based model

This paper presents Guidance and Control (G&C) systems for multi-satellite assembly in proximity operations. The systems utilize the twistor model, which is linearized through Taylor’s series. Decentralized control laws, designed using Linear Quadratic Regulator (LQR) and Model Predictive Control (MPC), are employed to track an energy-optimal trajectory generated using the Hamiltonian approach. Data exchange between satellites and their neighbors is represented using graph theory. The decentralized MPC framework is implemented using the CasADi package. To ensure collision avoidance between the satellites, a repulsive control law is designed, considering symmetric input saturation in the actuators. The proposed G&C systems are tested using a high-fidelity nonlinear satellite relative motion model that incorporates orbital perturbations. Numerical simulations are performed in a MATLAB® environment, and the results are visualized using STK®. Furthermore, a comparative study is conducted to evaluate tracking performance and fuel consumption between the two control methods. The results demonstrate that the use of an optimal trajectory reduces fuel consumption for both control algorithms.

Dynamic Event-Triggered Safe Control for Nonlinear Game Systems With Asymmetric Input Saturation.

This article focuses on the Pareto optimal issues of nonlinear game systems with asymmetric input saturation under dynamic event-triggered mechanism (DETM). First, the safe control is guaranteed by transforming the system with safety constraints into the one without state constraints utilizing barrier function. The united cost function integrating nonquadratic utility function is constructed to provide the foundation to achieve the Pareto optimal solutions. Then, the adaptive dynamic programming method with concurrent learning is proposed to approximate the Pareto optimal strategies wherein both current and historical data are utilized. To further lessen the consumptions of computation/communication resources, the DETM is integrated into the adaptive algorithm framework which can avoid Zeno phenomena. All the signals of the closed-loop system are proved to be uniformly ultimately bounded. Finally, the simulation results are given to validate the effectiveness of the proposed method from several aspects.

Improved Data-driven Adaptive Control Structure Against Input and Output Saturation

Improved Data-driven Adaptive Control Structure Against Input and Output Saturation

Inner loop model predictive control and outer loop PI reference governor for PMSMs with input and state saturation for torque control

This contribution considers a torque control scheme consisting of model predictive control (MPC) in the inner control loop together with PI reference governor in the outer control loop and a decoupling feedforward control for an isotropic permanent magnet synchronous machine (PMSM). This innovative approach is known in literature as PI-MPC dual loop control. A particular emphasis is given to the control governor strategy which is the outer loop PI reference governor and allows to regulate the machine in the flux weakening region and is therefore only active for field weakening. In this context the analysis of the stability based on Lyapunov’ approach of the control loop in flux weakening region is shown. The desired currents represent the reference currents for the MPC, which forms the inner control loop. The MPC is adapted using an extended Kalman filter (EKF), which estimates inductance of the electrical system in dq coordinates by using a bivariate polynomial. Compared measurements with a hardware-in-the-loop (HIL) system show the effectiveness of the proposed control scheme with respect to a standard PI controller in inner loop (PI-PI scheme) in the presence of saturated inputs and state of a PMSM. The proposed MPC uses just an optimal, proportional control and thus avoids windup effects. Measurement results in the presence of input and state saturations show that MPC is working without overshoot in the currents which leads to less needed power in input.

Robust 3-D Path Following Control Framework for Magnetic Helical Millirobots Subject to Fluid Flow and Input Saturation.

Precise trajectory control is imperative to ensure the safety and efficacy of in vivo therapy employing the magnetic helical millirobots. However, achieving accurate 3-D path following of helical millirobots under fluid flow conditions remains challenging due to the presence of the lumped disturbances, encompassing complex fluid dynamics and input frequency saturation. This study proposes a robust 3-D path following control framework that combines a disturbance observer for perturbation estimation with an adaptive finite-time sliding mode controller for autonomous navigation along the reference trajectories. First, a magnetic helical millirobot's kinematic model based on the 3-D hand position approach is established. Subsequently, a robust smooth differentiator is implemented as an observer to estimate disturbances within a finite time. We then investigate an adaptive finite-time sliding mode controller incorporating an auxiliary system to mitigate the estimated disturbance and achieve precise 3-D path tracking while respecting the input constraints. The adaptive mechanism of this controller ensures fast convergence of the system while alleviating the chattering effects. Finally, we provide a rigorous theoretical analysis of the finite-time stability of the closed-loop system based on the Lyapunov functions. Utilizing a robotically-actuated magnetic manipulation system, experimental results demonstrate the efficacy of the proposed approach in terms of the control accuracy and convergence time.

Composite adaptive neural control for automatic carrier landing system with input saturation and output constraints

This paper investigates the automatic carrier landing control problem in the presence of model uncertainty, airwake disturbances, input saturation, and output constraints. Considering the performance requirements of the carrier-based aircraft, a composite adaptive neural controller is proposed based on the time-varying barrier Lyapunov function and backstepping control techniques. The radial basis function neural network is used to approximate the model uncertainty, where the neural network weight update law incorporating prediction and tracking errors further improves the convergence rate of the neural network and mitigates high-frequency oscillations. Furthermore, an adaptive disturbance compensation model is established to mitigate the adverse effects of airwake disturbances and estimation errors in the neural network. Based on the Lyapunov stability theory, it is proven that the proposed controller maintains the aircraft trajectory within the prescribed constraints and also ensures that all signals in the closed-loop control system are semiglobally uniformly ultimately bounded. Finally, comparative simulations are performed to demonstrate the effectiveness and superiority of the proposed composite adaptive neural control method.

Cluster consensus for nonlinear multi‐agent systems restricted with input saturation by event triggered control

AbstractThis article studies the cluster consensus problem for the nonlinear multi‐agent systems subject to input saturation under the context of event triggered control. Taking ordinary consensus object as a special case, this article considers the problem of cluster consensus. The event triggered mechanism is designed and the Zeno phenomenon is ruled out. The sufficient conditions of control protocol and range estimation of domain of attraction are formulated by the linear matrix inequalities for the constraints of input saturation and nonlinear terms existed in the system dynamics. Finally, the proposed results are validated by one example in the background of spring damping system.

Adaptive Finite-Time Constrained Attitude Stabilization for an Unmanned Helicopter System under Input Delay and Saturation

Adaptive Finite-Time Constrained Attitude Stabilization for an Unmanned Helicopter System under Input Delay and Saturation

Observer-based time-varying formation-containment tracking of general linear multi-agent systems with input saturation

In this article, we study the time-varying formation-containment (TVFC) tracking problem for linear multi-agent systems (MASs) and take the input saturation problem of the systems into account. An observer-based TVFC tracking protocol is proposed. It has been proven that the real leaders can realize the expected formation and track the virtual leader’s trajectory, and followers can get into the convex envelope spanned by the leaders. In addition, to avoid unexpected large chattering caused by nonzero input, we propose a continuous protocol. Under this protocol, each error is uniformly ultimately bounded and is able to converge to any small zero neighborhood. At the end, the feasibility of the TVFC theory is demonstrated by simulation examples.

Fast fixed-time extended state observer based command filtering backstepping control of free-flying flexible-joint space robots

System parameter perturbations, external disturbances, and input saturation issues seriously affect the on-orbit operation precision and rapid response capabilities of the free-flying flexible-joint space robots (FFSR). To this end, a fixed-time extended state observer (ESO) based non-singular command filtering backstepping controller is proposed. The fast fixed-time ESO is designed to estimate the parameter perturbations and external disturbances. To avoid the “computational explosion” caused by multiple derivatives of the virtual control law in backstepping control, a second-order command filter is employed to obtain the derivative of virtual control laws. Meanwhile, to reduce the filtering errors induced by the command filter, a non-singular fixed-time filtering error compensation algorithm is developed. Furthermore, considering the constraints of control moment gyroscope (CMG) and joint motors, an anti-saturation compensation algorithm is introduced to drive the system out of the saturated region rapidly, thus reducing actuator saturation effects on the control system performance. Theoretical analysis shows the proposed controller can ensure the system tracking error converges to any arbitrarily small neighborhood of the origin within fixed time. Simulation results demonstrate that the designed non-singular fixed-time command filtering backstepping controller exhibits fast convergence speed and high tracking accuracy.

Semi‐global output regulation of continuous‐time linear systems subject to input saturation via output feedback: A model‐free method

SummaryThis article considers the output regulation problem of continuous‐time linear systems subject to input saturation in the scenario that the system dynamics are unknown. Based on the low‐gain technique and the output feedback technique, we construct an output feedback control law to solve the output regulation problem with input saturation. Since the system dynamics are unknown, we estimate the feedback and feedforward terms in the control law with a two‐step data‐driven method. An output feedback adaptive dynamic programming algorithm is proposed to estimate the feedback term. An online updating algorithm based on output tracking error is proposed to estimate the feedforward term directly without solving the output regulation equations. Both algorithms don't rely on the measurement of the internal states of the exosystem and the original system. We show that the input saturation caused by the iterative feedforward gain matrix in the online updating algorithm doesn't affect the convergence of the algorithm. With these two data‐driven algorithms, the control law doesn't rely on the dynamics anymore. The low‐gain control law obtained by the model‐free method prevents input saturation from occurring and hence solves the output regulation problem. Finally, a numerical example is provided to validate the theoretical results.

Protocol-based secure guaranteed cost control of sampled-data T-S fuzzy system with denial-of-service attack and input saturation

This paper proposes a protocol-based secure guaranteed cost sampled-data controller design problem of Takagi-Sugeno (T-S) fuzzy system under denial-of-service (DoS) attack and input saturation. First, in the absence of an effective description for the characteristics of received signals on controller, a novel scheduling protocol is proposed according to the characteristics of the round-robin protocol and DoS attack, which can guarantee the specific sequence characteristic for control updates. Then, via introducing input delay approach and switched system modeling method, a time-delay switched system with fixed switching sequence is introduced to describe the considered system with DoS phenomenon. Moreover, some novel control criteria are presented to ensure the resulting closed-loop system reaches a required cost level under the obtained control law. And an optimization problem is proposed to compute the optimal upper of the specified cost level. Finally, a simulation example is presented to demonstrate the effectiveness of the algorithm.

Antisaturation fixed-time backstepping fuzzy integral sliding mode control for automatic landing of fixed-wing unmanned aerial vehicles

This paper proposes a robust adaptive fixed-time control for automatic landing systems (ALS) of small-scale fixed-wing UAVs exposed to wind disturbances, parametric uncertainties, and input saturation. The control structure consists of three subsystems, i.e., the guidance system, the attitude control system, and the thrust control system. Considering the landing geometry, the guidance system computes the desired Euler angles to stabilize the dynamics of altitude deviation, lateral deviation, and lateral speed. An auxiliary system is designed to compensate for the effect of input saturation in the attitude control system. The fixed-time method, the backstepping control (BSC), the fuzzy logic control (FLC), and the integral sliding mode control (ISMC) techniques are adopted to synthesize the control law. All three functional parts of the proposed ALS are equipped with a fixed-time fuzzy sliding mode disturbance observer (FSMDO). FLC computes the gains of signum functions adaptively to attenuate the chattering. Fixed-time convergence of the system errors to an arbitrary residual set is proved by comprehensive stability analysis. Finally, the comparative simulation results verify the better dynamic response and stronger robustness under the proposed ALS.

Trajectory tracking control of unmanned surface vehicle based on optimized barrier Lyapunov function under real ocean wave modeling

The state-constrained trajectory tracking control problem of unmanned surface vehicle (USV) under real wave interference is studied in this paper. This method is closer to the actual situation. Firstly, the interference of real ocean waves measured by ocean wave experiments on USV is considered. The wave spectrum and the equal interval method are used to simulate ocean waves in combination with the classical long-crested wave model. Secondly, the simulated wave is innovatively transformed into wave interference force, and the interference of the real wave is applied to the state constraint control of USV. The disturbance observer is used to observe and compensate for the external real wave interference, and the input saturation problem in real situations is fully considered. Furthermore, this paper proposes an improved logarithmic constraint function, which pre-set the performance function to constrain the trajectory tracking position error of the USV within a reasonable range. Finally, the rationality and effectiveness of the control strategy are verified by simulation.

Finite-time error constraint control for multi-AUV systems with unknown uncertainties based on observer and tan-type barrier Lyapunov function

PurposeAutonomous underwater vehicle (AUV) is widely used in resource prospection and underwater detection due to its excellent performance. This study considers input saturation, nonlinear model uncertainties and external ocean current disturbances. The containment errors can be limited to a small neighborhood of zero in finite time by employing control strategy. The control strategy can keep errors within a certain range between the trajectory followed by AUVs and their intended targets. This can mitigate the issues of collisions and disruptions in communication which may arise from AUVs being in close proximity or excessively distant from each other.Design/methodology/approachThe tracking errors are constrained. Based on the directed communication topology, a cooperative formation control algorithm for multi-AUV systems with constrained errors is designed. By using the saturation function, state observers are designed to estimate the AUV’s velocity in six degrees of freedom. A new virtual control algorithm is designed through combining backstepping technique and the tan-type barrier Lyapunov function. Neural networks are used to estimate and compensate for the nonlinear model uncertainties and external ocean current disturbances. A neural network adaptive law is designed.FindingsThe containment errors can be limited to a small neighborhood of zero in finite time so that follower AUVs can arrive at the convex hull consisting of leader AUVs within finite time. The validity of the results is indicated by simulations.Originality/valueThe state observers are designed to approximate the speed of the AUV and improve the accuracy of the control method. The anti-saturation function and neural network adaptive law are designed to deal with input saturation and general disturbances, respectively. It can ensure the safety and reliability of the multiple AUV systems.

A novel control approach for discrete-time 2D Roesser systems under input saturation and intrinsic nonlinearity: A region of stability investigation

This paper presents the control system design for the nonlinear discrete-time Roesser systems under saturated control input. A deficiency in the existing literature has been addressed in this study for the control of two-dimensional (2D) systems. A generalized boundary condition analysis is presented in the form of tractable invariant sets for the derivation of region of stability to design a suitable state feedback control. A mechanism for the evaluation of controller parameters is presented by considering the generalized structure of 2D Lyapunov function. The work has been extended when external disturbances are present in the 2D systems, and a robust design condition by accounting the perturbations as well as the input saturation has been established. In comparison to the existing works, a control system design for 2D Roesser systems under input saturation and intrinsic nonlinearity by application of a generalized Lyapunov function has been revealed. Furthermore, a tractable 2D region of stability for the local control of the 2D systems is achieved, rather than the conventional global controllers. Furthermore, a method has also been studied for obtainment of the controller gain matrix through convex optimization regarding the complete structure of the 2D Lyapunov function. Simulation results are provided for the stabilization of an unstable nonlinear 2D system under input saturation.

Distributed state constraint containment control of multi-AUV formation with unknown control direction

The control problem of multi-autonomous underwater vehicle (multi-AUV) formation systems is a hot issue in current research. The research goal is to make the formation have a more comprehensive ability to deal with emergencies under higher control accuracy. In this paper, input saturation, disturbances, and system uncertainties are considered. To achieve the convergence of system containment errors, a state constraint containment control method is proposed for multi-AUV systems with unknown control direction. Combined with unknown control direction, new auxiliary variables are constructed to compensate the input saturation. On this basis, the follower reference trajectories and errors are defined. To constrain some system states, the tan-type barrier Lyapunov function (TBLF) is proposed. The estimated values of system uncertainties and disturbances can be obtained by neural network. Compared to other works, the amount of data generated by neural network is further reduced by the optimized adaptive law in this study. The unknown control direction problem is handled based on Nussbaum function, and its limitation range is expanded. The designed control method ensures the stable operation of formation systems. The containment errors can converge to a small neighborhood of zero. By comparing the numerical simulation results with other work, the advantages of the control algorithm proposed in this paper has been verified.

Optimal iterative learning control under varying iteration lengths with input saturation

Optimal iterative learning control under varying iteration lengths with input saturation

Research on the control of thrust vectoring turbojet aircraft with uncertainties and input saturation based on fixed‐time control

AbstractOne‐dimensional thrust vectoring turbojet vertical takeoff and landing (VTOL) aircraft have attracted research attention due to their high thrust‐to‐weight ratios and their solution for the slow speed response of turbojet engines. However, there are some uncertainties and physical limitations in their systems, such as external disturbances, unknown parameters and input saturation. To improve the accuracy and convergence speed of trajectory tracking, a fixed‐time control method that is robust to saturation is proposed. The system dynamics are established, and an auxiliary system is built within a fixed time control framework to address the influence of input saturation and increase the error convergence rate. Nonsingular fast terminal sliding mode technology is combined with a few adaptive laws to ensure the robustness of the closed‐loop system against dynamic uncertainties and improve the precision of steady‐state control. The stability of the control system is proven based on Lyapunov, and the controller parameters are optimized based on particle swarm optimization (PSO). The proposed method based on fixed‐time stability guarantees that the states of the closed‐loop system can reach the residual set around zero within the designed time, and an expression for the upper bound on the convergence time is given. Finally, numerical simulations demonstrate the superiority of the proposed method based on the error integral criterion.

Distributed avoidance-accommodating flexible performance approach for adaptive formation tracking of underactuated surface vehicles against moving obstacles

A novel strategy for formation tracking of multiple uncertain underactuated surface vehicles is introduced in this study, to maintain the prescribed formation performance in the presence of moving obstacles with unknown velocities. Unlike the existing methods for prescribed formation performance control, our key contribution is the development of distributed avoidance-accommodating flexible performance functions (FPFs). These functions prevent deviation from the prescribed performance bounds while navigating around moving obstacles, considering input saturation and model uncertainties. We design local adaptive formation controllers by using distributed posture errors and avoidance-accommodating FPFs. Auxiliary signals that facilitate adjustment of the posture errors and performance functions during obstacle avoidance are derived using a recursive design that ensures Lyapunov stability. Additionally, command filters for virtual control laws are redesigned as saturation-compensating filters to solve the input saturation problem. Consequently, the proposed controller ensures the prescribed distributed formation performance, even in scenarios involving moving obstacles and input saturation, a capability lacking in conventional prescribed performance-based formation controllers, which can become unstable in such scenarios. The theoretical findings of this study are validated through comparative simulations.