Input Saturation Nonlinearity Research Articles

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 Adaptive-Neural Finite-Time Consensus Control for Stochastic Nonlinear Multiagent Systems Subject to Saturated Inputs.

In this article, the problem of distributed finite-time consensus control for a class of stochastic nonlinear multiagent systems (MASs) (with directed graph communication) in the presence of unknown dynamics of agents, stochastic perturbations, external disturbances (mismatched and matched), and input saturation nonlinearities is addressed and studied. By combining the backstepping control method, the command filter technique, a finite-time auxiliary system, and artificial neural networks, innovative control inputs are designed and proposed such that outputs of follower agents converge to the output of the leader agent within a finite time. Radial-basis function neural networks (RBFNNs) are employed to approximate unknown dynamics, stochastic perturbations, and external disturbances. To overcome the complexity explosion problem of the conventional backstepping method, a novel finite-time command filter approach is proposed. Then, to deal with the destructive effects of input saturation nonlinearities, the finite-time auxiliary system is designed and developed. By mathematical analysis, it is proven that the mentioned MAS (injected by the proposed control inputs) is semiglobally finite-time stable in probability (SGFSP) and all consensus tracking errors converge to a small neighborhood of the zero during a finite time. Finally, a numerical simulation onto a group of four single-link robot manipulators is carried out to illustrate the effectiveness of the suggested control scheme.

Bipartite Consensus of Heterogeneous Multi-Agents Under Input Saturation Over Signed Graphs

This brief addresses the problem of bipartite consensus for linear multi-agent systems (MASs) with heterogeneous dynamics susceptible to input saturation over a signed graph under antagonistic interactions. Prior to extending the findings to directed signed graphs, a theoretical examination of the bipartite consensus for undirected signed graphs is conducted. Input saturation is addressed by using a generalized sector condition. With the aid of the Lyapunov theory, it has been shown that for the MASs with heterogeneous dynamics stability and bipartite consensus can be accomplished. To the best of our knowledge, a bipartite consensus control approach for heterogeneous MASs with input saturation nonlinearity, connected via directed signed graphs, has been considered for the first time. The validity of the given results is demonstrated by a numerical example.

A delay-kernel-dependent approach to saturated control of linear systems with mixed delays

This article proposes a delay-kernel-dependent approach to deal with the saturated control problem of linear systems subject to mixed delays: discrete delay and distributed delay considering kernel. By combining the state vector and the distributed delay with kernel, a new polytopic representation strategy is used to cope with the nonlinear input saturation function. By choosing a Lyapunov–Krasovskii functional and applying an integral inequality both related to the distributed delay kernel, novel and less conservative results are provided to ensure the system stability. Finally, an example is simulated to display the advantages of the developed approach.

Adaptive fixed‐time minimal learning force/position control of uncertain manipulators subject to input saturation

SummaryThis article solves the fixed‐time force/position control problem for constrained manipulators in the presence of input saturation and uncertain dynamics. Under the fixed‐time stability theory, a novel fixed‐time auxiliary dynamic system (ADS) is first presented to compensate for the effects of input saturation nonlinearity. System uncertainties are estimated by using radial basis function neural networks (RBF NNs) and only need to tune one neural parameter online. In addition, with a fixed‐time sliding mode surface and the proposed fixed‐time ADS, a novel fixed‐time adaptive neural force/position controller is designed which can not only ensure the fixed‐time stability of the position tracking error but also enable the manipulator to track the desired force trajectory. By using the Lyapunov method, the boundedness of all signals in the closed‐loop system is proved. Finally, the effectiveness of the proposed method is demonstrated by comparative simulation works.

A Barrier Neuroadaptive Dynamic Surface Control Approach for Tank Gun Control Systems With Input Saturation

In harsh battlefield environments, tanks have to encounter some nonlinear characteristics including frictional moment, gear backlash and parameter drifts, etc. The existence of such nonlinear characteristics makes the controller design of tank gun control systems (TGCSs) challenging. In this paper, a barrier neuroadaptive control approach is proposed to handle the uncertainties and nonlinearities, so as to achieve satisfactory tracking performance for TGCSs. With a time-varying barrier Lyapunov function employed in controller design, the output error of TGCS is restricted within the preset bound during the control process. A radial basis function (RBF) neural network is built to approximate the uncertainties in tank gun control systems. An anti-windup control strategy is developed to deal with the input saturation nonlinearity, with a Nussbaum function used to compensate for the nonlinear term arising from input saturation. By reasonably applying filtering error into output-constrained adaptive backstepping control design, the three steps in the traditional backstepping control design are reduced to two steps. The asymptotic stability of the closed-loop TGCSs is proven by Lyapunov theory. Finally, a simulation example is presented to verify the effectiveness of the proposed control scheme.

Adaptive Neural Network Control for a Class of Fractional-Order Nonstrict-Feedback Nonlinear Systems With Full-State Constraints and Input Saturation.

This article addresses an adaptive neural network (NN) constraint control scheme for a class of fractional-order uncertain nonlinear nonstrict-feedback systems with full-state constraints and input saturation. The radial basis function (RBF) NNs are used to deal with the algebraic loop problem from the nonstrict-feedback formation based on the approximation structure. In order to overcome the problem of input saturation nonlinearity, a smooth nonaffine function is applied to approach the saturation function. To arrest the violation of full-state constraints, the barrier Lyapunov function (BLF) is introduced in each step of the backstepping procedure. By using the fractional-order Lyapunov stability theory and the given conditions, it proves that all the states remain in their constraint bounds, the tracking error converges to a bounded compact set containing the origin, and all signals in the closed-loop system are ensured to be bounded. Finally, the effectiveness of the proposed control scheme is verified by two simulation examples.

ESHLOS guidance for neuro-adaptive path following control of underactuated surface vessels

This paper proposes a neuro-adaptive path following control scheme based on ESHLOS guidance law for underactuated surface vessels with unmeasured linear velocities. Based on two extended state observers, an ESHLOS guidance law is designed, where the guidance law not only calculates the desired heading angle and surge velocity signals, but also compensates the unknown sideslip angle. Then, neuro-adaptive path following controllers are proposed to track the desired signals via backstepping technique. The hyperbolic tangent function is applied to model input saturation nonlinearity, and adaptive radial basis function neural networks are used to offset the lumped disturbances including external environmental disturbances, model uncertainties. Besides, a high-order tracking differentiator is introduced to generate derivatives of desired heading angle, so that the computational burden inherent in backstepping technique is reduced. Based on the Lyapunov functions, it is proven that all error signals of the closed-loop system are bounded. Finally, simulation results are utilized to reveal the efficacy of the presented approach.

Adaptive finite‐time prescribed performance tracking control for unknown nonlinear systems subject to full‐state constraints and input saturation

AbstractIn this article, an adaptive finite‐time prescribed performance tracking control scheme is developed for a class of strict‐feedback unknown nonlinear systems with both full‐state constrained and input saturation. To deal with the full state constraint, a distinctive method of employing a barrier function based transformation is used rather than the barrier Lyapunov function based method, and thus the undesirable “feasibility conditions” are completely eliminated. To overcome the problem of input saturation nonlinearity, the smooth nonaffine function is adopted to approximate the input saturation function. Then, with the aid of a new nonlinear mapping technique, a low‐complexity adaptive finite‐time prescribed performance tracking controller is designed by the dynamic surface control based backstepping method, which can guarantee that the tracking error can converge to a small fixed region at settling time with fast convergence rate and always stays within the region later, simultaneously, all the signals in the closed‐loop system are bounded. Finally, simulation results show the effectiveness of the proposed control scheme.

Terminal sliding-mode control for input-constrained free-float space manipulator via learning-based adaptive uncertainty rejection

The free-float space manipulator (FFSM) control problem subject to coupling dynamics, uncertainties, and input saturation constraints is investigated in this paper. The screw-based dynamical model is established through the Lagrangian equation and Hamilton’s variational principle such that the posture of the rigid body can be described uniquely and globally. The derived dynamics is then reduced to a decoupled one in the light of the conservation of the momentum. On this basis, a novel anti-windup finite-time sliding-mode control strategy is investigated to guarantee the tracking performance in the joint space of FFSM, where a learning-based adaptive neural network is designed to estimate the uncertainties. The approximation error is inhibited by a tanh-type slow-varying adaptive law which is integrated into an auxiliary system to compensate for input saturation nonlinearities. With the contributions above, the stability of the proposed nonsingular terminal sliding-mode (NTSM) controller is comprehensively proved. Comparative simulations based on a 6-DOF FFSM confirm the validity of the proposed control scheme.

Robust Integrated Guidance and Control Design for Angle Penetration Attack of Multimissiles

Angle penetration attack ability plays a more and more important role for missiles in modern warfare, and the traditional separate guidance and control system design problem is the key to restrict the improvement of time-sensitive attack and cooperative attack ability of multimissiles. Firstly, the deviation control strategy of line-of-sight angle and attack angle is put forward in this paper, and the integrated guidance and control system model with impact angle constraint is established, according to the characteristics of angle penetration attack. Then, an integrated guidance and control controller for angle penetration attack is designed by using adaptive dynamic surface control, with the dynamic constraints, nonlinear input saturation, and terminal line-of-sight and attack angle constraints concerned. In order to ensure the robustness of the system, nonlinear disturbance observers are introduced to estimate the uncertainty of the system model. Finally, the stability of the integrated design method is proven based on the Lyapunov theory. Simulation results verify the effectiveness of the integrated guidance and control design method proposed in this paper in multimissile angle penetration attack.

Neuroadaptive learning algorithm for constrained nonlinear systems with disturbance rejection

AbstractFor practical plants, there are not only inevitable endogenous and exogenous disturbances, but also constraint demands for control input amplitude, output performance, and system states. The existing controllers are difficult to handle the aforementioned control issues simultaneously and may be affected by “explosion of complexity.” In this work, we will develop a neuroadaptive learning algorithm for constrained nonlinear systems with disturbance rejection. In detail, the performance prescribed function and time‐varying barrier Lyapunov functions will be constructed to achieve the prescribed output performance and time‐varying state constraints, respectively. Furthermore, the neural network adaptive control and the extended state observers will be combined to respectively estimate the endogenous uncertainties and exogenous disturbances on‐line and meanwhile compensate for them feedforwardly. In particular, a filter will be introduced to estimate the virtual control law at each procedure, and this filtered value will replace its actual value in synthesizing the controller. In addition, the filtering errors and input saturation nonlinearity will be compensated by introducing an auxiliary system. Eventually, the whole closed‐loop stability is strictly guaranteed and the achievable control performance is verified by the application results.

Event-triggered adaptive neural tracking control for MSVs under input saturation: An appoint-time approach

This paper addresses an event-triggered tracking control issue for marine surface vessels (MSVs), which suffers from uncertain dynamics, unknown external disturbances and input saturation. To facilitate the implementation of backstepping design procedure, the input saturation nonlinearity is replaced by a smooth Gaussian error function. Under the backstepping design framework, introducing a nonlinear transformation and integrating the indirect adaptive neural, single parameter learning and event-triggered control techniques, a novel event-triggered neuroadaptive appoint-time tracking control scheme is proposed. Compared with most existing results, the proposed control solution is of the following notable characteristics: (1) the convergence time and accuracy of the position and velocity errors are determined by designer offline; (2) only one unknown parameter needs to be updated, which reduces the computational burden of control system greatly; (3) it decreases mechanical wear of the MSV actuators by reducing the response frequency of actuators to the control command. The theoretical analyses validate that all signals of the closed-loop trajectory tracking control system are bounded. Simulation results illustrate the effectiveness of the developed scheme.

Adaptive neural networks force/position control of uncertain manipulators subject to input saturation and output constraints

In this work, considering the influence of input saturation and time-varying output constraints, an adaptive neural networks force/position control method is proposed for a class of uncertain robotic manipulators in contact with the external environment. Radial basis function neural networks are introduced to approximate the system uncertainty and only one parameter needs to be updated online. The output constraints are satisfied by converting the constrained system to an unconstrained one. Moreover, an auxiliary dynamic system is applied in the transformed unconstrained system to handle the input saturation nonlinearity and the Moore–Penrose pseudo-inverse term is introduced for controller design. All signals in the closed-loop system are proved to be bounded by using the Lyapunov method. To show the good performance of the given scheme, comparative simulation is conducted on a two-joint manipulator, which is controlled by the proposed adaptive neural networks force/position tracking controller and a conventional force/position controller without considering input saturation and output constraints. Simulation results show that the adaptive neural network force/position controller has better control performance than the traditional method.

ANN-Based vibration control of an aerial refueling hose system with input nonlinearity and prescribed output constraint

An adaptive artificial neural network (ANN) boundary control scheme is developed for an autonomous aerial refueling hose system in this study. The objectives of this paper are 1) to guarantee the state of the system uniformly bounded, 2) to make the system output meet the prescribed performance, that is, −χa(t)<y(l(t),t)<χb(t). The proposed novel control law can achieve control objectives by suppressing vibrations of the hose. The unmodeled dynamics of the system are handled by the approximation ability of the designed ANN. The Nussbaum function is employed to construct an auxiliary control signal to deal with the input saturation nonlinearity of the system. By applying the novel control law, the state of the closed-loop system is uniformly bounded which is proved by Lyapunov’s direct method. Without violating the asymmetric time-varying prescribed function on system output is obtained by the barrier Lyapunov function. Extensive numerical simulations are performed to confirm the efficiency and efficacy of the proposed novel control strategy which allows multiple control objectives. The simulation results show that the output constraint is never violated, which is guaranteed by the asymmetric Lyapunov function.

Event-Triggered Adaptive Neural Tracking Control of Flexible-Joint Robot Systems With Input Saturation

This paper investigates an event-triggered adaptive neural tracking control issue for flexible-joint robot (FJR) systems subject to unknown dynamic and input saturation. To enable the backstepping design framework to be implemented, the input saturation nonlinearity is replaced by a smooth function. In the control design, the dynamic surface control (DSC) and adaptive neural techniques are used to handle the “explosion of complexity” issue and unknown dynamics, respectively. Furthermore, to reduce the calculated burden caused by the adaptive neural reconstruction technique, three virtual parameters are updated by using the single-parameter-learning approach. To decrease the frequency of actuator response to the control command for reducing the mechanical wear of actuator, an event triggering mechanism is established between the control law and actuator. Finally, an event-triggered adaptive neural tracking control solution is proposed, which is endowed the advantages as: (1) it does not need any <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> knowledge of FJR systems; 2) it only needs to update three unknown parameters; 3) it can reduce the transmission frequency of the control commands and the response rate of the actuator. Using the Lyapunov stability theory, the proposed event-triggered control solution ensures that all signals of the closed-loop tracking control system are bounded. Finally, the simulation results verify the effectiveness and superiority of the proposed control scheme.

Observer-Based Control of LPV Systems with Input Delay and Saturation and Matched Disturbances via a Generalized Sector Condition

This paper examines the control design for parameter-dependent input-delay linear parameter-varying (LPV) systems with saturation constraints and matched input disturbances. A gain-scheduled dynamic output feedback controller, coupled with a disturbance observer to cancel out input disturbance effects, was augmented with an anti-windup compensator to locally stabilize the input-delay LPV system under saturation, model uncertainty, and exogenous disturbances. Sufficient delay-dependent conditions to asymptotically stabilize the closed-loop system were derived using Lyapunov-Krasovskii functionals and a modified generalized sector condition to address the input saturation nonlinearity. The level of disturbance rejection was characterized via the closed-loop inducedL2-norm of the closed-loop system in the form of linear matrix inequality (LMI) constraints. The results are examined in the context of the mean arterial pressure (MAP) control in the clinical resuscitation of critical hypotensive patients. The MAP variation response to the injection of vasopressor drugs was modeled as an LPV system with a varying input delay and was susceptible to model uncertainty and input/output disturbances. A Bayesian filtering method known as the cubature Kalman filter (CKF) was used to estimate the instantaneous values of the parameters. The varying delay was estimated via a multiple-model approach. The proposed input-delay LPV control was validated in closed-loop simulations to demonstrate its merits and capabilities in the presence of drug administration constraints.

Generation of stable limit cycles in nonlinear sandwich systems with dead-zone nonlinearity and input saturation

This paper is concerned with the problem of generating stable limit cycles for a class of nonlinear sandwich systems with the sandwiched dead-zone nonlinearity. In this study, the considered sandwich systems are restricted to the potential problems of non-symmetric input saturation nonlinearity and unknown parameters. In this regard, based on the set stabilization approach and the shape of the desired limit cycle, an adaptive state feedback controller is constructed by using the backstepping technique in such a way that forces the system's output to oscillate with the wanted amplitude and frequency. Besides, to estimate the value of unknown parameters, the adaptive laws are extracted and the problem of the explosion of complexity in the traditional backstepping approach is solved via an effective differentiator. The Lyapunov stability analysis proves that all signals of the closed-loop system keep bounded. Finally, the simulation results of a practical example are provided to demonstrate the effectiveness of the proposed method.

Leaderless consensus control of nonlinear multi-agent systems under directed topologies subject to input saturation using adaptive event-triggered mechanism

This paper deals with the leaderless consensus controller design for nonlinear multi-agent systems (MASs) subject to the input saturation nonlinearity by using an event-triggered (ET) mechanism. An adaptive ET scheme has been established with variable threshold parameter for attaining an efficient control bandwidth. Linear parameter varying (LPV) formulation and region of stability investigation for dealing with the inherent nonlinearity and input saturation, respectively, are focused in the study. A consensus controller design condition has been formulated to ensure the regional stability, to determine the consensus protocol gains, to choose the parameters of ET mechanism, and to select an appropriate adaptation law for ET control. Elimination of Zeno behavior, based on nonlinearity bounds, for the adaptive ET mechanism has been ensured through a rigorous analysis. In contrast to excising methods, a directed communication topology, adaptive ET mechanism, and removal of Zeno behavior as well as elimination of the windup effect of saturation have been considered in our work. A simulation study has been provided for six robotic agents and comparison results with the existing method are revealed.

Robust saturated dynamic surface controller design for underactuated fast surface vessels including actuator dynamics

In this paper, a saturated trajectory tracking controller is proposed for high-speed surface vessels whose actuator dynamics is not negligible in practice. The hyperbolic tangent function is used as a stabilizer term to design a tracking controller via the dynamic surface control approach to improve the controller performance for all subsystems in the presence of input saturation, unmodeled dynamics, external disturbances and actuator nonlinearity. To this end, adaptive neural networks and adaptive robust controllers are combined to develop a novel saturated dynamic surface controller. Moreover, the proposed controller also compensates the effects of unknown system dynamics, actuator nonlinearity, external kinematic, dynamic and actuator disturbances simultaneously. By using Lyapunov’s stability method, it is shown that all signals of the closed-loop system are uniformly ultimately bounded and simulations are performed to verify the efficacy of the proposed control scheme.