Saturation Constraints Research Articles

Adaptive Sliding Mode Control for Trajectory Tracking of Quadrotor Unmanned Aerial Vehicles Under Input Saturation and Disturbances

This paper addresses the challenging issue of trajectory tracking for uncertain quadrotor unmanned aerial vehicles (UAVs), particularly under the constraints of input saturation and external disturbances. It introduces adaptive laws for managing uncertainties in mass and inertia moments without requiring prior knowledge, ensuring effective control even with varying system parameters. To counteract the effects of input saturation, the study incorporates an auxiliary system designed to compensate for these limitations. Additionally, a disturbance observer (DO) is utilized to manage and mitigate the impact of time-varying external disturbances. The proposed control strategy integrates a sliding mode adaptive control approach with an inner–outer loop structure, enhancing robustness and adaptability. Numerical simulations demonstrate the effectiveness of the designed control strategy.

Event-triggered finite-time adaptive neural network control for quadrotor UAV with input saturation and tracking error constraints

In this article, an event-triggered finite-time adaptive neural network control tracking strategy is proposed for quadrotor unmanned aerial vehicle (UAV) with input saturation and error constraints. Firstly, the radial basis function neural networks (RBFNNs) are adopted to identify the unknown uncertainty of quadrotor UAV model from the installation errors, gyroscope errors and so on. An auxiliary equation is constructed to deal with input physical saturation from the actuator motors. Additionally, by combining the performance function and error transformation, the issue of error constraint is solved. Based on the Lyapunov stability theory and event-triggered mechanisms, a finite-time adaptive neural network scheme is developed to ensure that the closed-loop quadrotor UAV system is semi-globally practically finite-time stable, and save the computation, resources, and transmission load. Finally, the simulation results illustrate the good tracking performance of quadrotor UAV by using the proposed control strategy.

Event-based adaptive formation and tracking control with predetermined performance for nonlinear multi-agent systems

The article focuses on the event-based predetermined performance formation tracking control for uncertain nonlinear multi-agent systems. Each agent is subject to actuator saturation constraint and full-state constraints. To meet the full-state constraints, a barrier function-based nonlinear mapping method is employed instead of the barrier Lyapunov function, such that the undesirable “feasibility conditions” are eradicated. To overcome actuator saturation, the auxiliary systems are utilized to let the controller be designed under the framework of backstepping. The approximation capacity of RBF NNs and adaptive methods are adopted, which can solve unknown uncertainties. An event-triggered predetermined performance formation tracking control strategy is designed, which can guarantee that the agents form the prescribed formation shape in a predetermined settling time and have a fine transient and steady-state tracking performance, while reducing the communication burden from the controller to the actuator. At last, an example of unmanned aerial vehicles is given to test the availability of the results.

Data-Driven Model-Free Adaptive Containment Control for Uncertain Rehabilitation Exoskeleton Robots with Input Constraints

This paper presents a data-driven model-free adaptive containment control (MFACC) scheme for uncertain rehabilitation exoskeleton robots, where the robotic exoskeleton dynamics are uncertain with saturation constraints. To handle uncertainties of the robotic dynamics, a model-free adaptive control (MFAC) strategy is established by linearizing the robotic exoskeleton dynamics into an equivalent data model. Considering the integral additive effect of the traditional MFAC method, an improved MFAC controller is designed in this paper. Since actuators with saturation constraints constantly affect the safety of patients during rehabilitation training, we construct a new criterion function with active constraints for the critical function of the MFAC algorithm and adopt the Hildreth quadratic programming algorithm to find the constrained optimal solution to overcome this limitation. The proposed MFACC scheme is rigorously proven by the compression mapping method to demonstrate model-free stability. Finally, the proposed control scheme is verified to be effective by simulation studies of the robotic SimMechanics model.

Impulsive Formation Tracking of Nonlinear Fuzzy Multiagent Systems With Input Saturation Constraints

Impulsive Formation Tracking of Nonlinear Fuzzy Multiagent Systems With Input Saturation Constraints

Adaptive formation control for obstacle avoidance of USVs with asymmetric input saturation

Due to the complex maritime navigation environment, Unmanned Surface Vessels (USVs) are influenced by unknown nonlinear dynamics arising from external disturbances and internal uncertainties. Achieving effective formation control while maintaining obstacle avoidance performance presents significant challenges. This article proposes a Neural Networks (NNs) adaptive formation Artificial Potential Field (APF) obstacle avoidance control method for multiple USVs. By employing online updates of Radial Basis Function (RBF) NNs technology, the unknown nonlinear dynamics are approximated, thus addressing complex nonlinear dynamics problems. In scenarios involving multiple USVs navigating under high wind and wave conditions, collisions with obstacles frequently occur. To tackle this issue, a leader-follower control strategy is designed that effectively addresses risk assessment and obstacle avoidance under such challenging conditions. Additionally, to account for saturation constraints or potential faults in the controller inputs commonly encountered in engineering applications, it implements an asymmetric auxiliary control system. Furthermore, the Lyapunov stability theorem is utilized to ensure the stability of both the formation control and obstacle avoidance algorithms for multiple USVs. Finally, the effectiveness of the proposed algorithm is validated through simulations.

Manual steering and robust adaptive constrained control of ship autopilot

This study proposes two schemes for ship autopilot: the first is a follow-up mode, applying manual dynamics to the state-space-based underactuated large merchant ship (ULMS) model, using a steering wheel and joystick to emulate manual operation; the second is a Nav mode developed by path-following control. In this mode, a novel path-following control strategy is developed for ULMS with input saturation and delay, two novel auxiliary systems are employed to stabilize the plant with input constraints. The input delay auxiliary system (IDAS) effectively tackles the design challenges posed by input delay, while the input saturation auxiliary system (ISAS) is dedicated to generating actual control inputs under the constraint of saturation. Furthermore, the dynamic surface control (DSC) technique and the roust neural damping technique are introduced to mitigate the computational burden and simplify the controller structure, thereby enhancing the efficiency and performance of the entire control system. Lyapunov stability analysis proves the ship motion system is semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of these two schemes is verified through turning experiment, comparative simulations and a semi-physical simulation platform that integrates physical models with computer simulation technology.

Constrained H∞ control with gain switching for a nonlinear active suspension system matching non-pneumatic wheel

In this study, a constrained H ∞ controller with gain switching is put forward for the active suspension system to improve the overall performance of vehicles equipped with non-pneumatic wheels, considering the nonlinearity of wheel stiffness, actuator saturation, and output constraints. Firstly, a quarter-vehicle model incorporating active suspension and non-pneumatic wheel (NPW) is established experimentally. Secondly, the system model is linearized using Taylor series expansion and linear fractional transformation (LFT). A constrained H ∞ control strategy and a gain switching method based on road classification are proposed, taking into account the parameter uncertainty in linearization process and the variation of performance demands under different road conditions. Then, an L ∞ state observer is designed for the required system state, and the road roughness classifier based on grey wolf optimization (GWO) and probabilistic neural network (PNN) is developed to obtain the necessary road information. A bench test is finally performed using the reconstructed actual road as input. The test results validate the effectiveness and superiority of the proposed control strategy.

Saturation-tolerant prescribed control of MIMO nonlinear systems with actuator faults

This paper addresses the tracking control problem of a class of multiple-input-multiple-output nonlinear systems subject to actuator faults. Achieving a balance between input saturation and performance constraints, rather than conducting isolated analyses, especially in the presence of frequently encountered unknown actuator faults, becomes an interesting yet challenging problem. First, to enhance the tracking performance, Tunnel Prescribed Performance (TPP) is proposed to provide narrow tunnel-shape constraints instead of the common over-relaxed trumpet-shape performance constraints. A pair of non-negative signals produced by an auxiliary system is then integrated into TPP, resulting in Saturation-tolerant Prescribed Performance (SPP) with flexible performance boundaries that account for input saturation situations. Namely, SPP can appropriately relax TPP when needed and decrease the conservatism of control design. With the help of SPP, our developed Saturation-tolerant Prescribed Control (SPC) guarantees finite-time convergence while satisfying both input saturation and performance constraints, even under serious actuator faults. Simulations are conducted to illustrate the effectiveness of the proposed SPC.

Adaptive Tracking Control for Uncertain Unmanned Fire Fighting Robot With Input Saturation and Full-State Constraints

Adaptive Tracking Control for Uncertain Unmanned Fire Fighting Robot With Input Saturation and Full-State Constraints

Trajectory tracking control based on deep reinforcement learning and ensemble random network distillation for robotic manipulator

Abstract In general, the trajectory tracking of robotic manipulator is exceptionally challenging due to the complex and strongly coupled mechanical architecture. In this paper, precise track control of the robotic manipulator is formulated as a dense reward problem for reinforcement learning(RL). A deep RL(DRL) approach combining the soft actor-critic (SAC) algorithm and ensemble random network distillation (ERND) is proposed to address the tracking control problem for robotic manipulator. Firstly, an ERND model is designed, consisting of a module list of multiple RND models. Each RND model obtains the error by learning the target features and the predicted features of the environment. The resulting error serves as internal rewards that drive the robotic agent to explore unknown and unpredictable environmental states. The ensemble model obtains the total internal reward by summing the internal rewards of each RND model, thereby obtaining more accurately reflecting the characteristics of the manipulator in tracking control tasks and improving control performance. Secondly, combining the SAC algorithm with ERND facilitates more robust exploration capabilities in environments with input saturation and joint angle constraints, thereby enabling faster learning of effective policies and enhancing the performance and efficiency of robotic manipulator tracking control tasks. Finally, the simulation results demonstrate that the robotic manipulator tracking control task is effectively completed in dense reward problems through the combination of the SAC algorithm and ERND.

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.

Observer‐based adaptive control of vehicle platoon with uncertainty and input constraints

AbstractThis study focuses on the highway platoon driving mode and proposes a distributed adaptive control algorithm based on an observer. Firstly, the adaptive observer is designed to compensate for the effect of unknown driving resistance and thus enhance the adaptation ability of the system to uncertainty. Secondly, an auxiliary system is introduced to specifically address actuator saturation constraints, ensuring the stability of the platoon driving in extreme conditions. Lastly, combining an event‐triggered mechanism, a control strategy is designed to achieve the stability of the entire platoon while maximizing the conservation of communication resources. The algorithm's viability and efficiency are confirmed through simulation outcomes.

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.

Enhanced trajectory tracking control algorithm for ROVs considering actuator saturation, external disturbances, and model parameter uncertainties

In this study, an augmented model-based predictive control (AMPC) algorithm was designed for a work-class remotely operated vehicles (ROV) with actuator saturation constraints, model parameter uncertainty, and external disturbances. Firstly, model parameter uncertainties and external disturbances (primarily umbilical cable forces) were considered in the kinematic model of the ROV. The ROV's actuator saturation constraints were introduced when designing the optimal control problem (OCP). Secondly, Bellman's principle of optimality was applied to the solution process of the OCP, decomposing it into multiple easily solvable sub-optimization problems to reduce computational complexity. Then, the recursive feasibility and input-to-state practical stability (ISpS) of the AMPC algorithm were proven in the presence of model parameter uncertainties and external disturbance forces. It was also demonstrated that the state convergence region of the system employing the AMPC algorithm was smaller than that of the system using the min-max MPC algorithm when reaching a steady state. Finally, numerical simulations verified that under the influence of external disturbance forces, model parameter uncertainties, and positioning system noise, the ROV using the AMPC algorithm achieved higher accuracy in tracking the desired trajectory compared to the min-max MPC algorithm.

Consensus algorithms for double-integrator dynamics with different velocity and actuator saturation constraints

This paper considers consensus strategy design for double-integrator multi-agent systems with matched disturbances under a directed graph. Specifically, we consider the case where both the control inputs and velocities of the agents are subject to different and asymmetric constraints. A novel distributed algorithm exploiting saturation functions is proposed to achieve asymptotic consensus without violating the predefined velocity and actuator saturation constraints. Subsequently, we extend the obtained results to event-triggered communication, where agent position broadcasting occurs only when specific triggering conditions are met. We rigorously prove that there exists a positive minimum inter-event time to rule out Zeno behavior. Finally, the simulation results confirm the theoretical findings and illustrate the achievable performance.

Finite-time composite learning control for flexible-link manipulator based on disturbance observer

With the development of robotic technology and theory, there is an expectation for robots to operate in complex environments. This paper addresses the joint tracking control problem of flexible-link manipulator system under unknown external disturbances, modelling uncertainties, and actuator saturation constraints. A research is conducted, proposing a composite learning control scheme based on adaptive finite-time disturbance observer (AFTDO). The designed AFTDO can estimate the upper bound of unknown disturbances by adaptive laws, and a neural network controller is developed based on the AFTDO algorithm to compensate and suppress disturbances from multiple sources, ensuring the stability of all variables within a finite time. Simultaneously, a barrier Lyapunov function (BLF) is chosen to guarantee that the system satisfies constraints under flexible vibrations. Finally, through simulation comparisons with other control strategies, the feasibility and superiority of the proposed method are convincingly demonstrated.

Adaptive Iterative Learning Tracking Control for Nonlinear Teleoperators with Input Saturation

Addressing input saturation, external disturbances, and uncertain system parameters, this paper investigates the position tracking control problem for bilateral teleoperation systems with a time delay communication channel. Based on a composite energy function, we propose an adaptive iterative learning control (AILC) method to achieve the objective of position tracking under the alignment condition. This extends the existing research on the control of nonlinear teleoperation systems with time delay. The saturation constraint property of the Softsign function ensures that no state of the system exceeds its constraints. The controller learns to simultaneously deal with the uncertainty of system parameters online, reject external disturbances, and eliminate positional errors along the time and iteration axes. All signals in the system for any constant time delay are proved to be bounded. Ultimately, the performance of the proposed controller is further verified through numerical simulations.

Leader-Following Connectivity Preservation and Collision Avoidance Control for Multiple Spacecraft with Bounded Actuation

This paper investigates the distributed formation control of a group of leader-following spacecraft with bounded actuation and limited communication ranges. In particular, connectivity-preserving and collision-avoidance controllers are proposed for the leader with constant or time-varying velocity, respectively. The communication graph between the spacecraft is modeled via a distance-induced proximity graph. By designing a virtual proxy for each spacecraft, the spacecraft–proxy couplings address the actuator saturation constraints. The inter-proxy dynamics incorporated with a bounded artificial potential function fulfill the coordination of all proxies. In addition, the bounded potential function can simultaneously tackle connectivity preservation and collision avoidance problems. The distributed formation controllers are proposed for multiple spacecraft with constant or time-varying velocities relative to the leader. A sliding mode control approach and the proxies’ dynamics are used in the design of a distributed cooperative controller for spacecraft to address the cooperative problem between the followers and the leader. Numerical simulations confirm the effectiveness of the anti-saturation distributed connectivity preservation controller.

A new distributed robust H∞ control strategy for a class of uncertain interconnected large-scale time-delay systems subject to actuator saturation and disturbance

In the realm of large-scale systems, the complexity of controller design has long been exacerbated by the proliferation of decision variables and inherent conservatism. This study introduces a novel approach to address these challenges, presenting a new distributed robust controller design methodology tailored for large-scale systems grappling with disturbances, uncertainties, and actuator saturations. The primary objectives include reducing conservatism, minimizing decision variables, and significantly curtailing computation time. To surmount these hurdles, the research leverages descriptive and reciprocally convex methods, formulating the design procedure using linear matrix inequalities. This enables the adjustment of uncertain parameters and robust disturbance rejection, thereby ensuring stability in large-scale systems. Additionally, a feedback control law is proposed to accommodate saturation constraints and ensure the closed-loop system’s stability. Notably, the effectiveness of the proposed control scheme is demonstrated through the evaluation of a full-car active suspension system, which is partitioned into interconnected subsystems to a large-scale system. Comparative analyses underscore the superior performance and technical advancements offered by the proposed methodology over existing approaches.