Robust Tracking Control Research Articles

Robust tracking control for uncertain fuzzy systems with time delay and external disturbances

AbstractIn this article, robust tracking and disturbance rejection problem for Takagi–Sugeno fuzzy systems with time delay and external disturbances are discussed. Specifically, proportional‐integral controller with an enhanced equivalent‐input‐disturbance technique is constructed to force the output trajectories to track the bounded reference input signal even in the presence of external disturbances. Further, the resulting fuzzy control system can be represented as an augmented system with state delay and uncertainties and the output tracking problem is transformed into stabilization problem of the augmented system. In the stabilization analysis, the considered fuzzy system does not share the same membership functions with the proposed control. Moreover, the delay‐dependent stabilization criteria for the addressed fuzzy system are presented in the form of linear matrix inequalities by the virtue of augmented Lyapunov–Krasovskii functional. To be specific, the symmetric matrices involved in the Lyapunov–Krasovskii functional need not be positive definite. Ultimately, three numerical examples are offered to support the validity of the established theoretical results.

Design of robust path tracking controller using model predictive control based on steady state input

Design of robust path tracking controller using model predictive control based on steady state input

Robust adaptive finite-time course tracking control of vessel under actuator attacks

This paper studies the course tracking control problem of unmanned surface vessels under the influence of uncertain dynamics, external unknown disturbances, constraints, and actuator attacks. In the design of the control scheme, adaptive technology is applied to approach the uncertain dynamics of the system, and a nonlinear finite-time disturbance observer is established to reconstruct the actuator attack signal and the unknown time-varying disturbances online. Combining disturbance compensation and adaptive technology, a finite-time course tracking control scheme is designed. The control scheme does not need to obtain the prior knowledge of the model in advance, and it has good robustness in the face of uncertain dynamics within the system, external disturbances, and actuator attacks. A rigorous stability analysis is provided for the control scheme based on the Lyapunov stability theory. Finally, the simulation shows that the proposed control scheme can effectively resist the influence of actuator attacks and external uncertain disturbances.

Robust observer-based tracking control for polynomial uncertain systems via a homogeneous Lyapunov approach

In this paper, an observer-based tracking control problem is considered for a polynomial system with parameter uncertainties and external disturbances. Noting that some states are difficult to measure in practice, a polynomial state observer is employed to obtain the unknown states. Then a robust observer-based tracking controller is designed to force the states of the polynomial uncertain system to follow the ones of the reference model and satisfy H ∞ performance. By using a full-state-dependent homogeneous polynomial function, the solvability condition is derived for the observer-based tracking control strategy, which reduces conservatism. Sum of squares technique is utilised to calculate the corresponding observer and controller, effectively dealing with the calculation problem in polynomial systems. Simulation examples are given to illustrate the effectiveness of the presented control strategy.

Robust trajectory tracking control for collaborative robots based on learning feedback gain self-adjustment

Abstract. A robust position control algorithm with learning feedback gain automatic adjustment for collaborative robots under uncertainty is proposed, aiming to compensate for the disturbance effects of the system. First, inside the proportional-derivative (PD) control framework, the robust controller is designed based on model and error. All of the model's uncertainties are represented by functions with upper bounds in order to surmount the uncertainties induced by parameter changes and unmodeled dynamics. Secondly, the feedback gain is automatically adjusted by learning, so that the control feedback gain is automatically adjusted iteratively to optimize the desired performance of the system. Thirdly, the Lyapunov minimax method is used to demonstrate that the proposed controller is both uniformly bounded and uniformly ultimately bounded. The simulations and experimental results of the robot experimental platform demonstrate that the proposed control achieves outstanding performance in both transient and steady-state tracking. Also, the proposed control has a simple structure with few parameters requiring adjustment, and no manual setting is required during parameter setting. Moreover, the robustness and efficacy of the robot's trajectory tracking with uncertainty are significantly enhanced.

Multidimensional-Taylor-network-based robust optimal tracking control for MIMO nonlinear discrete-time systems

In practical engineering, system control is indispensable. However, due to the influence of model uncertainty, speed unavailability, input nonlinearity (such as actuator dead zone/fault), and multi-input coupling, the control results are not satisfactory. In this paper, a robust optimal tracking control strategy is proposed for a class of nonlinear multi-input-multi-output discrete-time systems with unknown uncertainties. This control strategy is to minimize the cost function in the process of uncertainty processing and stabilize the closed-loop system by establishing an adaptive controlling approach based on a combination of actor MTN and critic MTN based on the Multi-dimensional Taylor Network (MTN). By using the approximation property of MTN, the optimal control signal is generated by action MTN, which is used to approach the controller, and the cost function is approximated by critic MTN, which is tuned online because the cost function cannot be obtained in hands-on experience. By designing a new cost function, the amount of calculation in the control process is reduced, and the adaptive critic design control idea is integrated into the controller design to deal with the uncertainty of the system. The simulation results verify the effectiveness of the control strategy proposed in the essay.

Robust trajectory tracking control scheme using transformed velocities for asymmetric underactuated marine vehicles

The paper addresses the issue of trajectory tracking control for underactuated underwater vehicles whose model is described by quasi-velocities resulting from the decomposition of the inertia matrix. The control algorithm takes into account unmodeled dynamics and external disturbances. It is shown that such mathematical models can be diagonalized and described by inertial quasi-velocities (IQV). The control scheme consists of a kinematic velocity controller and a dynamic adaptive integral sliding mode control algorithm. The paper extends the concept based on velocity transformation and backstepping methods to systems with a symmetric inertia matrix. A proof of the stability of a closed system in IQV space was carried out. The proposed approach was verified on two 3 DOF models of underwater vehicles with constraints due to the application of thruster force limitations.

Robust fixed-time trajectory tracking control of the dynamic positioning ship with actuator saturation

This paper addresses the fixed-time trajectory tracking control and setpoint regulation problems for dynamic positioning (DP) ships subject to unknown time-varying disturbances, system uncertainties, and actuator saturation. To meet the resistance of the low-frequency disturbances and system uncertainties, a continuous fixed-time disturbance observer (FTDO) based on integral sliding mode and fixed-time control is constructed. A nonlinear auxiliary dynamic system is introduced to mitigate the inconsistency between command forces and actual control forces, in which the feedback of the bias Δτ guarantees the input constraints for the design of the proposed controller. The explosion-of-complexity problem inherent in traditional backstepping is addressed based on a nonlinear first-order filter. Furthermore, a robust fixed-time control law with constraints is developed to track the predefined trajectory and the desired setpoint. Theoretical analyses demonstrate the fixed-time stability of the closed-loop system via Lyapunov analysis. Numerical simulation results illustrate the effectiveness and robustness of the proposed control approach.

Robust adaptive three-dimensional trajectory tracking control scheme design for small fixed-wing UAVs

This paper aims to tackle the three-dimensional trajectory tracking problems of small fixed-wing unmanned aerial vehicles subject to nonlinearities, uncertainties and wind disturbances via adaptive techniques. The control objective is to efficiently control the thrust and the deflections of control surfaces to ensure the unmanned aerial vehicle arrives at a specified location within a given time frame. However, achieving this goal for small fixed-wing unmanned aerial vehicles can be challenging because the precise dynamic model and several parameters are not accessible, making most existing control strategies unworkable. Motivated by these facts, based on feedback linearization techniques, we derive linear models with equivalent disturbances to describe the translational dynamics without requiring precise aerodynamic force model information. To deal with the dilemmas where the norm bounds of equivalent disturbances depend on control inputs, system states, and unknown disturbances, a novel robust adaptive control strategy is designed for position control. Based on the assumption of two-time separation, the control scheme incorporates two parts, namely, a position controller containing the horizontal-plane and altitude parts and a robust filter-based attitude regulator. Also, to prevent chattering issues, we design a practical and robust adaptive position controller under which the tracking error is ultimately bounded The overall closed-loop stability is theoretically investigated based on the Lyapunov arguments. Hardware-in-loop simulation experiments are performed to testify our developed control scheme.

Robust Preview Path Tracking Control of Autonomous Vehicles Under Time-Varying System Delays and Saturation

Realistic uncertainties and disturbances cannot be ignored when striving towards high-performance autonomous driving. Meanwhile, advanced vehicular sensing technology enables more and more self-driving techniques to come out. Against this backdrop, this paper aims to holistically address the system uncertainties and disturbances in the path tracking control of autonomous vehicles (AVs) by the preview control theory to achieve superior control performance. First, unmeasureable multi-uncertainties and the external disturbance are considered simultaneously into the robust gain-scheduling framework with variable longitudinal velocity. Then, by the equivalent delay approach, ineluctable time-varying system delays are effectively handled. Next, the physical constraints of the steering system and direct yaw moment control (DYC) system are considered for practical implementation through robust set invariance theory. The parallel distributed compensation (PDC) technique and auxiliary feedback matrices approach are introduced for reducing design conservatism. After that, by incorporating the road curvature into the augmented system state, the path tracking preview control problem can be solved without online optimization. Thereafter, the closed-loop system stability and guaranteed performance have been proved through the Lyapunov- Krasovski approach. The proposed controller design is finally reformulated as the optimization problem based on linear matrix inequalities (LMIs) via specific convexification techniques. Finally, to verify the validity of the proposed controller, Software in Loop (SIL) tests with Carsim full-vehicle model under different dynamic conditions have been implemented.

Continuous–Discrete Observation-Based Robust Tracking Control of Underwater Vehicles: Design, Stability Analysis, and Experiments

This study addresses the tracking control problem of underwater vehicles using a new robust observation-based control scheme. The advantages of the robust integral of the sign of the error (RISE) control, as well as the saturation function and well-known super-twisting algorithm, have been exploited to design a saturated super-twisting RISE (S <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{+}$</tex-math> </inline-formula> RISE) control scheme. However, the proposed S <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{+}$</tex-math> </inline-formula> RISE method requires continuous state measurements. To resolve this issue, a continuous–discrete time observer (CDO) is proposed, which works in tandem with the proposed controller. The resulting control scheme is known as CDO-S <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{+}$</tex-math> </inline-formula> RISE. In addition to estimating disturbances, the proposed CDO solves the problem of multiple sampling rates of the sensors. To demonstrate the asymptotic stability of the resulting nonobservation-based closed-loop dynamics with the proposed S <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{+}$</tex-math> </inline-formula> RISE control scheme, Lyapunov arguments are proposed. Then, the exponential stability of the unperturbed closed loop with the proposed CDO, as well as with the proposed S <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{+}$</tex-math> </inline-formula> RISE controller, is studied based on the Lyapunov–Krasovskii concept. To verify the performance recovery of the overall observation-based closed-loop system CDO-S <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{+}$</tex-math> </inline-formula> RISE (controlled by the proposed S <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{+}$</tex-math> </inline-formula> RISE control scheme), an invariant set <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{A}_{\mathbb{R}}$</tex-math> </inline-formula> is determined using a composite Lyapunov–Krasovskii functional, which guarantees the convergence of the tracking errors to the origin. Several real-time experimental scenarios were conducted on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Leonard</i> underwater vehicle prototype to validate the efficiency and robustness of the proposed CDO-S <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{+}$</tex-math> </inline-formula> RISE scheme.

Robust Trajectory Tracking Control for Constrained Small Fixed-Wing Aerial Vehicles with Adaptive Prescribed Performance

A novel approximation-free adaptive prescribed performance control scheme for the longitudinal motion tracking of input and state constrained small fixed-wing UAVs is designed in this work. The proposed controller employs the adaptive prescribed performance technique to impose output performance specifications in accordance with actuation limitations regarding the amplitude and the rate of the control signal. Furthermore, state constraints are introduced to ensure the proper operation of the closed-loop system. The adoption of PPC methodology results in a low complexity control algorithm with easy gain selection which facilitates its practical implementation. Finally, a comprehensive simulation study as well as comparative simulation paradigms on an Aerosonde model clarifies and verifies the superiority and the effectiveness of the proposed controller to control the longitudinal motion of UAVs in the presence of wind gusts.

Practical adaptive robust tracking control of the dual-valve parallel electro-hydraulic servo system with reduced-order model

To meet the increasing demand for trajectory tracking accuracy and high-efficiency requirements in modern mobile machinery, this paper proposes a practical adaptive robust control method based on the dual-valve parallel electro-hydraulic servo system. Existing tracking control strategies for such servo systems rely on a backstepping method and assume that full states are known, which is stringent in practice. To cope with the problem, we reduce the mathematical model order of the studied system using singular perturbation theory in this paper, and only the position feedback is required for the control implementation. Then, to achieve high accuracy tracking control, a direct adaptive robust control scheme combing with a dynamic flow allocation layer is adopted to synthesize the controller. With this method, parameter uncertainties and load disturbance are rejected, and valve characteristics are considered in the dynamic flow allocation layer to solve the flow redundancy problem, respectively. Convergence of the simplified system tracking results is proved theoretically. Extensive co-simulations and experimental tests are carried out to illustrate the effectiveness of the proposed strategy, both tracking precision and flow distribution can be achieved efficiently by simple parameter adjustments in the field.

Distributed robust model predictive control-based formation-containment tracking control for autonomous underwater vehicles

The autonomous underwater vehicle (AUV) formation may be carried out in a complex maritime environment. The formation-containment tracking problem is faced with challenges due to limited input saturation and maritime safety constraints. Based on communication-measurement union, a navigation control integration framework is proposed to solve the poor observability of underwater acoustic communication interactions. Moreover, a control protocol based on distributed robust model predictive control is designed to efficiently coordinate cooperation between AUVs. With the proof of the Lyapunov theory, the proposed control method can achieve formation-containment tracking even in the presence of external disturbances. Finally, a 7-AUV formation-containment tracking numerical simulation is designed to verify the effectiveness of the proposed method.

Observer-based Finite-time Adaptive Robust Tracking Control for Nonlinear Stochastic Time-delay Systems With Full State Constraints and Input Saturation

Observer-based Finite-time Adaptive Robust Tracking Control for Nonlinear Stochastic Time-delay Systems With Full State Constraints and Input Saturation

Barrier function-based prescribed-performance adaptive attitude tracking control for spacecraft with uncertainties

This paper addresses the problem of robust adaptive attitude tracking control for spacecraft with mismatched and matched uncertainties. The idea of disturbance estimation and compensation is introduced into the control design. First, finite-time disturbance observers are developed for different channels of spacecraft based on barrier functions for achieving finite-time asymptotic estimates of unknown bounded uncertainties in the system. Second, a class of prescribed performance functions is considered in the design of the barrier function. The spacecraft attitude adaptive tracking control strategy with finite-time convergence capability and prescribed performance is proposed based on the designed finite-time disturbance observers and barrier function. Finally, the theoretical findings are verified by numerical simulations and compared with the simulation results of existing methods.

Design, analysis and experiment of robust adaptive repetitive angle tracking control for a one-DOF manipulator driven by pneumatic artificial muscles

There exist nonlinearities, uncertainties and time-varying characteristics in the system dynamics of manipulators driven by pneumatic artificial muscles (PAMs), which makes the accurate dynamic modeling and controller design challenging. In this paper, a robust adaptive repetitive control scheme is proposed to solve the periodic-trajectory tracking problem for a one-degree of freedom (one-DOF) manipulator driven by two PAMs. First, the system model of the one-DOF PAM-driven manipulator is analyzed and derived. Next, during output constraint design by using a barrier Lyapunov function, a sliding mode surface is reasonably constructed to compensate for the differential term of time-varying constraint parameter. Then, with the help of Lipchitz condition, signal replacement technique and reparameterization are implemented to deal with nonparametric uncertainties in the manipulator system for the subsequent uncertainty compensation by using difference learning method and robust feedback strategy. Moreover, the stability of closed-loop PAM-driven manipulator is proven theoretically by using Lyapunov synthesis. In the end, comparative experiments are provided on a self-built PAM testbed to demonstrated the effectiveness of the proposed robust adaptive repetitive control scheme.

Event-triggered adaptive finite time trajectory tracking control for Underactuated Vessel considering unknown time-varying disturbances

Abstract This paper aims to solve the finite-time trajectory tracking problem of underactuated surface ships under the influence of dynamic uncertainty, unknown external time-varying interference and limited communication resources, an event-triggered robust adaptive finite-time trajectory tracking control method for underactuated ships is designed by combing the existing trajectory tracking control methods and engineering needs in actual navigation. It can obviously improve the tracking accuracy of the ship, and complete the tracking task safely and efficiently. This scheme transforms the composite uncertain vector synthesized by uncertain parameters and external disturbances into a linear parameterized form. Next, considering the limitation of communication resources, a relative threshold event triggering mechanism is introduced to further extend the triggering time interval on the basis of the fixed threshold triggering scheme. Then, an event-triggered robust adaptive finite-time trajectory tracking control scheme is designed for underactuated ships, and a rigorous stability proof is provided for the finite-time trajectory tracking control scheme designed above through Lyapunov stability theory. Simulation experiment is carried out in MATLAB and the results show that the finite-time trajectory tracking control scheme proposed in this paper can effectively solve the problems of dynamic uncertainty, unknown time-varying interference from the outside world, and limitation of communication resources. This paper can provide theoretical support for the autonomous navigation of intelligent ships.

Neural Network-Based Robust Bipartite Consensus Tracking Control of Multi-Agent System with Compound Uncertainties and Actuator Faults

This paper addresses the challenging problem of bipartite consensus tracking of multi-agent systems that are subject to compound uncertainties and actuator faults. Specifically, the study considers a leader agent with fractional-order nonlinear dynamics unknown to the followers. In addition, both cooperative and competitive interactions among agents are taken into account. To tackle these issues, the proposed approach employs a fully distributed robust bipartite consensus tracking controller, which integrates a neural network approximator to estimate the uncertainties of the leader and the followers. The adaptive laws of neural network parameters are continuously updated online based on the bipartite consensus tracking error. Furthermore, an adaptive control technique is utilized to generate the fault-tolerant component to mitigate the partial loss caused by actuator effectiveness faults. Compared with the existing works on nonlinear multi-agent systems, we consider the compound uncertainties, actuator faults and cooperative–competition interactions simultaneously. By implementing the proposed control scheme, the robustness of the closed-loop system can be significantly improved. Finally, numerical simulations are performed to validate the effectiveness of the control scheme.

Robust Flight-Path Angle Consensus Tracking Control for Non-Minimum Phase Unmanned Fixed-Wing Aircraft Formation in the Presence of Measurement Errors

The robust flight-path angle consensus tracking control problem for multiple unmanned fixed-wing aircrafts is investigated in this paper, where the non-minimum phase properties and the presence of measurement errors are systematically addressed. A three-module control scheme is proposed for each aircraft: a Distributed Observer that obtains the available information from the reference system and the neighbor aircraft to provide the estimates of the reference states; a Casual Stable Inversion that calculates the bounded estimates of the desired input, desired external states, and most importantly, desired internal states to resolve the divergence issues caused by the non-minimum phase properties; and a Local Measurement Error Rejection Controller that includes a measurement error estimator (MEE) to actively compensate for the adverse effect of measurement errors to achieve robust consensus tracking control. Stability, convergence, and robustness of the proposed control are analyzed, showing that (1) the non-minimum phase issue can be systematically resolved by the designed Casual Stable Inversion to ensure aircraft internal stability and flight safety, and (2) the consensus tracking accuracy can be improved by tuning a single MEE parameter, which is favorable in practical applications to large-scale unmanned aircraft formations. Comparative simulation results with classic PID-based consensus control demonstrate the advantage of the proposed control in transient oscillations, steady-state tracking accuracy, and robustness against measurement errors.