Prescribed Tracking Performance Research Articles

A composite adaptive robust control for pneumatic servo systems with time-varying inertia

This article proposes a composite adaptive robust control for a pneumatic servo system with time-varying inertia to achieve a good tracking performance. The proposed design not only preserves the merits of both direct adaptive robust control and indirect adaptive robust control but also obtains a better performance of the working condition with time-varying inertias. Firstly, prescribed tracking performance is guaranteed without knowing the bounds of parametric and non-parametric uncertainties by leveraging a discontinuous projection and deterministic robust control technique. And a nonlinear tracking differentiator is used to obviate differential signal in backstepping. Secondly, the online parametric estimation algorithm is developed by intelligently integrating tracking error dynamics and physical plant dynamics. By effectively using the information of both tracking error and prediction error, a high adaptation gain can be used for achieving a faster parameter convergence and smaller tracking error. Moreover, exponential convergence of both tracking error and prediction error can be obtained under certain conditions. Lastly, comparative experiments on different conditions are carried out for a single-rod pneumatic cylinder driven by a proportional directional valve to demonstrate the superiority of the proposed method.

Trajectory planning and prescribed performance tracking control based on fractional-order observers for unmanned helicopters with unmeasurable states

The trajectory planning and tracking control problem is studied in this paper based on prescribed performance method (PPM) for the small-scale unmanned autonomous helicopter (UAH) with wind-gust disturbances (WGDs) and unmeasurable states. For the purpose, the nonlinear model with flapping dynamics is established, and the transformation performance function is used to ensure that the errors of trajectory tracking satisfy the corresponding performance. A fractional-order observer is designed for unmeasurable states to estimate the flapping angles in actual flight, and the fractional-order extended state observer (ESO) is constructed to estimate the WGDs, respectively. On the basis of PPM and the designed observers, the fractional-order theory-based backstepping trajectory tracking control scheme is developed for the UAH system, and the three-dimensional trajectory is planned by the improved wolf pack algorithm. Then the stability of the entire system is proven through strict theoretical analysis. Finally, the simulation analysis on the UAH is presented to demonstrate the efficiency of the designed method.

Adaptive global prescribed performance tracking control of uncertain robotic systems with unknown control directions

AbstractIn this article, we develop an adaptive global prescribed performance tracking control scheme for nonlinear multiple‐input multiple‐output (MIMO) robotic systems in the presence of unknown control directions and nonparametric uncertainties, in which the proposed solution mainly includes the following steps. Firstly, by constructing a global prescribed performance function, together with a series of transformations, the corresponding control guarantees the position tracking error evolves strictly within the prespecified region for all time, which is independent of initial conditions; Secondly, in order to cope with the problem of multiple unknown control directions, we make use of a symmetric matrix lemma to convert the underlying problem from matrix form to scalar form, so that the Nussbaum‐gain lemma for SISO systems becomes effective for MIMO systems with multiple inputs; In addition, we employ the integrable function to handle the nonparametric uncertainties, enabling the control scheme with the capability to drive the tracking error toward zero asymptotically. The effectiveness of the proposed control is validated via a two‐link rigid robotic manipulator.

A composite adaptive robust control for nonlinear systems with model uncertainties

AbstractThis article is concerned with a composite adaptive robust control (CARC) for non‐strict feedback nonlinear systems with model uncertainties including parametric uncertainties and uncertain nonlinearities. It is assumed that the model uncertainties of the nonlinear system are bounded but unknown. Firstly, prescribed tracking performance is achieved by the CARC control law even the unknown parameters are time‐varying. This is accomplished firstly by designing a discontinuous projection that confines the unknown parameters in an estimated region. Then the robustness of the closed‐loop system is guaranteed by leveraging the deterministic robust control philosophy. Also, a command filter has been designed to avoid computing complex derivatives of virtual control law in the backstepping procedure. Secondly, a composite adaptation law that intelligently integrates information of both tracking error and prediction error is constructed for improving the performance of controllers. The high adaptation gain of CARC leads to higher parameter convergence speed and smaller tracking errors. Moreover, if the actual parameters are within the design range, asymptotic stability can be achieved in presence of parametric uncertainties only. In addition, exponential convergence of tracking errors and parameters can be shown under certain conditions. Finally, numerical examples are made to validate the superiority and effectiveness of the proposed control scheme.

Fast fixed‐time attitude tracking control of spacecraft with prescribed performance

AbstractThe attitude tracking control problem of rigid spacecraft subjected to external disturbance and prescribed performance is studied. A fast fixed‐time stability theorem is firstly developed. A continuous disturbance observer is then designed with its estimation error can be driven into a tiny neighborhood containing zero within fixed time. Moreover, the spacecraft attitude tracking error constrained by prescribed performance function is transformed into an unconstrained dynamics. A disturbance observer‐based prescribed performance tracking controller is designed to stabilize the unconstrained dynamics within fixed time. It also means that the attitude tracking errors meet the prescribed performance as the stabilization of the unconstrained dynamics. Spacecraft simulation examples are finally given to validate the effectiveness of the proposed controller.

Prescribed Performance Back-Stepping Tracking Control for a Class of High-Order Nonlinear Systems via a Disturbance Observer.

Due to the widespread presence of disturbances in practical engineering and widespread applications of high-order systems, this paper first pays attention to a class of high-order strict-feedback nonlinear systems subject to bounded disturbance and investigates the prescribed performance tracking control and anti-disturbance control problems. A novel composite control protocol using the technique of a disturbance observer-prescribed performance control-is designed using the back-stepping method. The disturbance observer is introduced for estimating and compensating for unknown disturbances in each step, and the prescribed performance specifications guarantee both transient and steady-state performance of the tracking error to improve the control performance and result in better disturbance rejection. Moreover, the technique of adding a power integrator is modified to tackle controller design problems for the high-order systems. The Lyapunov function method is utilized for rigorous stability analysis. It is revealed that while the control performance completely remains in the prescribed bound, all states in the closed-loop system are input-to-state stable, and the tracking error and the disturbances estimating error asymptotically converge to zero simultaneously. Then, the feasibility and effectiveness of the proposed control protocol are verified by a simulation result.

Prescribed Performance Bipartite Consensus Control for Stochastic Nonlinear Multiagent Systems Under Event-Triggered Strategy.

In this article, the event-triggered bipartite consensus problem for stochastic nonlinear multiagent systems (MASs) with unknown dead-zone input under the prescribed performance is studied. To surmount the influence of the dead-zone input, the dead-zone model is transformed into a linear term and a disturbance term. Meanwhile, the prescribed tracking performance is realized by developing a speed function, which means that all tracking errors of MASs can converge to a predefined set in a given finite time. Moreover, the unknown nonlinear dynamics are approximated by fuzzy-logic systems. By combining the dynamic surface approach and the Lyapunov stability theory, we design an adaptive event-triggered control algorithm, such that the bipartite consensus problem of stochastic nonlinear MASs can be achieved, and all signals are semiglobally uniformly ultimately bounded in probability of the closed-loop systems. Finally, simulation examples are proposed to verify the feasibility of the algorithm.

Prescribed Performance Tracking of Uncertain MIMO Nonlinear Systems in the Presence of Delays

In this article, we design a low-complexity state-feedback controller for uncertain multi-input and multi-output (MIMO) nonlinear systems, capable of imposing prespecified performance attributes (in terms of maximum steady-state error and minimum convergence rate) on the output tracking errors, in the presence of time-varying delays both in the state measurement and control input signals. The state measurement delay is considered known and the control input delay unknown though bounded by some known constant. The control design does not incorporate any knowledge regarding the controlled system nonlinearities and does not require derivatives of the desired trajectories. We verify the theoretical results by simulation studies performed on a two-link robotic manipulator.

Prescribed Performance Tracking Control for 2-D Plane Vehicle Platoons with Actuator Faults and Saturations

This paper studies the multi-lane fusion tracking control problem for the two-dimensional third-order nonlinear vehicle platoons with actuator faults and saturations. A novel class of performance functions is designed to guarantee that the platoon tracking errors under asymmetric constraints satisfy the pre-given performance. To achieve the multi-lane fusion tracking control, new third-order prescribed performance sliding-mode surfaces are proposed for nonlinear vehicle platoons. Further, the saturation steering wheel input and the fault-tolerant throttle/brake input are designed by using the adaptive neural network sliding mode control technique, respectively. They can steer the platoon tracking errors approach the predefined region in the preset finite time while avoiding collisions and maintaining communications. Finally, the effectiveness of the proposed control scheme is verified by using two simulation examples with comparisons.

Neural Network-Based Adaptive Asymptotic Prescribed Performance Tracking Control of Hydraulic Manipulators

Hydraulic manipulators are extremely complicated systems due to the highly nonlinear characteristics, strong coupling among multiple joints, and heavy modeling uncertainties, which greatly complicate the high-performance tracking controller development compared with conventional manipulators driven by electrical motors. To overcome the above obstacles, this article proposes a novel radial basis function neural network (RBFNN)-based adaptive asymptotic prescribed performance controller for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> -degrees of freedom (DOF) hydraulic manipulators. First, the entire manipulator system model containing actuator dynamics is derived. Then, the adaptive asymptotic prescribed performance controller is synthesized based on the backstepping framework, in which the RBFNN is employed to estimate the unknown joint coupling dynamics, while the RBFNN reconstruction error and uncertainties of the actuator dynamics are handled by the robust integral of the sign of the error (RISE) feedbacks. Meanwhile, a prescribed performance function (PPF), which characterizes both the certain transient and steady-state performance, is innovatively incorporated into the control design to restrict the joint tracking errors. The theoretical analysis proves that the proposed control strategy can achieve a prescribed tracking performance and the asymptotic stability of the whole closed-loop system can also be ensured. Finally, comparative simulations are conducted to verify the validity of the proposed controller.

Command‐filtered‐based neuroadaptive control for multi‐input multi‐output saturated nonstrict‐feedback nonlinear systems with prescribed tracking performance

SummaryIn this article, the prescribed performance control strategy is extended to multi‐input multi‐output nonstrict‐feedback nonlinear systems with asymmetric input saturation, and not only each element in tracking error vector converges to a prescribed small region within preassigned finite time, but also the converging mode during the preset time is prespecifiable and controllable explicitly. By blending the barrier function with novel speed function, a prescribed performance controller using command‐filtered‐based vector‐backstepping design framework is proposed to steer the tracking error vector for the first time, where the boundedness of filter errors is guaranteed by sufficiently small time constant and an error compensator is constructed to handle the effects of filter errors. To attenuate the adverse effects resulted from nondifferentiable input saturation, hyperbolic tangent function is utilized to estimate asymmetric saturation function such that the control input is designed as a new state variable with initial value of zero in augmented system. Nussbaum function is employed to overcome singularity problem caused by the differentiation of hyperbolic tangent function. At each step of backstepping design, the universal approximation property of neural network and the command filter system are utilized to approximate uncertain dynamics and to solve algebraic loop obstacle due to nonstrict‐feedback structure, respectively. Moreover, only one parameter needs to be updated online to cope with the lumped uncertain dynamics by virtual parameter technology, rendering a control strategy with low complexity computation. The validity of the presented controller is verified by theoretical analysis and two‐link robotic system.

Event-triggered adaptive tracking control of uncertain nonlinear systems with prescribed performance and actuator failures

This article studies adaptive prescribed performance tracking control problem for a class of strict-feedback nonlinear systems with parametric uncertainties and actuator failures. Firstly, in order to compensate the multiple uncertainties and eliminate the influence of actuator failure, a new adaptive tracking controller based on first-order filter technology will be proposed, which simplifies the algorithm design process. Then, by introducing an asymmetric state transition function, the transient and steady performances of the output tracking error are both constrained such that the predetermined performance control goal is achieved. Moreover, to reduce the communication burden from the controller to the actuator, the event-triggered mechanism is designed, and there will be no Zeno phenomenon. Based on Lyapunov stability theory, it is strictly proved that output signal can track the reference signal and all the signals of the closed-loop system are bounded. Finally, a simulation example is performed and the results demonstrate effectiveness of the proposed strategy.

Fixed-Time Prescribed Performance Adaptive Fixed-Time Sliding Mode Control for Vehicular Platoons With Actuator Saturation

This paper investigates a prescribed tracking performance vehicular platoon control problem with actuator saturation, dynamics uncertainties, and unknown disturbances. First, a novel Gaussian error function (GEF)-based saturation function is introduced to approximate nonsmooth actuator saturation of each vehicle in a smooth way. Then, a fixed-time performance function (FPF) is proposed. Subsequently, an adaptive fixed-time sliding mode control scheme is developed based on the GEF and the FPF, which guarantees all signals of the closed-loop system are bounded and the tracking error converges to a predetermined region in fixed time. Meanwhile, string stability and traffic stability are also guaranteed. Finally, the effectiveness of the proposed algorithm is verified through numerical simulations.

Global Output-Feedback Prescribed Performance Control of Nonlinear Systems With Unknown Virtual Control Coefficients

This article is concerned with the output-feedback tracking control problem for a class of nonlinear systems. The challenge lies in how to drive the tracking error to a prescribed region in a given time globally, under both unknown nonlinear functions and unknown virtual control coefficients. To deal with the unknown control direction, an orientation function is exploited in lieu of the Nussbaum gain technique, the supervisory switching strategy, and the parameter estimation approach. To attain global tracking performance, a tuning function is employed to adjust the tracking error, and a barrier function is used to combat this error. The resulting controller guarantees the prescribed tracking performance and the boundedness of the signals in the closed loop for any initial condition.

Funnel function-based adaptive prescribed performance output feedback control of hydraulic systems with disturbance observers

This study structures an adaptive prescribed performance output feedback controller for hydraulic systems with large uncertainties including disturbances and parametric uncertainties. Adaptive control is structured to approximate real system parameters. Based on estimated parameters, a nonlinear disturbance observer for largely mismatched disturbance and an extended state observer for matched disturbance and unmeasurable system states are integrated. Then, to guarantee prescribed tracking performance, an output feedback controller is proposed with uncertainty compensation based on the funnel function using the backstepping method. In addition, to avoid the occurrence of complex analytical calculations and “complexity explosion” in the backstepping method, a differentiator is adopted. Then, the Lyapunov method is utilized to prove the stability of the closed-loop system with estimation errors. Finally, experimental results were obtained to demonstrate that the proposed controller is valid.

Real-Time Implementation of the Prescribed Performance Tracking Control for Magnetic Levitation Systems

For magnetic levitation systems subject to dynamical uncertainty and exterior perturbations, we implement a real-time Prescribed Performance Control (PPC). A modified function of Global Fast Terminal Sliding Mode Manifold (GFTSMM) based on the transformed error of the novel PPC is introduced; hence, the error variable quickly converges to the equilibrium point with the prescribed performance, which means that maximum overshoot and steady-state of the controlled errors will be in a knowledge-defined boundary. To enhance the performance of Global Fast Terminal Sliding Mode Control (GFTSMC) and to reduce chattering in the control input, a modified third-order sliding mode observer (MTOSMO) is proposed to estimate the whole uncertainty and external disturbance. The combination of the GFTSMC, PPC, and MTOSMO generates a novel solution ensuring a finite-time stable position of the controlled ball and the possibility of performing different orbit tracking missions with an impressive performance in terms of tracking accuracy, fast convergence, stabilization, and chattering reduction. It also possesses a simple design that is suitable for real-time applications. By using the Lyapunov-based method, the stable evidence of the developed method is fully verified. We implement a simulation and an experiment on the laboratory magnetic levitation model to demonstrate the improved performance of the developed control system.

Compound conditions event‐triggered tracking control for nonlinear multiagent systems with nonlinear output faults

SummaryThis article is devoted to investigating the compound conditions event‐triggered prescribed performance tracking problem for strict‐feedback nonlinear multiagent systems with nonlinear output faults and unknown disturbances. A simplified event‐triggered sampling condition is designed to successfully reduce the number of state triggered design parameters. Besides, a compound conditions event‐triggered mechanism is constructed, which integrates state triggered and controller triggered simultaneously to reduce communication burden. Furthermore, by using disturbance observers and prescribed performance functions, unknown external disturbances are compensated and the tracking errors can converge into the prescribed boundary, respectively. Moreover, all the signals of the closed‐loop system are semiglobally uniformly ultimately bounded. Finally, the availability of the proposed control strategy is testified via simulation results.

Adaptive Tracking for Uncertain Switched Nonlinear Systems With Prescribed Performance Under Slow Switching

This article considers the problem of adaptive prescribed performance tracking control via slow switching for a general class of uncertain switched nonlinear systems (SNSs) with unmodeled dynamics (UDs) and nonstrict-feedback structure. The UDs are not in their form of the input-to-state practical stability and their state information is unmeasurable. By reassigning the function variables, the coupling effects between UDs and the prescribed performance function are eliminated through the iterative process. In virtue of the neural networks (NNs) approximation capability, a novel adaptive backstepping procedure is proposed without adding extra first-order filters. By choosing an appropriate slow switching law, all the signals of the closed-loop system are bounded, and the system output tracks the reference signal with a prescribed performance level (PPL).

An Adaptive Prescribed Performance Tracking Motion Control Methodology for Robotic Manipulators with Global Finite-Time Stability.

In this paper, the problem of an APPTMC for manipulators is investigated. During the robot’s operation, the error states should be kept within an outlined range to ensure a steady-state and dynamic attitude. Firstly, we propose the modified PPFs. Afterward, a series of transformed errors is used to convert “constrained” systems into equivalent “unconstrained” ones, to facilitate control design. The modified PPFs ensure position tracking errors are managed in a pre-designed performance domain. Especially, the SSE boundaries will be symmetrical to zero, so when the transformed error is zero, the tracking error will be as well. Secondly, a modified NISMS based on the transformed errors allows for determining the highest acceptable range of the tracking errors in the steady-state, finite-time convergence index, and singularity elimination. Thirdly, a fixed-time USOSMO is proposed to directly estimate the lumped uncertainty. Fourthly, an ASTwCL is applied to deal with observer output errors and chattering. Finally, an observer-based-control solution is synthesized from the above techniques to achieve PCP in the sense of finite-time Lyapunov stability. In addition, the precision, robustness, as well as harmful chattering reduction of the proposed APPTMC are improved significantly. The Lyapunov theory is used to analyze the stability of closed-loop systems. Throughout simulations, the proposed PPTMC has been shown to perform well and be effective.

Fuzzy adaptive observer–based resilient formation control for heterogeneous multiple unmanned aerial vehicles with false data injection attacks and prescribed performance

This paper addresses the resilient formation control problem for heterogeneous multiple unmanned aerial vehicles (multi-UAV) under false data injection (FDI) attacks and prescribed performance constraints. The case of both actuator and sensor attacks is considered simultaneously, and the multi-UAV can exchange the information through a directed communication network. A fuzzy adaptive observer (FAO) is first proposed to estimate the FDI attacks and the unmeasurable velocity information for each UAV. In order to transform the formation control of heterogeneous multi-UAV into a trajectory tracking control problem of individual UAVs, a bank of distributed estimators is designed to achieve the leader’s states by only using local information among neighboring UAVs. Then, by incorporating a novel tracking error transform method and fractional-order sliding mode control technique, a resilient prescribed performance tracking controller without velocity measurements is constructed. Furthermore, it is proved that all signals of the closed-loop formation control systems are uniformly ultimately bounded (UUB) stable under FDI attacks. Finally, the simulation results are given to verify the effectiveness and superiority of the proposed control strategy.