State Feedback Designs for Nonlinear Systems

Actuator failure compensation for nonlinear systems which can be transformed into parametric strict-feedback form with zero dynamics is investigated. Direct adaptive compensation control schemes are developed to ensure asymptotic output tracking and stabilize the system despite the uncertainties in actuator failures as well as in system parameters. Two main cases are studied for adaptive actuator failure compensation: systems with stable zero dynamics, and systems with extra controls for stabilization. Design conditions on systems suitable for actuator failure compensation are clarified.

SummaryThis article develops a new framework of adaptive actuator failure compensation control for cooperative manipulator systems with parameter uncertainties in addition to actuator failures, and designs and analyzes effective actuator failure compensation schemes for such robotic systems. The new adaptive control design uses an integration of multiple individual failure compensators and direct adaptation to handle various types of uncertainties in such robotic systems. The design can also be used for concurrent actuator failure cases, to expand the capability of adaptive actuator failure compensation. With a complete proof and performance analysis, it is shown that the proposed control scheme guarantees the desired closed‐loop stability and asymptotic output tracking, despite actuator failures whose patterns, time instants and values are all unknown. Simulation results of a benchmark cooperative manipulator system are presented to verify the desired control performance of the system with both typical constant and square‐wave actuator failure signals.

An output feedback model reference adaptive controller is developed for a class of linear systems with multiple unknown time-varying state delays and in the presence of actuator failures. The adaptive controller is designed based on SPR-Lyapunov approach and is robust with respect to multiple unknown time-varying plant delays and to an external disturbance with unknown bounds. Closed-loop system stability and asymptotic output tracking are proved using suitable Lyapunov-Krasovskii functional and Simulation results are provided to demonstrate the effectiveness of the proposed controller.

This paper presents an output-feedback adaptive controller for a class of linear systems with unknown time-varying state delay and in the presence of actuator failures. We consider a common type of actuator failure in which some unknown system inputs may be stuck at some unknown fixed values and at unknown time instants. The adaptive controller is designed based on SPR–Lyapunov approach for relative degree one and two cases. Closed-loop system stability and asymptotic output tracking are proved using suitable Lyapunov–Krasovskii functional for each case. Simulation results are provided to demonstrate the effectiveness of the proposed results.

An optimal adaptive actuator failure compensation control scheme is proposed for a class of multi-input multi-output (MIMO) uncertain nonlinear continuous-time systems with redundant actuators subject to uncertain failures. Only single neural network is used in the proposed adaptive dynamic programming (ADP) scheme to simultaneously learn the infinite horizon cost function and the approximate optimal control input that minimizes the Hamilton-Jacobi-Bellman (HJB) equation. Besides, an uncertainty estimator is designed to estimate the uncertain dynamics and an adaptive parameter adjustment law is designed to estimate the actuator failure coefficients. Stability analysis and simulation results can demonstrate the effectiveness of the proposed method.

Actuator failure compensation problem for nonlinear systems is formulated and adaptive actuator failure compensation control with state feedback is investigated for feedback linearizable systems. Under different structure conditions which characterize different classes of systems, adaptive state feedback control schemes are developed for systems with uncertain actuator failures. It is proved that the proposed control schemes ensure asymptotic output tracking and closed-loop signal boundedness.

Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance

An adaptive failure compensation control scheme is developed based on linear quadratic (LQ) control for discrete-time possibly nonminimum phase systems with unknown actuator failures with characterizations that some unknown system inputs are stuck at some unknown fixed or varying values at unknown time instants. The failure compensation control problem is formulated as a new LQ control problem. Based on some results on new controller structures and design conditions developed in [9], a stable adaptive law is proposed for the estimation of uncertain parameters from both the plant and actuator-failures. The adaptive failure compensation controller is implemented with adaptive parameter estimates, for achieving closed-loop stability and output regulation. Simulation results are presented to verify the desired adaptive control performance in the presence of uncertain actuator failures.

This paper develops a framework of adaptive compensation of actuator nonlinearities with unknown parameters, for output feedback control of unknown multi-input multi-output linear time-invariant dynamic systems. A new controller parametrization is derived to deal with bilinear parameters from the actuator nonlinearity parameters and the dynamic system parameters, which, based on the LDU decomposition of the system high frequency gain matrix, is capable of overcoming the difficulty caused by a nondiagonal high frequency gain matrix and a special actuator nonlinearity parameter structure. The adaptive actuator nonlinearity compensation control scheme is a model reference adaptive control based design, employing an adaptive output feedback control law combined with an adaptive actuator nonlinearity inverse, to deal with parameter uncertainties in the system dynamics and actuator nonlinearities. Simulation results show the desired adaptive control system performance.

This study presents an adaptive decentralised dynamic surface control (DSC) approach for a class of large‐scale non‐linear systems with unknown non‐linear functions, unknown control gains, time‐varying delays and in the presence of unknown actuator failures. The considered actuator failures are modelled to cover both loss of effectiveness and stuck at some time‐varying values where the values, patterns and time occurrences of the failures are unknown. With the help of neural networks to approximate the unknown non‐linear functions, a novel adaptive actuator failure compensation controller is developed based on the backstepping method and the DSC approach. The appropriate Lyapunov–Krasovskii functionals are introduced to design new adaptive laws to compensate the unknown actuator failures as well as uncertainties from unknown non‐linearities and time delays. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed‐loop signals is guaranteed and the tracking errors are proved to converge to a small neighbourhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark and a chemical reactor system. The simulation results show the effectiveness of the proposed method.

This paper develops a new adaptive compensation control scheme for two linked mobile robots with actuator failurs. A configuration with two linked two-wheel drive (2WD) mobile robots is proposed, and the modelling of its kinematics and dynamics are given. An adaptive failure compensation scheme is developed to compensate actuator failures, consisting of a kinematic controller and a multi-design integration based dynamic controller. The kinematic controller is a virtual one, and based on which, multiple adaptive dynamic control signals are designed which covers all possible failure cases. By combing these dynamic control signals, the dynamic controller is designed, which ensures system stability and asymptotic tracking properties. Simulation results verify the effectiveness of the proposed adaptive failure compensation scheme.

Active vibration control using piezoelectric actuators in a networked and embedded environment has been widely applied to solve the rocket fairing vibration problem. However, actuator failures may lead to performance deterioration or system dysfunction. To guarantee the desired system performance, the remaining actuators should be able to coordinate with each other to compensate for the damaging effects caused by the failed actuator in a timely manner. Further, in the networked control environment, timing issues such as sampling jitter and network-induced delay should be considered in the controller design. In this study, a timing compensation approach is implemented in an adaptive actuator failure compensation controller to maintain the fairing system performance by also considering the detrimental effects from real-time constraints. In addition, time-delay compensation in the networked control system is discussed, which is able to reduce damaging effects of network-induced delays.

A state feedback output tracking adaptive control scheme is developed for plants with actuator failures characterized by the failure pattern that some inputs are stuck at some unknown fixed values at unknown time instants. This scheme relaxes the conditions on the controlled plant for desired plant-model output matching in the presence of actuator failures. New controller parametrization and adaptive law are developed under less restrictive conditions. All closed-loop signals are bounded and the plant output tracks a given reference output asymptotically, despite the uncertainties in actuator failures and plant parameters. Simulation results verify the desired adaptive control system performance.

An adaptive compensation control scheme is developed for a morphing aircraft model with actuator failures. Morphing actuators are special in the sense that they operate only at two states: on or off, and that they are used in large numbers to fulfill certain actuation function. We derive a failure model for morphing actuators and develop an adaptive scheme to estimate the actuation effectiveness and to update the number of actuators to be activated. A feedback control scheme is redesigned for adaptive actuator failure compensation, which ensures desired closed-loop stability and tracking properties. A simulation study with a linearized lateral dynamics model of the ICE aircraft is presented to demonstrate the system performance in the presence of uncertain actuator failures.

ABSTRACTA new neural adaptive compensation control approach for a class of multi-input multi-output (MIMO) uncertain nonlinear systems with actuator failures is proposed in this paper. In order to enlarge the set of compensable actuator failures, an actuator grouping scheme based on multiple model switching and tuning (MMST) is proposed for the nonlinear MIMO minimum phase systems with multiple actuator failures, and RBF neural networks are used to approximate the error of plant model. Then an adaptive compensation scheme based on prescribed performance bound (PPB) which characterizes the convergence rate and maximum overshoot of the tracking error is designed for the system to ensure closed-loop signal boundedness and asymptotic output tracking despite unknown actuator failures. Simulation results are given to show the effectiveness of the control design.