Adaptive Barrier-Lyapunov-Functions Based Control Scheme of Nonlinear Pure-Feedback Systems with Full State Constraints and Asymptotic Tracking Performance

In this paper,the authors propose an adaptive Barrier-Lyapunov-Functions(BLFs)based control scheme for nonlinear pure-feedback systems with full state constraints.Due to the coexist of the non-affine structure and full state constraints,it is very difficult to construct a desired controller for the considered system.According to the mean value theorem,the authors transform the pure-feedback system into a system with strict-feedback structure,so that the well-known backstepping method can be applied.Then,in the backstepping design process,the BLFs are employed to avoid the violation of the state constraints,and neural networks(NNs)are directly used to online approximate the unknown packaged nonlinear terms.The presented controller ensures that all the signals in the closed-loop system are bounded and the tracking error asymptotically converges to zero.Meanwhile,it is shown that the constraint requirement on the system will not be violated during the operation.Finally,two simulation examples are provided to show the effectiveness of the proposed control scheme.

Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints

A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.

Asymmetric time-varying integral barrier Lyapunov function based adaptive optimal control for nonlinear systems with dynamic state constraints

This paper investigates the issue of adaptive optimal tracking control for nonlinear systems with dynamic state constraints.An asymmetric time-varying integral barrier Lyapunov function(ATIBLF)based integral reinforcement learning(IRL)control algorithm with an actor–critic structure is first proposed.The ATIBLF items are appropriately arranged in every step of the optimized backstepping control design to ensure that the dynamic full-state constraints are never violated.Thus,optimal virtual/actual control in every backstepping subsystem is decomposed with ATIBLF items and also with an adaptive optimized item.Meanwhile,neural networks are used to approximate the gradient value functions.According to the Lyapunov stability theorem,the boundedness of all signals of the closed-loop system is proved,and the proposed control scheme ensures that the system states are within predefined compact sets.Finally,the effectiveness of the proposed control approach is validated by simulations.

Time-Varying Asymmetrical BLFs Based Adaptive Finite-Time Neural Control of Nonlinear Systems With Full State Constraints

This paper concentrates on asymmetric barrier Lyapunov functions(ABLFs)based on finite-time adaptive neural network(NN)control methods for a class of nonlinear strict feedback systems with time-varying full state constraints.During the process of backstepping recursion,the approximation properties of NNs are exploited to address the problem of unknown internal dynamics.The ABLFs are constructed to make sure that the time-varying asymmetrical full state constraints are always satisfied.According to the Lyapunov stability and finitetime stability theory,it is proven that all the signals in the closedloop systems are uniformly ultimately bounded(UUB)and the system output is driven to track the desired signal as quickly as possible near the origin.In the meantime,in the scope of finitetime,all states are guaranteed to stay in the pre-given range.Finally,a simulation example is proposed to verify the feasibility of the developed finite time control algorithm.

Adaptive Consensus Quantized Control for a Class of High-Order Nonlinear Multi-Agent Systems With Input Hysteresis and Full State Constraints

For a class of high-order nonlinear multi-agent systems with input hysteresis,an adaptive consensus output-feedback quantized control scheme with full state constraints is investigated.The major properties of the proposed control scheme are:1)According to the different hysteresis input characteristics of each agent in the multi-agent system,a hysteresis quantization inverse compensator is designed to eliminate the influence of hysteresis characteristics on the system while ensuring that the quantized signal maintains the desired value.2)A barrier Lyapunov function is introduced for the first time in the hysteretic multi-agent system.By constructing state constraint control strategy for the hysteretic multi-agent system,it ensures that all the states of the system are always maintained within a predetermined range.3)The designed adaptive consensus output-feedback quantization control scheme allows the hysteretic system to have unknown parameters and unknown disturbance,and ensures that the input signal transmitted between agents is the quantization value,and the introduced quantizer is implemented under the condition that only its sector bound property is required.The stability analysis has proved that all signals of the closed-loop are semi-globally uniformly bounded.The Star Sim hardware-in-the-loop simulation certificates the effectiveness of the proposed adaptive quantized control scheme.

Output Constrained Adaptive Controller Design for Nonlinear Saturation Systems

This paper considers the adaptive neuro-fuzzy control scheme to solve the output tracking problem for a class of strict-feedback nonlinear systems.Both asymmetric output constraints and input saturation are considered.An asymmetric barrier Lyapunov function with time-varying prescribed performance is presented to tackle the output-tracking error constraints.A high-gain observer is employed to relax the requirement of the Lipschitz continuity about the nonlinear dynamics.To avoid the"explosion of complexity",the dynamic surface control(DSC)technique is employed to filter the virtual control signal of each subsystem.To deal with the actuator saturation,an additional auxiliary dynamical system is designed.It is theoretically investigated that the parameter estimation and output tracking error are semi-global uniformly ultimately bounded.Two simulation examples are conducted to verify the presented adaptive fuzzy controller design.

Fixed-Time Controller Design for a Quadrotor UAV with Asymmetric Output Error Constraints

In this article,a fixed-time tracking control strategy is proposed for a quadrotor UAV(QUAV)with external disturbance and asymmetric output error constraints.Firstly,a dynamic model of the QUAV is transformed into a strict feedback system with external disturbance,and it is decoupled into attitude subsystem and position subsystem for simplifying controller design.Secondly,an asymmetric tangent barrier Lyapunov function(ATBLF)is applied to solve the tracking error constraints problem,and a fixed-time control law is designed.Meanwhile,a fixed-time disturbance observer(FTDO)is designed to cope with external disturbance.Then,it is proved that the designed controller guarantees the tracking error remains within the constraint ranges and converges to zero in fixed-time by Lyapunov stability theory.Finally,the effectiveness of the proposed control scheme is verified by numerical simulations.

Robust control for an unmanned helicopter with constrained flapping dynamics

In this paper, a neural network based adaptive prescribed performance control scheme is proposed for the altitude and attitude tracking system of the unmanned helicopter in the presence of state and output constraints. For handling the state constraints, the barrier Lyapunov function and the saturation function are employed. And, the prescribed performance method is used to deal with the flapping angle constraints for the unmanned helicopter. It is proved that the proposed control approach can ensure that all the signals of the resulting closed-loop system are bounded, and the tracking errors are within the prescribed performance bounds for all time. The numerical simulation is given to illustrate the performance of the proposed scheme.

Adaptive tracking control for air-breathing hypersonic vehicles with state constraints

We investigate the adaptive tracking problem for the longitudinal dynamics of state-constrained airbreathing hypersonic vehicles, where not only the velocity and the altitude, but also the angle of attack(AOA) is required to be tracked. A novel indirect AOA tracking strategy is proposed by viewing the pitch angle as a new output and devising an appropriate pitch angle reference trajectory. Then based on the redefined outputs(i.e., the velocity,the altitude, and the pitch angle), a modified backstepping design is proposed where the barrier Lyapunov function is used to solve the state-constrained control problem and the control gain of this class of systems is unknown.Stability analysis is given to show that the tracking ob jective is achieved, all the closed-loop signals are bounded,and all the states always satisfy the given constraints. Finally, numerical simulations verify the effectiveness of the proposed approach.

Fixed-time constrained acceleration reconstruction scheme for robotic exoskeleton via neural networks

Accurate acceleration acquisition is a critical issue in the robotic exoskeleton system,but it is difficult to directly obtain the acceleration via the existing sensing systems.The existing algorithm-based acceleration acquisition methods put more attention on finite-time convergence and disturbance suppression but ignore the error constraint and initial state irrelevant techniques.To this end,a novel radical bias function neural network(RBFNN)based fixed-time reconstruction scheme with error constraints is designed to realize high-performance acceleration estimation.In this scheme,a novel exponential-type barrier Lyapunov function is proposed to handle the error constraints.It also provides a unified and concise Lyapunov stability-proof template for constrained and non-constrained systems.Moreover,a fractional power sliding mode control law is designed to realize fixed-time convergence,where the convergence time is irrelevant to initial states or external disturbance,and depends only on the chosen parameters.To further enhance observer robustness,an RBFNN with the adaptive weight matrix is proposed to approximate and attenuate the completely unknown disturbances.Numerical simulation and human sub ject experimental results validate the unique properties and practical robustness.

Phase plane design based fast altitude tracking control for hypersonic flight vehicle with angle of attack constraint

In this paper, fast setpoint altitude tracking control for Hypersonic Flight Vehicle(HFV)satisfying Angle of Attack(AOA) constraint is studied with a two-loop structure controller, in the presence of parameter uncertainties and disturbances. For the outer loop, phase plane design is adopted for the simplified model under Bang-Bang controller to generate AOA command guaranteeing fast tracking performance. Modifications based on Feedback-Linearization(FL) technique are adopted to transform the phase trajectory into a sliding curve. Moreover, to resist mismatch between design model and actual model, Fast Exponential Reaching Law(FERL) is augmented with the baseline controller to maintain state on the sliding curve. The inner-loop controller is based on backstepping technique to track the AOA command generated by outer-loop controller. Barrier Lyapunov Function(BLF) design is employed to satisfy AOA requirement. Moreover, a novel auxiliary state is introduced to remove the restriction of BLF design on initial tracking errors. Dynamic Surface Control(DSC) is utilized to ease the computation burden. Rigorous stability proof is then given, and AOA is guaranteed to stay in predefined region theoretically. Simulations are conducted to verify the efficiency and superior performance of the proposed method.

Adaptive Human-Robot Collaboration Control Based on Optimal Admittance Parameters

In order to help the operator perform the human-robot collaboration task and optimize the task performance,an adaptive control method based on optimal admittance parameters is proposed.The overall control structure with the inner loop and outer loop is first established.The tasks of the inner loop and outer loop are robot control and task optimization,respectively.An inner-loop robot controller integrated with barrier Lyapunov function and radial basis function neural networks is then proposed,which makes the robot with unknown dynamics securely behave like a prescribed robot admittance model sensed by the operator.Subsequently,the optimal parameters of the robot admittance model are obtained in the outer loop to minimize the task tracking error and interaction force.The optimization problem of the robot admittance model is transformed into a linear quadratic regulator problem by constructing the human-robot collaboration system model.The model includes the unknown dynamics of the operator and the task performance details.To relax the requirement of the system model,the integral reinforcement learning is employed to solve the linear quadratic regulator problem.Besides,an auxiliary force is designed to help the operator complete the specific task better.Compared with the traditional control scheme,the security performance and interaction performance of the human-robot collaboration system are improved.The effectiveness of the proposed method is verified through two numerical simulations.In addition,a practical human-robot collaboration experiment is carried out to demonstrate the performance of the proposed method.