Adaptive Control of Full-State Constrained High-Order Nonlinear Systems With Time-Varying Powers

Robust fixed-time H∞ tracking control of UUVs with partial and full state constraints and prescribed performance under input saturation

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 StarSim hardware-in-the-loop simulation certificates the effectiveness of the proposed adaptive quantized control scheme.

This article discusses the adaptive fuzzy asymptotic tracking control for high-order nonlinear time-delay systems with full-state constraints. Fuzzy-logic systems and a separation principle are utilized to relax growth assumptions imposed on unknown nonlinearities. The adverse effect caused by unknown time delays is eliminated by choosing appropriate Lyapunov-Krasovskii functionals. By integrating nonlinear-transformed functions with a key coordinate transformation into the control design and constructing a specific compact set on the initial values of system states, the desired trajectory and parameter estimates, it is rigorously proved that all closed-loop signals are semiglobally bounded, the fuzzy approximation is valid, the full-state constraints are not violated without feasibility conditions on virtual controllers, and asymptotic tracking is achieved. The effectiveness and advantages of this control scheme are confirmed by two examples including a single-link robotic system.

ABSTRACTThis article proposes an adaptive tracking control scheme for a class of switched stochastic non‐linear systems subject to full state constraints (FSCs). A unified framework is established by integrating the adaptive backstepping technique with barrier Lyapunov functions (BLFs) to address the time‐varying full state constraints (TFSCs). Accordingly, utilizing the theorem of stochastic non‐linear systems, a new adaptive state feedback control scheme is developed for a class of switching signals with the mode‐dependent average dwell time (MDADT) property. The proposed adaptive controller is mode‐dependent while the adaptive laws are mode‐independent so as to facilitate an easy deployment of the controller. It is rigorously proven that all signals in the closed‐loop system are bounded in probability, the tracking error converges to a bounded compact set, and the TFSCs are not violated. Finally, simulation examples are conducted to validate the effectiveness of the controller.

In this paper, we develop a systematic Lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration. The only assumptions we make about the system are well-posedness of the algebraic loop and local stability. Problems to be considered include the estimation of the domain of attraction, the reachable set under a class of bounded energy disturbances and the nonlinear L2 gain. The regional analysis is established through an effective treatment of the algebraic loop and the saturation/deadzone function. This treatment yields two forms of differential inclusions, a polytopic differential inclusion (PDI) and a norm-bounded differential inclusion (NDI) that contain the original system. Adjustable parameters are incorporated into the differential inclusions to reflect the regional property. The main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain Lyapunov function where the PDI or the NDI is valid. With quadratic Lyapunov functions, conditions for stability and performances are derived as linear matrix inequalities (LMIs). To obtain less conservative conditions, we use a pair of conjugate non-quadratic Lyapunov functions, the convex hull quadratic function and the max quadratic function. These functions yield bilinear matrix inequalities (BMIs) as conditions for stability and guaranteed performance level. The BMI conditions cover the corresponding LMI conditions as special cases, hence the BMI results are guaranteed to be as good as the LMI results. In most examples, the BMI results are significantly better than the LMI results

This article presents an asymptotic tracking controller for high-order uncertain nonlinear systems. Compared to the existing results, some restrictive assumptions are relaxed and the requirement of the variables being bounded is removed. At the same time, a prescribed time tracking control strategy is constructed to make that the system has better-transient performance during operation. Specifically, a global prescribed time function is proposed and an unconstrained variable is constructed to replace the constrained tracking error. Under this framework, an appealing feature of the designed controller is that the tracking error can converge to a specified range within a prescribed time and eventually converge to zero asymptotically starting from any initial conditions, where the prescribed time and accuracy can be directly given. Finally, the simulation results validate the effectiveness of the control strategy.

<abstract><p>This paper investigates the problem of adaptive distributed consensus control for stochastic multi-agent systems (MASs) with full state constraints. By utilizing adaptive backstepping control technique and barrier Lyapunov function (BLF), an adaptive distributed consensus constraint control method is proposed. The developed control method can ensure that all signals of the controlled system are semi-globally uniformly ultimately bounded (SGUUB) in probability, and outputs of the follower agents keep consensus with the output of leader. In addition, system states are not transgressed their constrained sets. Finally, simulation results are provided to illustrate the feasibility of the developed control algorithm and theorem.</p></abstract>

The adaptive tracking control is extended to the nonlinear system with multiple uncertainties consisting of input saturation, unknown parameter and full-state constraints. To deal with the input saturation, a distinctive method of introducing an auxiliary system is used instead of directly approximating it by a smooth function. Then, the adaptive backstepping technique is combined with the barrier Lyapunov function (BLF) to solve the parametric nonlinearities and give a systematic design procedure. Based on this design procedure, an adaptive state-feedback controller is obtained with rigourous stability analysis. It is verified that all the signals are uniformly ultimately bounded, the tracking error is bounded in a compact set of the origin, and the full-states are not violated. Finally, the proposed controller is used to a mass-spring mechanical system, and demonstrates the proposed scheme is effective.

Barrier Lyapunov Functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints

This work proposed a vision-guided articulated manipulator controller design using the Barrier Lyapunov function. In a closed-loop system, vision guiding uses camera feedback to control the motion of an articulated manipulator. For vision guidance to operate the articulated manipulator, an object must be in the camera's field of view. Image-based and position-based visual servoing are used to improve the vision-guiding controller. Using this method, an offline trajectory is produced to perform position- and image-based visual servoing operations on the articulated manipulator. Two different control strategies are presented: the vision guiding controller with the limit orientation using the Barrier Lyapunov function and the vision guiding controller with a quadratic Lyapunov function. Simulation results from two vision-guiding controllers, as well as proof of asymptotic stability, are used to validate the efficacy of the proposed controller.

This study proposes the time-/event-triggered adaptive neural control strategies for the asymptotic tracking problem of a class of uncertain nonlinear systems with full-state constraints. First, we design a time-triggered strategy. The effect caused by the residuals of the estimation via radial basis function (RBF) neural networks (NNs), and the reasonable upper bounds on the first derivative of the reference signal and the derivative of each virtual control, can be eliminated by designing appropriate adaptive laws and utilizing the basic properties of RBF NNs. Moreover, the construction of the barrier Lyapunov functions (BLFs) in this work ensures the compliance of the full-state constraints and also holds the asymptotic output tracking performance. Then, based on the time-triggered strategy, we further design a relative threshold event-triggered strategy. The proposed event-triggered adaptive neural controller can solve the main control objective of this work, that is: 1) the full-state constraint requirements of the system are not violated and 2) the output signal asymptotically tracks the reference signal. Compared with the traditional method, the event-triggered strategy can improve the utilization of communication channels and resources and has greater practical significance. Finally, an example of single-link robot under the proposed two strategies illustrates the validity of the constructed controllers.

We construct a generic, simple, and efficient scheduling policy for stochastic processing networks, and provide a general framework to establish its stability. Our policy is randomized and prioritized: with high probability it prioritizes jobs that have been least routed through the network. We show that the network is globally stable under this policy if there exists an appropriate quadratic local Lyapunov function that provides a negative drift with respect to nominal loads at servers. Applying this generic framework, we obtain stability results for our policy in many important examples of stochastic processing networks: open multiclass queueing networks, parallel server networks, networks of input-queued switches, and a variety of wireless network models with interference constraints. Our main novelty is the construction of an appropriate global Lyapunov function from quadratic local Lyapunov functions, which we believe to be of broader interest.

Adaptive fuzzy control of uncertain stochastic nonlinear systems with full state constraints

In recent decades, controller design has been attracted a great deal of interest of many researchers in control community which can make the job of many other researchers in different area of research easier. The present study aims to design a finite time adaptive control input for a high-order nonlinear system in presence of a variety of mismatched uncertainties and external disturbances. Adaptive terminal sliding mode control (ATSMC) method is used to design robust controller in a finite time. Also, adaptive concept is employed in ATSMC to estimate the upper bound of mismatched uncertainties and external disturbances and their estimations are used in control input. The finite time stability proof is performed by defining a proper candidate Lyapunov function. Numerical simulation results are carried out in Simulink/MATLAB to reveal the correctness of proposed design in this research. Finally, the performance criterion, integral of the square value (ISV), is defined to provide a numerical comparison between the proposed adaptive controller and non-adaptive controller.

In this paper, an adaptive backstepping controller is designed for positioning servo system driven by a hydraulic actuator. The constraints on both output velocity and acceleration are taken into consideration due to performance and/or physical limitations. The mechanism of these constraints satisfaction uses a barrier Lyapunov function, which grows to infinity when its arguments approach some pre-set limits, to prevent constraint violation. By ensuring the stabilization of the barrier Lyapunov function in the dynamic motion closed loop, and propagating a hard-bound imposed on associated error signals through the steps of the backstepping procedure, we guarantee that the system output velocity and acceleration constraints are not transgressed. Furthermore, a stable discontinuous projection based adaptive controller is constructed to tackle systems unknown parameters. Asymptotic tracking is achieved without violation of the constraints under mild initial conditions. Extensive simulation results are provided to illustrate the performance of the proposed control scheme, compared with a standard adaptive backstepping controller based on a Quadratic Lyapunov function.