Data‑driven disturbance observer‑based control: an active disturbance rejection approach

In this paper, a data-driven method for disturbance estimation and rejection is presented. The proposed approach is divided into two stages: an inner stabilization loop, to set the desired reference model, together with an outer loop for disturbance estimation and compensation. Inspired by the active disturbance rejection control framework, the exogenous and endogenous disturbances are lumped into a total disturbance signal. This signal is estimated using an on-line algorithm based on a datadriven predictor scheme, whose parameters are chosen to satisfy high robustness-performance criteria. The above process is presented as a novel enhancement to design a disturbance observer, which constitutes the main contribution of the paper. In addition, the control strategy is completely presented in discrete time, avoiding the use of discretization methods for its digital implementation. As a case study, the voltage control of a DC-DC synchronous buck converter afected by disturbances in the input voltage and the load is considered. Finally, experimental results that validate the proposed strategy and some comparisons with the classical disturbance observer-based control are presented.     

Event-triggered H∞ consensus control for input-constrained multi-agent systems via reinforcement learning

This article presents an event-triggered H∞ consensus control scheme using reinforcement learning (RL) for nonlinear second-order multi-agent systems (MASs) with control constraints. First, considering control constraints, the constrained H∞ consensus problem is transformed into a multi-player zero-sum game with non-quadratic performance functions. Then, an event-triggered control method is presented to conserve communication resources and a new triggering condition is developed for each agent to make the triggering threshold independent of the disturbance attenuation level. To derive the optimal controller that can minimize the cost function in the case of worst disturbance, a constrained Hamilton–Jacobi–Bellman (HJB) equation is defined. Since it is difficult to solve analytically due to its strongly non-linearity, reinforcement learning (RL) is implemented to obtain the optimal controller. In specific, the optimal performance function and the worst-case disturbance are approximated by a time-triggered critic network; meanwhile, the optimal controller is approximated by event-triggered actor network. After that, Lyapunov analysis is utilized to prove the uniformly ultimately bounded (UUB) stability of the system and that the network weight errors are UUB. Finally, a simulation example is utilized to demonstrate the effectiveness of the control strategy provided.     

Adaptive feedback control for nonlinear triangular systems subject to uncertain asymmetric dead-zone input

In this paper, an adaptive control strategy is proposed to investigate the issue of uncertain dead-zone input for nonlinear triangular systems with unknown nonlinearities. The considered system has no precise priori knowledge about the dead-zone feature and growth rate of nonlinearity. Firstly, a dynamic gain is introduced to deal with the unknown growth rate, and the dead-zone characteristic is processed by the adaptive estimation approach without constructing the dead-zone inverse. Then, by virtue of hyperbolic functions and sign functions, a new adaptive state feedback controller is proposed to guarantee the global boundedness of all signals in the closed-loop system. Moreover, the uncertain dead-zone input problem for nonlinear upper-triangular systems is solved by the similar control strategy. Finally, two simulation examples are given to verify the effectiveness of the control scheme.     

Fast adaptive regression-basedmodel predictive control

Model predictive control (MPC) is an optimal control method that predicts the future states of the system being controlled and estimates the optimal control inputs that drive the predicted states to the required reference. The computations of the MPC are performed at pre-determined sample instances over a finite time horizon. The number of sample instances and the horizon length determine the performance of the MPC and its computational cost. A long horizon with a large sample count allows the MPC to better estimate the inputs when the states have rapid changes over time, which results in better performance but at the expense of high computational cost. However, this long horizon is not always necessary, especially for slowly-varying states. In this case, a short horizon with less sample count is preferable as the same MPC performance can be obtained but at a fraction of the computational cost. In this paper,we propose an adaptive regression-based MPC that predicts the bestminimum horizon length and the sample count from several features extracted from the time-varying changes of the states. The proposed technique builds a synthetic dataset using the system model and utilizes the dataset to train a support vector regressor that performs the prediction. The proposed technique is experimentally compared with several state-of-the-art techniques on both linear and non-linear models. The proposed technique shows a superior reduction in computational time with a reduction of about 35–65% compared with the other techniques without introducing a noticeable loss in performance.     

Extended state observer‑based pressure control for pneumatic actuator servo systems

A pneumatic actuator is a fast and economical tool that converts compressed air into mechanical motion. In this paper, an extended state observer (ESO)-based sliding mode controller (SMC) is developed to adjust the air pressure of the actuator for accurate position control. Specifcally, an impedance control module is established to produce desired air pressure based on the relationship between forces and desired positions. Then, the ESO-based SMC is implemented to adjust the air pressure to the required level despite the presence of system uncertainties and disturbances. As a result, the position of the actuator is controlled to a setpoint through the regulation of pressure. The performance of ESO-based SMC is compared with that of a classic active disturbance rejection controller (ADRC) and a SMC. Simulation results demonstrate that the ESO-based SMC shows comparable performance to ADRC in terms of precise pressure control. In addition, it requires the least control efort necessary to excite valves among the three controllers. The stability of ESO-based SMC is theoretically justifed through Lyapunov approach.     

Distributed data-driven consensus control ofmulti-agent systems under switched uncertainties

Cooperative control of multi-agent systems (MASs), particularly consensus control, has gained significant attention in the last two decades, thanks to the rapid and sustained development of distributed and networked systems. In this paper, we present some new results focused on consensus control of a set of unknown linear MASs (whose system matrices are unknown) under unknown switched uncertainties, with an emphasis on distributed data-driven controllers. The proposed controller is end-toend, designed by solving two data-based semi-definite programs (SDPs), which adjust to the changes of the uncertainty modes. Our approach achieves asymptotic consensus of the MAS provided that the switching is slow enough and the uncertainty is small. We illustrate the effectiveness of our proposed method through a numerical example.     

On disturbance rejection proportional–integral–differential control with model-free adaptation

In this paper, an adaptive disturbance-rejection proportional–integral–differential (PID) control method is proposed for a class of nonlinear systems. First, PID-type criterion is introduced in a model-free adaptive control (MFAC) framework, which gives an optimal control interpretation for PID controller. Then, the design of adaptive disturbance rejection PID is proposed based on this new interpretation to realize controller gain auto-tuning. Due to the ingenious integration of active disturbance rejection and adaptive mechanism, the proposed adaptive disturbance rejection PID control scheme exhibits better control performance than MFAC case. Furthermore, the boundedness of controller gain, the convergence of tracking error and the bounded-input–bounded-output stability are proved for the proposed control system. Finally, the effectiveness of the proposed method is verified by numerical simulation.     

Quantum‑enhanced reinforcement learning for control: a preliminary study

Reinforcement learning is one of the fastest growing areas in machine learning, and has obtained great achievements in biomedicine, Internet of Things (IoT), logistics, robotic control, etc. However, there are still many challenges for engineering applications, such as how to speed up the learning process, how to balance the trade-off between exploration and exploitation. Quantum technology, which can solve complex problems faster than classical methods, especially in supercomputers, provides us a new paradigm to overcome these challenges in reinforcement learning. In this paper, a quantum-enhanced reinforcement learning is pictured for optimal control. In this algorithm, the states and actions of reinforcement learning are quantized by quantum technology. And then, a probability amplification method, which can effectively avoid the trade-off between exploration and exploitation via quantized technology, is presented. Finally, the optimal control policy is learnt during the process of reinforcement learning. The performance of this quantized algorithm is demonstrated in both MountainCar reinforcement learning environment and CartPole reinforcement learning environment—one kind of classical control reinforcement learning environment in the OpenAI Gym. The preliminary study results validate that, compared with Q-learning, this quantized reinforcement learning method has better control performance without considering the trade-off between exploration and exploitation. The learning performance of this new algorithm is stable with different learning rates from 0.01 to 0.10, which means it is promising to be employed in unknown dynamics systems.     

Neural network-based adaptive decentralized learning control for interconnected systems with input constraints

In this paper, the neural network-based adaptive decentralized learning control is investigated for nonlinear interconnected systems with input constraints. Because the decentralized control of interconnected systems is related to the optimal control of each isolated subsystem, the decentralized control strategy can be established by a series of optimal control policies. A novel policy iteration algorithm is presented to solve the Hamilton–Jacobi–Bellman equation related to the optimal control problem. This algorithm is implemented under the actor-critic structure where both neural networks are simultaneously updated to approximate the optimal control policy and the optimal cost function, respectively. The additional stabilizing term is introduced and an improved weight updating law is derived, which relaxes the requirement of initial admissible control policy. Besides, the input constraints of interconnected systems are taken into account and the Hamilton–Jacobi–Bellman equation is solved in the presence of input constraints. The interconnected system states and the weight approximation errors of two neural networks are proven to be uniformly ultimately bounded by utilizing Lyapunov theory. Finally, the effectiveness of the proposed decentralized learning control method is verified by simulation results.     

Explicit solution to forward and backward stochastic differential equations with state delay and its application to optimal control

This paper is concerned with linear forward–backward stochastic differential equations (FBSDEs) with state delay, the solvability which is much more complex than the case of no delay or input delay caused by the prediction of the backward processes of the future time. To overcome this difficulty, we innovatively establish the non-homogeneous relationship between the backward and forward processes with the help of the corresponding discrete-time system. The main contribution is to give the explicit solution to the FBSDEs with state delay in terms of partial Riccati equations for the first time. The presented results form the basis to solve the challenging problem of linear quadratic optimal control for multiplicative-noise stochastic systems with state delay.     

Trajectory tracking anti-disturbance control for unmanned aerial helicopter based on disturbance characterization index

This work studies the trajectory tracking control for unmanned aerial helicopter (UAH) system under both matched disturbance and mismatched ones. Initially, to tackle the strong coupling, an input–output feedback linearization method is utilized to simplify the nonlinear UAH system. Secondly, a set of finite-time disturbance observers (FTDOs) are proposed to estimate mismatched disturbances with their successive derivatives, which are utilized to design the feedforward controller via backstepping. Thirdly, as for matched disturbance, by defining the disturbance characterization index (DCI) to determine whether the disturbance is harmful or not for the UAH system, a feedback controller is proposed and a sufficient condition is established to ensure the convergence of the tracking error. Finally, some numerical simulations and comparisons illustrate the validity and advantages of our control scheme.     

Simplifying ADRC design with error‑based framework: case study of a DC–DC buck power converter

In this work, the problem of designing a robust control algorithm for a DC-DC buck power converter is investigated. The applied solution is based on a recently proposed error-based version of the active disturbance rejection control (ADRC) scheme, in which the unknown higher-order terms of the reference signal are treated as additional components of the system “total disturbance”. The motivation here is to provide a practical following of a reference voltage trajectory for the buck converter in specifc cases where neither the analytical form of the desired signal nor its future values are known a’priori, hence cannot be directly used for control synthesis. In this work, the application of the error-based ADRC results in a practically appealing control technique, with compact structure, simplifed control rule, and intuitive tuning (inherited from the conventional output-based ADRC scheme). Theoretical, numerical, and experimental results are shown to validate the efcacy of the error-based ADRC in buck converter control, followed by a discussion about the revealed theoretical and practical limitations of this approach.     

Early detection of rotating stall in axial flow compressors via deterministic learning: detectability analysis

Rotating stall and surge are two violent unstable phenomena of an aero-engine compressor. The early detection of rotating stall is a critical and difficult issue in the operation of a compressor. Recently, a deterministic learning based stall inception detection approach (SIDA) has been developed for modeling and detecting stall inception in aero-engine compressors. This paper considers the derivation of analytical results on the detection capabilities for the SIDA based on deterministic learning. First, by utilizing the input/output stability of the residual system, a detectability condition of the SIDA is presented, and how to choose the parameters of the diagnostic system is also analyzed. Second, based on the relationship between NN approximation capabilities and radial basis function (RBF) network structures, the influence of RBF network structures on the performance properties of the SIDA is analyzed. Finally, a simulation study is presented, in which the Mansoux-C2 compressor model is utilized to verify the effectiveness of the proposed SIDA.     

System identification and control of the ground operationmode of a hybrid aerial–ground robot

This paper presents an in-depth analytical and empirical assessment of the performance of DoubleBee, a novel hybrid aerial– ground robot. Particularly, the dynamic model of the robot with ground contact is analyzed, and the unknown parameters in the model are identified. We apply an unscented Kalman filter-based approach and a least square-based approach to estimate the parameters with given measurements and inputs at every time step. Real data are collected and used to estimate the parameters; test data verify that the values obtained are able to model the rotation of the robot accurately. A gain-scheduled feedback controller is proposed, which leverages the identified model to generate accurate control inputs to drive the system to the desired states. The system is proven to track a constant-velocity reference signal with bounded error. Simulations and real-world experiments using the proposed controller show improved performance than the PID-based controller in tracking step commands and maintaining attitude under robot movement.     

Stabilization of an axially moving tape system with boundary disturbances via the ADRC approach

In this paper, the boundary stabilization problem of an axially moving tape system is considered. The tape moves between two sets of rollers, where the right roller is fixed and the left roller, with its mass taken into account, is free to move, rotate, and subject to external disturbances. The active disturbance rejection control approach is adopted in the investigation. First, extended state observers are designed to estimate the disturbances, and then, feedback controllers are proposed to cancel the effect of the disturbances. The well-posedness of the closed-loop system is proved by the semigroup theory. Furthermore, the exponential stability is achieved by constructing a suitable Lyapunov function. Finally, numerical simulations are given to support these results.     

Minimum energy optimal external torque control of human binocular vision

In this paper, we consider eyes from the human binocular system, that simultaneously gaze on stationary point targets in space, while optimally skipping from one target to the next, by rotating their individual gaze directions. The head is assumed fixed on the torso and the rotating gaze directions of the two eyes are assumed restricted to pass through a point in the visual space. It is further assumed that, individually the rotations of the two eyes satisfy the well known Listing’s law. We formulate and study a combined optimal gaze rotation for the two eyes, by constructing a single Riemannian metric, on the associated parameter space. The goal is to optimally rotate so that the convergent gaze changes between two pre-specified target points in a finite time interval [0, 1]. The cost function we choose is the total energy, measured by the L2 norm, of the six external torques on the binocular system. The torque functions are synthesized by solving an associated ‘two-point boundary value problem’. The paper demonstrates, via simulation, the shape of the optimal gaze trajectory of the focused point of the binocular system. The Euclidean distance between the initial and the final point is compared to the arc-length of the optimal trajectory. The consumed energy, is computed for different eye movement chores and discussed in the paper. Via simulation we observe that certain eye movement maneuvers are energy efficient and demonstrate that the optimal external torque is a linear function in time. We also explore and conclude that splitting an arbitrary optimal eye movement into optimal vergence and version components is not energy efficient although this is how the human oculomotor control seems to operate. Optimal gaze trajectories and optimal external torque functions reported in this paper is new.     

Tuning of active disturbance rejection control for diferentially fat systems under an ultimate boundedness analysis: a unifed integer‑fractional approach

An adaptation of the active disturbance rejection control (ADRC) approach is applied to a fractional-order system with a fat output. Albeit the rather scarce information about the system, the conditions to establish an ultimate bound for a specifc confguration of the system are found and compiled in a guideline for the tuning of the observer implemented in the ADRC.     

Adaptive output consensus for heterogeneous nonlinear multi‑agent systems with multi‑type input constraints under switching‑directed topologies

This study concentrates on solving the output consensus problem for a class of heterogeneous uncertain nonstrict-feedback nonlinear multi-agent systems under switching-directed communication topologies, in which all followers are subjected to multi-type input constraints such as unknown asymmetric saturation, unknown dead-zone and their integration. A unified representation is presented to overcome the difficulties originating from multi-agent input constraints. Moreover, the uncertain system functions in a non-lower triangular form and the interaction terms among agents are dealt with by exploiting the fuzzy logic systems and their special property. Furthermore, by introducing a nonlinear filter to alleviate the problem of “explosion of complexity” during the backstepping design, a distributed common adaptive control protocol is proposed to ensure that the synchronization errors converge to a small neighborhood of the origin despite the existence of multiple input constraints and arbitrary switching communication topologies. Both stability analysis and simulation results are conducted to show the effectiveness and performance of the proposed control methodology.     

Multi-agent graphical games with input constraints: an online learning solution

This paper studies an online iterative algorithm for solving discrete-time multi-agent dynamic graphical games with input constraints. In order to obtain the optimal strategy of each agent, it is necessary to solve a set of coupled Hamilton-Jacobi-Bellman (HJB) equations. It is very difficult to solve HJB equations by the traditional method. The relevant game problem will become more complex if the control input of each agent in the dynamic graphical game is constrained. In this paper, an online iterative algorithm is proposed to find the online solution to dynamic graphical game without the need for drift dynamics of agents. Actually, this algorithm is to find the optimal solution of Bellman equations online. This solution employs a distributed policy iteration process, using only the local information available to each agent. It can be proved that under certain conditions, when each agent updates its own strategy simultaneously, the whole multi-agent system will reach Nash equilibrium. In the process of algorithm implementation, for each agent, two layers of neural networks are used to fit the value function and control strategy, respectively. Finally, a simulation example is given to show the effectiveness of our method.     

Global output feedback control of feedforward nonlinear time-delay systems with unknown growth rate and unknown measurement sensitivity

This paper discusses the problem of global state regulation via output feedback for a class of feedforward nonlinear time-delay systems with unknown measurement sensitivity. Different from previous works, the nonlinear terms are dominated by upper triangular linear unmeasured (delayed) states multiplied by unknown growth rate. The unknown growth rate is composed of an unknown constant, a power function of output, and an input function. Furthermore, due to the measurement uncertainty of the system output, it is more difficult to solve this problem. It is proved that the presented output feedback controller can globally regulate all states of the nonlinear systems using the dynamic gain scaling technique and choosing the appropriate Lyapunov–Krasovskii functionals.