Novel model reference adaptive control laws for improved transient dynamics and guaranteed saturation constraints

In classical model reference adaptive control (MRAC), the adaptive rates must be tuned to meet multiple competing objectives. Large adaptive rates guarantee rapid convergence of the trajectory tracking error to zero. However, large adaptive rates may also induce saturation of the actuators and excessive overshoots of the closed-loop system’s trajectory tracking error. Conversely, low adaptive rates may produce unsatisfactory trajectory tracking performances. To overcome these limitations, in the classical MRAC framework, the adaptive rates must be tuned through an iterative process. Alternative approaches require to modify the plant’s reference model or the reference command input. This paper presents the first MRAC laws for nonlinear dynamical systems affected by matched and parametric uncertainties that constrain both the closed-loop system’s trajectory tracking error and the control input at all times within user-defined bounds, and enforce a user-defined rate of convergence on the trajectory tracking error. By applying the proposed MRAC laws, the adaptive rates can be set arbitrarily large and both the plant’s reference model and the reference command input can be chosen arbitrarily. The user-defined rate of convergence of the closed-loop plant’s trajectory is enforced by introducing a user-defined auxiliary reference model, which converges to the trajectory tracking error obtained by applying the classical MRAC laws before its transient dynamics has decayed, and steering the trajectory tracking error to the auxiliary reference model at a rate of convergence that is higher than the rate of convergence of the plant’s reference model. The ability of the proposed MRAC laws to prescribe the performance of the closed-loop system’s trajectory tracking error and control input is guaranteed by barrier Lyapunov functions. Numerical simulations illustrate both the applicability of our theoretical results and their effectiveness compared to other techniques such as prescribed performance control, which allows to constrain both the rate of convergence and the maximum overshoot on the trajectory tracking error of uncertain systems.     

Online adaptive policy iteration based fault-tolerant control algorithm for continuous-time nonlinear tracking systems with actuator failures

In this paper, a novel tracking control scheme for continuous-time nonlinear affine systems with actuator faults is proposed by using a policy iteration (PI) based adaptive control algorithm. According to the controlled system and desired reference trajectory, a novel augmented tracking system is constructed and the tracking control problem is converted to the stabilizing issue of the corresponding error dynamic system. PI algorithm, generally used in optimal control and intelligence technique fields, is an important reinforcement learning method to solve the performance function by critic neural network (NN) approximation, which satisfies the Lyapunov equation. For the augmented tracking error system with actuator faults, an online PI based fault-tolerant control law is proposed, where a new tuning law of the adaptive parameter is designed to tolerate four common kinds of actuator faults. The stability of the tracking error dynamic with actuator faults is guaranteed by using Lyapunov theory, and the tracking errors satisfy uniformly bounded as the adaptive parameters get converged. Finally, the designed fault-tolerant feedback control algorithm for nonlinear tracking system with actuator faults is applied in two cases to track the desired reference trajectory, and the simulation results demonstrate the effectiveness and applicability of the proposed method.     

漂浮基空间机器人的基于模糊神经网络的自适应补偿控制

针对自由漂浮状态的空间机器人模型不确定性及其动力传动机构的摩擦死区非线性,将一种自适应模糊小脑模型关联控制( FCMAC)补偿策略用于轨迹跟踪及补偿问题.利用模糊神经网络并引入GL矩阵及其乘法算子“.”分别对执行机构中的摩擦死区及系统模型不确定部分进行自适应补偿,其补偿误差及外界扰动通过滑模控制器来消除.基于Lyapunov理论证明了闭环系统跟踪误差的有界性.仿真表明控制器可以达到较高精度,且能满足实时性要求.     

Optimization-based adaptive neural sliding mode control for nonlinear systems with fast and accurate response under state and input constraints

The high-performance control requires the system to be stable, fast and accurate simultaneously. However, various systems (e.g., motors, industrial robots) generally face technical challenges such as nonlinearities, uncertainties, external disturbances and physical constraints, which make it difficult to reach the hardware potential of the systems to track the desired trajectories when satisfying the high-performance control requirements. Therefore, take a two-order nonlinear system for example, an optimization-based adaptive neural sliding mode control based on a two-loop control structure is proposed in this paper, where the outer and inner loops are designed separately to achieve different control requirements. Namely, the outer loop is designed as a model predictive control (MPC)-based optimization problem, which can optimize the desired trajectories to meet the state and input constraints, and maximize the converging speed of transient response as fast as possible, and the inner loop is designed with a recurrent neural network (RNN)-based adaptive neural sliding mode controller, which can guarantee the tracking of the replanned desired trajectories from outer loop as accurate as possible. The stability of the system is guaranteed by Lyapunov theorem, the optimal tracking performance is achieved under nonlinearities, uncertainties, external disturbances and physical constraints, and comparative simulation with a motor system is carried out to verify the effectiveness and superiority of the proposed approach.     

Trajectory tracking control for rotary steerable systems using interval type-2 fuzzy logic and reinforcement learning

Rotary steerable system (RSS) is a directional drilling technique which has been applied in oil and gas exploration under complex environment for the requirements of fossil energy and geological prospecting. The nonlinearities and uncertainties which are caused by dynamical device, mechanical structure, extreme downhole environment and requirements of complex trajectory design in the actual drilling work increase the difficulties of accurate trajectory tracking. This paper proposes a model-based dual-loop feedback cooperative control method based on interval type-2 fuzzy logic control (IT2FLC) and actor-critic reinforcement learning (RL) algorithms with one-order digital low-pass filters (LPF) for three-dimensional trajectory tracking of RSS. In the proposed RSS trajectory tracking control architecture, an IT2FLC is utilized to deal with system nonlinearities and uncertainties, and an online iterative actor-critic RL controller structured by radial basis function neural networks (RBFNN) and adaptive dynamic programming (ADP) is exploited to eliminate the stick–slip oscillations relying on its approximate properties both in action function (actor) and value function (critic). The two control effects are fused to constitute cooperative controller to realize accurate trajectory tracking of RSS. The effectiveness of our controller is validated by simulations on designed function tests for angle building hole rate and complete downhole trajectory tracking, and by comparisons with other control methods.     

Adaptive synchronization for a class of faulty and sampling coupled networks with its circuit implement

This paper is concerned with the asymptotic synchronization problem of a class of nonlinear complex networks with faulty and sampling couplings. A new version of the adaptive control strategy is proposed to adjust control parameters to compensate for the adverse impact of network attenuation faults, nonlinearities and sampling errors. Based on the adaptive adjustment laws, an approach that is application of knowledge of electricity is introduced to physically realize the adaptive controllers. Using Lyapunov stability theory for the synchronization error system, asymptotic synchronization of the overall networks can be established for the nonlinearly sampling and faulty couplings. Finally, the proposed adaptive control schemes are tested by simulation on Chua?s circuit network.     

Adaptive perturbation rejection control and driving voltage circuit designs of wheeled mobile robots

This paper addresses the robust trajectory tracking control problem for a class of wheeled robotic systems with perturbations caused by measurement errors, internal uncertainties, and exogenous disturbances. An adaptive technique is utilized to estimate the effects of perturbations. Then, on the basis of the adaptive estimations, perturbation rejection control schemes are developed to construct the kinematic control and dynamic control strategies. By utilizing Lyapunov stability theory, bounded tracking of the desired trajectory and asymptotic tracking of auxiliary azimuthal angular velocity and forward speed of the robot can be achieved respectively in the fact of perturbations. Furthermore, the adaptive perturbation rejection control (APRC) strategies are implemented physically by analog circuits to generate driving voltages of DC motors in the robot reality. The efficiency of the proposed trajectory tracking control method is validated by a robotic system.     

Flatness-based adaptive sliding mode tracking control for a quadrotor with disturbances

In this paper, a flatness-based adaptive sliding mode control strategy is presented to solve the trajectory tracking problem of a quadrotor. According to the differential flatness theory, the typical under-actuated quadrotor dynamics is transformed into a fully-actuated one. Based on this model, backstepping sliding mode controllers are designed to solve the trajectory tracking problem. To improve the robustness to disturbances, extended state observers are applied as a feedforward compensation of disturbances. Moreover, considering the high-order dynamics and possible instability caused by large observer gains, the adaptive method is applied to compensate for the estimation error. The effectiveness of the proposed control scheme is verified in simulations.     

Adaptive prescribed performance control for nonlinear robotic systems

This paper investigates the problem of asymptotic tracking control of nonlinear robotic systems with prescribed performance. The control strategy is developed based on a modified prescribed performance function (PPF) to guarantee the transient behavior, while the requirements on the accurate initial tracking error in the classical PPF can be remedied. The fuzzy logic system (FLS) is used to approximate the unknown dynamics. In the existing PPF based adaptive control schemes with FLSs, the tracking error does not achieve asymptotic convergence. To address this issue, a robust integral of the sign of the error (RISE) term is incorporated into the control design to reject the FLS approximation errors and external disturbances, such that the asymptotic convergence is achieved. Finally, numerical simulation and experimental results validate the effectiveness of the proposed control scheme.     

Quantized adaptive tracking control for nonlinear systems with actuator backlash compensation

In this paper, the problem of adaptive tracking control is investigated for nonlinear systems with asymmetric actuator backlash. We assume that the nonlinearities of the systems are unknown and the external disturbances are bounded. First, the control input will be quantized by a hysteresis-type quantizer, which can reduce the communication rate of the control signal. Then, the asymmetric actuator backlash is approximated to a new model, and a novel adaptive controller with the quantizer is designed via an adaptive backstepping technique to guarantee all the signals of the closed-loop tracking error system are uniform ultimate boundedness. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed algorithm.     

Adaptive sliding mode trajectory tracking control of robotic airships with parametric uncertainty and wind disturbance

An adaptive sliding mode trajectory tracking controller is developed for fully-actuated robotic airships with parametric uncertainties and unknown wind disturbances. Based on the trajectory tracking model of robotic airships, an adaptive sliding mode control strategy is proposed to ensure the asymptotic convergence of trajectory tracking errors and adaptive estimations. The crucial thinking involves an adaptive scheme for the controller gains to avoid the off-line tuning. Specially, the uncertain physical parameters and unknown wind disturbances are rejected by variable structure control, and boundary layer technique is employed to avoid the undesired control chattering phenomenon. Computer experiments are performed to demonstrate the performance and advantage of the proposed control method.     

High dynamic adaptive robust control of load emulator with output feedback signal

This paper is concerned with the high performance adaptive robust control problem for an aircraft load emulator (LE). High dynamic capability is a key performance index of load emulator. However, physical load emulators exist a lot of nonlinearities and modeling uncertainties, which are the main obstacles for achieving high performance of load emulator. To handle the modeling uncertainty and achieve adjustable model-based compensation, firstly, the mathematical model of the load emulator is built, and then a nonlinear adaptive robust controller only with output feedback signal is proposed to improve the tracking accuracy and dynamic response capability. The controller is constructed based on the adaptive robust control framework with necessary design modifications required to accommodate uncertainties and nonlinearities of hydraulic load emulator. In this approach, nonlinearities are canceled by output feedback signal; and modeling errors, including parametric uncertainties and uncertain nonlinearities, are dealt with adaptive control and robust control respectively. The resulting controller guarantees a prescribed disturbance attenuation capability in general while achieving asymptotic output tracking in the absence of time-varying uncertainties. Experimental results are obtained to verify the high performance nature of the proposed control strategy, especially the high dynamic capability.     

Output-feedback binary adaptive control of MIMO systems using monitoring function

The problem of adaptive control design for multivariable linear time-invariant plants with unknown control direction is considered. A solution is proposed based on the SDU factorization of the high frequency gain matrix (HFG) and the monitoring function approach. The adaptation scheme is the binary model reference adaptive control (BMRAC) which utilizes parameter projection and sufficiently high adaptation gains. The signs of the leading principal minors of the HFG define the control directions, and the lack of knowledge of which is a major challenge in the multivariable framework. The role of the monitoring function is to monitor the output error transient and then provide the necessary changes of the adaptation gain signs to guarantee a stable adaptive control. In addition to proving the signal boundedness of the resulting closed-loop system, the output tracking error is shown to be asymptotically as well as exponentially practically stable, i.e., exponentially stable with respect to a small residual compact set of size inversely proportional to the BMRAC adaptation gain. The latter implies good transient properties of the output tracking error in contrast to conventional adaptive laws which only guarantee asymptotic stability but can lead to extremely slow error convergence. The extension of the proposed approach to matched disturbances is also briefly discussed following the classical paradigm of disturbance estimators. Numerical results with a visual servoing application illustrate the efficiency of the proposed method.     

Distributed adaptive fault-tolerant formation control for heterogeneous multiagent systems under switching directed topologies

This paper studies the cooperative fault-tolerant formation control problem of tracking a dynamic leader for heterogeneous multiagent systems consisting of multipile unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults under switching directed interaction topologies. Based on local neighborhood formation information, the distributed fault-tolerant formation controllers are constructed to ensure that all follower UAVs and UGVs can accomplish the demanding formation configuration in the state space and track the dynamic leader’s trajectory. By incorporating the sliding mode control and adaptive control technique, the actuator faults and unknown parameters of follower agents can be compensated. Through the theoretical analysis, it is proved that the cooperatively semiglobally uniformly ultimately boundedness of the closed-loop system is guaranteed, and the formation tracking errors converge to a small adjustable neighborhood of the origin. A simulation example is introduced to show the validity of the proposed distributed fault-tolerant formation control algorithm.     

Funnel-based adaptive fuzzy finite-time control for non-affine nonlinear systems preceded by unknown actuators

In this paper, an adaptive finite-time funnel control for non-affine strict-feedback nonlinear systems preceded by unknown non-smooth input nonlinearities is proposed. The input nonlinearities include backlash-like hysteresis and dead-zone. Unknown nonlinear functions are handled using fuzzy logic systems (FLS), based on the universal approximation theorem. An improved funnel error surface is utilized to guarantee the steady-state and transient predetermined performances while the differentiability problem in the controller design is averted. Using the Lyapunov approach, all the adaptive laws are extracted. In addition, an adaptive continuous robust term is added to the control input to relax the assumption of knowing the bounds of uncertainties. All the signals in the closed-loop system are shown to be semi-globally practically finite-time bounded with predetermined performance for output tracking error. Finally, comparative numerical and practical examples are provided to authenticate the efficacy and applicability of the proposed scheme.     

Prescribed performance adaptive control for an uncertain robotic manipulator with input compensation updating law

This paper investigates an adaptive prescribed performance control strategy with specific time planning for trajectory tracking of robotic manipulator subject to input constraint and external disturbances. By constructing an accumulated error vector embedded with a performance enhancement function and introducing an input auxiliary function, a specified-time control framework with built-in prescribed performance is further designed to ensure that the trajectory tracking performance. More particularly, the proposed control law is compatible with the control input saturation suppression algorithm, which is capable of improving the robustness of closed loop system. Under the framework of the proposed control strategy, it is proved by theory that all the signals in the closed-loop system are bounded, and moreover the tracking error can reach the exact convergence domain in a given time. At last, a numerical example is presented to indicate the feasibility and effectiveness of the proposed method.     

Compound tracking control based on MPC for quadrotors with disturbances

In this paper, a compound control strategy is proposed to realize the trajectory tracking task of quadrotors under operating constraints and disturbances. Disturbances caused by model uncertainties, environmental noises, and measurement disturbances are divided into matched disturbances and unmatched ones, which are compensated and suppressed separately by using two control components. The integral sliding mode control component is designed to actively reject the matched disturbances, and the control system is then transformed into an equivalent control system subject to equivalent disturbances only related to the unmatched disturbances. The remaining equivalent disturbances are treated by a robust model predictive control component based on the idea of constraints tightening, which minimizes the tracking error in an optimization framework and takes both state and input constraints into account explicitly. The derived compound control strategy is based on these two control components. Conditions are provided to guarantee the robust constraint satisfaction, recursive feasibility and closed-loop stability of the tracking error system. An illustrative example on the quadrotors shows the efficiency and robustness of this compound tracking control algorithm.     

Predictor-based optimal robust guaranteed cost control for uncertain nonlinear systems with completely tracking errors constraint

In this paper, a novel composite controller is proposed to achieve the prescribed performance of completely tracking errors for a class of uncertain nonlinear systems. The proposed controller contains a feedforward controller and a feedback controller. The feedforward controller is constructed by incorporating the prescribed performance function (PPF) and a state predictor into the neural dynamic surface approach to guarantee the transient and steady-state responses of completely tracking errors within prescribed boundaries. Different from the traditional adaptive laws which are commonly updated by the system tracking error, the state predictor uses the prediction error to update the neural network (NN) weights such that a smooth and fast approximation for the unknown nonlinearity can be obtained without incurring high-frequency oscillations. Since the uncertainties existing in the system may influence the prescribed performance of tracking error and the estimation accuracy of NN, an optimal robust guaranteed cost control (ORGCC) is designed as the feedback controller to make the closed-loop system robustly stable and further guarantee that the system cost function is not more than a specified upper bound. The stabilities of the whole closed-loop control system is certified by the Lyapunov theory. Simulation and experimental results based on a servomechanism are conducted to demonstrate the effectiveness of the proposed method.     

Coordinated decentralized sliding mode MRAC with control cost optimization for a class of nonlinear systems

In this paper, we develop an approach for solving the problem of sliding mode decentralized adaptive state-feedback tracking with continuous control actions for a class of uncertain nonlinear dynamical systems. In addition to the traditional asymptotic zero error tracking specification in the sliding mode decentralized model reference adaptive control (MRAC) problem formulation, here an additional requirement is specified explicitly in the problem statement. The tracking objective is described by a set of admissible reference trajectories, called a performance tube. The input signal to the reference model, selected within specified bounds, is used as a design parameter. The best reference trajectory is found by solving an additional optimization problem whose criterion penalizes the variance of the control signal.     

Barrier function-based prescribed-performance adaptive attitude tracking control for spacecraft with uncertainties

This paper addresses the problem of robust adaptive attitude tracking control for spacecraft with mismatched and matched uncertainties. The idea of disturbance estimation and compensation is introduced into the control design. First, finite-time disturbance observers are developed for different channels of spacecraft based on barrier functions for achieving finite-time asymptotic estimates of unknown bounded uncertainties in the system. Second, a class of prescribed performance functions is considered in the design of the barrier function. The spacecraft attitude adaptive tracking control strategy with finite-time convergence capability and prescribed performance is proposed based on the designed finite-time disturbance observers and barrier function. Finally, the theoretical findings are verified by numerical simulations and compared with the simulation results of existing methods.