Further results on adaptive control for a class of nonlinear systems using neural networks

Real-Time Terrain-Following of an Autonomous Quadrotor by Multi-Sensor Fusion and Control

For the application of the autonomous guidance of a quadrotor from confined undulant ground, terrain-following is the major issue for flying at a low altitude. This study has modified the open-source autopilot based on the integration of a multi-sensor receiver (a Global Navigation Satellite System (GNSS)), a Lidar-lite (a laser-range-finder device), a barometer and a low-cost inertial navigation system (INS)). These automatically control the position, attitude and height (a constant clearance above the ground) to allow terrain-following and avoid obstacles based on multi-sensors that maintain a constant height above flat ground or with obstacles. The INS/Lidar-lite integration is applied for the attitude and the height stabilization, respectively. The height control is made by the combination of an extended Kalman filter (EKF) estimator and a cascade proportional-integral-derivative (PID) controller that is designed appropriately for the noise characteristics of low accuracy sensors. The proposed terrain-following is tested by both simulations and real-world experiments. The results indicate that the quadrotor can continuously navigate and avoid obstacles at a real-time response of reliable height control with the adjustment time of the cascade PID controller improving over 50% than that of the PID controller.

Adaptive Neural Control of Underactuated Surface Vessels With Prescribed Performance Guarantees

This paper presents adaptive neural tracking control of underactuated surface vessels with modeling uncertainties and time-varying external disturbances, where the tracking errors consisting of position and orientation errors are required to keep inside their predefined feasible regions in which the controller singularity problem does not happen. To provide the preselected specifications on the transient and steady-state performances of the tracking errors, the boundary functions of the predefined regions are taken as exponentially decaying functions of time. The unknown external disturbances are estimated by disturbance observers and then are compensated in the feedforward control loop to improve the robustness against the disturbances. Based on the dynamic surface control technique, backstepping procedure, logarithmic barrier functions, and control Lyapunov synthesis, singularity-free controllers are presented to guarantee the satisfaction of predefined performance requirements. In addition to the nominal case when the accurate model of a marine vessel is known a priori, the modeling uncertainties in the form of unknown nonlinear functions are also discussed. Adaptive neural control with the compensations of modeling uncertainties and external disturbances is developed to achieve the boundedness of the signals in the closed-loop system with guaranteed transient and steady-state tracking performances. Simulation results show the performance of the vessel control systems.

Output-Feedback Adaptive Neural Controller for Uncertain Pure-Feedback Nonlinear Systems Using a High-Order Sliding Mode Observer

A novel adaptive neural output-feedback controller for SISO nonaffine pure-feedback nonlinear systems is proposed. The majority of the previously described adaptive neural controllers for pure-feedback nonlinear systems were based on the dynamic surface control (DSC) or backstepping schemes. This makes the control law as well as the stability analysis highly lengthy and complicated. Moreover, there has been very limited research till date on the output-feedback neural controller for this class of the systems. The proposed controller evades adopting adaptive backstepping or DSC scheme through reformulating the original system into the Brunovsky form, which considerably simplifies the control law. Combining a high-order sliding mode observer and single radial-basis function network with universal approximation property, it is shown that the controller guarantees closed-loop system stability in the Lyapunov sense.

Adaptive Neural Control for Robotic Manipulators With Output Constraints and Uncertainties

This paper investigates adaptive neural control methods for robotic manipulators, subject to uncertain plant dynamics and constraints on the joint position. The barrier Lyapunov function is employed to guarantee that the joint constraints are not violated, in which the Moore-Penrose pseudo-inverse term is used in the control design. To handle the unmodeled dynamics, the neural network (NN) is adopted to approximate the uncertain dynamics. The NN control based on full-state feedback for robots is proposed when all states of the closed loop are known. Subsequently, only the robot joint is measurable in practice; output feedback control is designed with a high-gain observer to estimate unmeasurable states. Through the Lyapunov stability analysis, system stability is achieved with the proposed control, and the system output achieves convergence without violation of the joint constraints. Simulation is conducted to approve the feasibility and superiority of the proposed NN control.

Adaptive neural network control of unknown nonlinear affine systems with input deadzone and output constraint

In this paper, we aim to solve the control problem of nonlinear affine systems, under the condition of the input deadzone and output constraint with the external unknown disturbance. To eliminate the effects of the input deadzone, a Radial Basis Function Neural Network (RBFNN) is introduced to compensate for the negative impact of input deadzone. Meanwhile, we design a barrier Lyapunov function to ensure that the output parameters are restricted. In support of the barrier Lyapunov method, we build an adaptive neural network controller based on state feedback and output feedback methods. The stability of the closed-loop system is proven via the Lyapunov method and the performance of the expected effects is verified in simulation.

Global asymptotic stabilization using adaptive fuzzy PD control

It is well-known that standard adaptive fuzzy control (AFC) can only guarantee uniformly ultimately bounded stability due to inherent fuzzy approximation errors (FAEs). This paper proves that standard AFC with proportional-derivative (PD) control can guarantee global asymptotic stabilization even in the presence of FAEs for a class of uncertain affine nonlinear systems. Variable-gain PD control is designed to globally stabilize the plant. An optimal FAE is shown to be bounded by the norm of the plant state vector multiplied by a globally invertible and nondecreasing function, which provides a pivotal property for stability analysis. Without discontinuous control compensation, the closed-loop system achieves global and partially asymptotic stability in the sense that all plant states converge to zero. Compared with previous adaptive approximation-based global/asymptotic stabilization approaches, the major advantage of our approach is that global stability and asymptotic stabilization are achieved concurrently by a much simpler control law. Illustrative examples have further verified the theoretical results.

Adaptive learning control for finite interval tracking based on constructive function approximation and wavelet

Using a constructive function approximation network, an adaptive learning control (ALC) approach is proposed for finite interval tracking problems. The constructive function approximation network consists of a set of bases, and the number of bases can evolve when learning repeats. The nature of the basis allows the continuous adaptive learning of parameters when the network undergoes any structural changes, and consequently offers the flexibility in tuning the network structure. The expandability of the bases guarantees precision of the function approximation and avoids the trial-and-error procedure in structure selection for any fixed structure network. Two classes of unknown nonlinear functions, namely, either global L(2) or local L(2) with a known bounding function, are taken into consideration. Using the Lyapunov method, the existence of solution and the convergence property of the proposed ALC system are discussed in a rigorous manner. By virtue of the celebrated orthonormal and multiresolution properties, wavelet network is used as the universal function approximator, with the weights tuned by the proposed adaptive learning mechanism.

Projection-based adaptive neurocontrol with switching logic deadzone tuning

In this brief, an adaptive neural network (NN) controller is proposed for multiple-input-multiple-output (MIMO) nonlinear systems with triangular control structure and unknown control directions. Deadzones are employed in the projection-based NN weight learning laws and the Nussbaum parameter update laws with levels tuned by an innovative switching logic tuning mechanism. Detailed analysis using a family of Lyapunov-like integral functions and the function approximation capability of NNs proves that all the tracking errors are semiglobal uniform ultimate bounded in small neighborhoods of the origin while the closed-loop system variables (state vector, NN weights, Nussbaum parameters) and the control law remain bounded. A simulation study confirms the theoretical results and verifies the effectiveness of the proposed design.

Adaptive neural control for strict-feedback nonlinear systems without backstepping

In this brief, a new adaptive neurocontrol algorithm for a single-input-single-output (SISO) strict-feedback nonlinear system is proposed. Most of the previous adaptive neural control algorithms for strict-feedback nonlinear systems were based on the backstepping scheme, which makes the control law and stability analysis very complicated. The main contribution of the proposed method is that it demonstrates that the state-feedback control of the strict-feedback system can be viewed as the output-feedback control problem of the system in the normal form. As a result, the proposed control algorithm is considerably simpler than the previous ones based on backstepping. Depending heavily on the universal approximation property of the neural network (NN), only one NN is employed to approximate the lumped uncertain system nonlinearity. The Lyapunov stability of the NN weights and filtered tracking error is guaranteed in the semiglobal sense.

Robust dynamic sliding-mode control using adaptive RENN for magnetic levitation system

In this paper, a robust dynamic sliding mode control system (RDSMC) using a recurrent Elman neural network (RENN) is proposed to control the position of a levitated object of a magnetic levitation system considering the uncertainties. First, a dynamic model of the magnetic levitation system is derived. Then, a proportional-integral-derivative (PID)-type sliding-mode control system (SMC) is adopted for tracking of the reference trajectories. Moreover, a new PID-type dynamic sliding-mode control system (DSMC) is proposed to reduce the chattering phenomenon. However, due to the hardware being limited and the uncertainty bound being unknown of the switching function for the DSMC, an RDSMC is proposed to improve the control performance and further increase the robustness of the magnetic levitation system. In the RDSMC, an RENN estimator is used to estimate an unknown nonlinear function of lumped uncertainty online and replace the switching function in the hitting control of the DSMC directly. The adaptive learning algorithms that trained the parameters of the RENN online are derived using Lyapunov stability theorem. Furthermore, a robust compensator is proposed to confront the uncertainties including approximation error, optimal parameter vectors, and higher order terms in Taylor series. Finally, some experimental results of tracking the various periodic trajectories demonstrate the validity of the proposed RDSMC for practical applications.

Direct Adaptive Controller for Nonaffine Nonlinear Systems Using Self-Structuring Neural Networks

A direct adaptive state-feedback controller is proposed for highly nonlinear systems. We consider uncertain or ill-defined nonaffine nonlinear systems and employ a neural network (NN) with flexible structure, i.e., an online variation of the number of neurons. The NN approximates and adaptively cancels an unknown plant nonlinearity. A control law and adaptive laws for the weights in the hidden layer and output layer of the NN are established so that the whole closed-loop system is stable in the sense of Lyapunov. Moreover, the tracking error is guaranteed to be uniformly asymptotically stable (UAS) rather than uniformly ultimately bounded (UUB) with the aid of an additional robustifying control term. The proposed control algorithm is relatively simple and requires no restrictive conditions on the design constants for the stability. The efficiency of the proposed scheme is shown through the simulation of a simple nonaffine nonlinear system.