Approximation-based Adaptive Control Research Articles

Guaranteeing Global Stability for Neuro-Adaptive Control of Unknown Pure-Feedback Nonaffine Systems via Barrier Functions.

Most existing approximation-based adaptive control (AAC) approaches for unknown pure-feedback nonaffine systems retain a dilemma that all closed-loop signals are semiglobally uniformly bounded (SGUB) rather than globally uniformly bounded (GUB). To achieve the GUB stability result, this article presents a neuro-adaptive backstepping control approach by blending the mean value theorem (MVT), the barrier Lyapunov functions (BLFs), and the technique of neural approximation. Specifically, we first resort the MVT to acquire the intermediate and actual control inputs from the nonaffine structures directly. Then, neural networks (NNs) are adopted to approximate the unknown nonlinear functions, in which the compact sets for maintaining the approximation capabilities of NNs are predetermined actively through the BLFs. It is shown that, with the developed neuro-adaptive control scheme, global stability of the resulting closed-loop system is ensured. Simulations are conducted to verify and clarify the developed approach.

Neural Approximation-Based Adaptive Control Using Reinforced Gain for Steering Wheel Torque Tracking of Electric Power Steering System

In practice, steering wheel torque (SWT) control performance for an electric power steering (EPS) system may degrade owing to various reasons, such as model/parameter uncertainties and unpredictable large external disturbances (e.g., reaction force). Furthermore, the desired SWT suddenly varies and its sign also changes because the direction of the steering wheel angle (SWA) often changes according to the driver. In this article, a neural network (NN) approximation-based adaptive nonlinear control (ANC) using reinforced gain (RG) for an EPS system is proposed to resolve the above-mentioned problems using an SWT model. The proposed control method employs an NN approximator, ANC, and RG. The NN approximator is designed to estimate the unknown complex nonlinear function in EPS modeling. The ANC is designed via backstepping to compensate for parametric uncertainties and external disturbances. Further, the RG is designed as a positive nonlinear function of the error to sufficiently suppress the error according to variations in the desired SWT and external disturbance. The RG increases to suppress the error at a rapid transient response, owing to the sudden change in the sign of the desired SWT and the external disturbance. Thus, a high gain (increased RG) is used only when necessary so that an unnecessarily high gain can be avoided.

Locally Weighted Learning Robot Control With Improved Parameter Convergence

An adaptive robot control approach that can achieve an accurate approximation of the complex robot dynamics without knowledge unlearning in the case of multiple sequential tasks is proposed in this article. A locally weighted learning (LWL) model with automatic structure growth according to the size of the learning domain is introduced to approximate unknown robot dynamics, and a composite learning technique with regressor extension is applied to improve parameter convergence. The LWL ensures that learning in one area of the learning domain does not cause unlearning in another area, and the composite learning theoretically guarantees the identification performance of the LWL model. By the exploitation of both stored data in memory and instantaneous data, parameter convergence in the LWL model is achieved under a more achievable interval-excitation condition than the stringent persistent-excitation condition. This further enhances the trajectory tracking performance for multiple sequential tasks, which is generally not achievable by existing approximation-based adaptive robot control approaches. Experimental studies have verified the superiority of the proposed approach over prevalent approaches.

Neural-Network Approximation-Based Adaptive Periodic Event-Triggered Output-Feedback Control of Switched Nonlinear Systems.

This study considers an adaptive neural-network (NN) periodic event-triggered control (PETC) problem for switched nonlinear systems (SNSs). In the system, only the system output is available at sampling instants. A novel adaptive law and a state observer are constructed by using only the sampled system output. A new output-feedback adaptive NN PETC strategy is developed to reduce the usage of communication resources; it includes a controller that only uses event-sampling information and an event-triggering mechanism (ETM) that is only intermittently monitored at sampling instants. The proposed adaptive NN PETC strategy does not need restrictions on nonlinear functions reported in some previous studies. It is proven that all states of the closed-loop system (CLS) are semiglobally uniformly ultimately bounded (SGUUB) under arbitrary switchings by choosing an allowable sampling period. Finally, the proposed scheme is applied to a continuous stirred tank reactor (CSTR) system and a numerical example to verify its effectiveness.

Fuzzy approximation-based adaptive finite-time control for nonstrict feedback nonlinear systems with state constraints

This paper solves the adaptive fuzzy finite-time control (AFFTC) problem for nonstrict feedback nonlinear systems with state constraints. Different from the recently works that mainly focus on the C0 finite-time design scheme, in our context, an innovative C1 AFFTC method is created by combining the fuzzy approximation with backstepping technique. The singularity problem existing the traditional finite-time scheme is skillfully tackled by creating the smooth switch function. The barrier Lyapunov function is exploited to make all states maintain the predefined regions. By means of Lyapunov stability analysis, the devised AFFTC can make all error signals converge into a small neighborhood of the zero in a finite time. Finally, simulation results illustrate the validity of the designed method.

Quantized-Feedback-Based Adaptive Event-Triggered Control of a Class of Uncertain Nonlinear Systems

A quantized-feedback-based adaptive event-triggered tracking problem is investigated for strict-feedback nonlinear systems with unknown nonlinearities and external disturbances. All state variables are quantized through a uniform quantizer and the quantized states are only measurable for the control design. An approximation-based adaptive event-triggered control strategy using quantized states is presented. Compared with the existing recursive quantized feedback control results, the primary contributions of the proposed strategy are (1) to derive a quantized-states-based function approximation mechanism for compensating for unknown and unmatched nonlinearities and (2) to design a quantized-states-based event triggering law for the intermittent update of the control signal. A Lyapunov-based stability analysis is provided to conclude that closed-loop signals are uniformly ultimately bounded and there exists a minimum inter-event time for excluding Zeno behavior. In simulation results, it is shown that the proposed quantized-feedback-based event-triggered control law can be implemented with less than 10% of the total sample data of the existing quantized-feedback continuous control law.

Tracking Control Strategy Using Filter-Based Approximation for the Unknown Control Direction Problem of Uncertain Pure-Feedback Nonlinear Systems

A filter-based recursive tracker design approach is presented for the problem of unknown control directions of pure-feedback systems with completely unknown non-affine nonlinearities. In the controller design procedure, the first-order filters for error surfaces, a control input, and state variables are employed to design nonadaptive virtual and actual control laws independent of adaptive function approximators. In addition, for the unknown control direction problem, the filtering signals are incorporated with Nussbaum functions. Different from existing adaptive approximation-based control schemes in the presence of unknown control directions, the proposed approach does not require any adaptive technique regardless of completely unknown nonlinear functions. Therefore, a simplified tracking structure can be constructed. Using the Lyapunov stability analysis, it is shown that the tracking error is reduced within an adjustable neighborhood of the origin while ensuring all the closed-loop signals are bounded.

Adaptive neural consensus tracking control for a class of 2-order multi-agent systems with nonlinear dynamics

This paper investigates the problem of finite-time consensus tracking control for a class of 2-order nonlinear multi-agent systems (MASs). In order to present a consensus control protocol by adaptive neural control approach, a novel fast finite-time stability criterion is first set up, which provides a theoretical basis for applying approximation-based adaptive control approaches to solve the finite-time control issues. Furthermore, an adaptive neural fast finite-time consensus tracking controller is constructed based on the developed finite-time stability criterion. The suggested adaptive neural backstepping control design scheme successfully avoids the problem of singularity of controllers. Under the action of the presented protocol, the output of each follower tracks the reference signal and other signals of the closed-loop system remain bounded in finite time. The efficacy of the proposed control scheme is confirmed by simulation study.

Approximation-Based Event-Triggered Control Against Unknown Injection Data in Full States and Actuator of Uncertain Lower-Triangular Nonlinear Systems

This paper addresses an approximation-based adaptive event-triggered control problem against unknown injection data in full state measurements and an actuator of systems with unknown strict-feedback nonlinearities. It is assumed that full state variables measured for state-feedback control are corrupted by unknown injection data that denote cyber attacks or fault signals, and all system nonlinearities are unknown. Owing to the corrupted state feedback information, error surfaces using exactly measured state variables become unknown during the recursive control design procedure for strict-feedback nonlinear systems. Thus, they cannot be used to implement the adaptive event-triggered controller. To address this problem, an approximation-based adaptive recursive event-triggered control design using the corrupted state variables is established to ensure that error surfaces using exactly measured state variables converge to an adjustable neighborhood of the origin in the Lyapunov sense. The adaptive controller and its event-triggering law using corrupted states are designed under uncertain injection data where the adaptive injection data compensators using the neural networks are constructed to deal with the unknown injection data effects. The stability of the closed-loop systems and the exclusion of Zeno behavior are analyzed.

Adaptive Control of Proton Exchange Membrane Fuel Cell Air Supply Systems With Asymmetric Oxygen Excess Ratio Constraints

This paper investigates the oxygen starvation and parasitic loss prevention problem of the adaptive oxygen excess ratio (OER) control system of nonlinear proton exchange membrane fuel cells (PEMFCs). Asymmetric OER constraints are considered to avoid oxygen starvation and parasitic loss in the air supply system of PEMFCs. An approximation-based adaptive control strategy is established to ensure robust regulation of the OER while not violating the OER constraints, regardless of unknown system parameters, nonlinearities, and the abrupt changes of the load current. A dynamic surface design technique using an asymmetric barrier Lyapunov function is employed for a recursive control design. Compared with existing control approaches for uncertain nonlinear air supply systems of PEMFCs, this paper first considers the oxygen starvation and parasitic loss prevention problem for the regulation of optimal OER in the control field of nonlinear PEMFCs. Using the Lyapunov stability theorem, the boundedness of all closed-loop signals and the convergence of the output tracking error to the vicinity of zero are proved.

Approximation-Based Adaptive Control of Constrained Uncertain Thermal Management Systems With Nonlinear Coolant Circuit Dynamics of PEMFCs

This paper addresses an adaptive temperature control problem for preventing the membrane dehydration and electrode flooding of nonlinear proton exchange membrane fuel cells (PEMFCs). Compared with the previous thermal control results of PEMFC temperature systems, the main contributions of this paper are two-fold: (i) nonlinear thermal management systems with nonlinear coolant circuit dynamics are firstly adopted in the temperature control field of PEMFCs and (ii) temperature constraints are considered to avoid the membrane dehydration and electrode flooding phenomena of PEMFCs. It is assumed that all system parameters and nonlinearities of thermal management systems including nonlinear coolant circuit dynamic are unknown. A recursive control design methodology is presented to guarantee the robust regulation and constraint satisfaction of the stack temperature. From the Lyapunov theorem, the stability of the resulting closed-loop system is analyzed.

Fuzzy Approximation-Based Adaptive Control of Nonlinear Uncertain State Constrained Systems With Time-Varying Delays

In this paper, a novel adaptive fuzzy tracking control strategy is developed for nonlinear time-varying delayed systems with full state constraints. State constraints and time delays are normally found in various real-life plants, which are two important factors for degrading system performance significantly. In the framework of adaptive control, the effects of state constraints and time-varying delays are removed simultaneously. The integral Barrier Lyapunov functionals (IBLFs) are applied to achieve full-state-constraint satisfactions and remove the need of the transformed error constraints in previous BLFs. The unknown time-varying delays are completely compensated by introducing the separation technique and Lyapunov–Krasovskii functionals (LKFs). The unknown functions existing in systems are approximated by employing fuzzy logic systems (FLSs). With the help of less-adjustable parameters, only one parameter is needed to be adjusted online in each step of control design. The novel strategy can guarantee that a satisfactory tracking performance is achieved and the signals existing in the closed-loop system are bounded. Finally, by presenting simulation results, the efficiency of the proposed approach is revealed.

A Hybrid Adaptive Control Strategy for Industrial Robotic Joints

This paper presents a hybrid adaptive approximation-based control (HAAC) strategy for a class of uncertain robotic joints' system. The proposed control structure consists of a robust sliding mode controller and an adaptive approximation-based controller. The robust sliding mode controller is designed by using the super-twisting algorithm, which is a particularly effective method to decrease the chattering caused by the traditional sliding mode control (SMC) and compensate the disturbances. Another improvement of the robust sliding mode controller is that the robust control parameters only subject to the upper bound of the derivative of the external disturbances, rather than choosing a relatively large value. Moreover, the designed adaptive approximation-based controller has the following two distinctive features: 1) the control parameters are designed to be adjusted in real time and 2) the prior knowledge of actual robotic model is not required to be known. These features contribute to compensating the uncertainties. The stability of the closed-loop system is proved by using the Lyapunov theory, and the simulation results demonstrate the effectiveness of the proposed control method. Finally, the proposed HAAC could apply in the experiments of industrial robotic joints' system.

Nussbaum gain adaptive neural control for stochastic pure-feedback nonlinear time-delay systems with full-state constraints

Abstract In this paper, the problem concerned with adaptive approximation-based control is discussed for a class of stochastic pure-feedback nonlinear time-delay systems with unknown direction control gains and full-state constraints. In the controller design process, the approximation capability of neural networks is utilized to identify the unknown nonlinearities, the appropriate Lyapunov–Krasovskii functionals are constructed to compensate the unknown time-delay terms, barrier Lyapunov functions (BLFs) are designed to ensure that the state variables are constrained, and the Nussbaum-type gain function is used to solve the difficulties caused by the unknown virtual control gains. Then, based on adaptive backstepping technique and Lyapunov stability theory, a robust control scheme is presented, and the developed controller decreases the number of learning parameters and thus reduces the computational burden. It is shown that the proposed controller can guarantee that all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a compact set of the origin. Finally, two simulation examples are included to validate the effectiveness of the proposed approach.

On local approximation-based adaptive control with applications to robotic manipulators and biped robots

The adaptive approximation control is a powerful tool for controlling robotic systems with unmodeled dynamics. The local (partitioned) approximation-based adaptive control includes representation of the uncertain matrices and vectors in the robot model as finite combinations of basis functions. Update laws for the weighting matrices are obtained by the Lyapunov-like design. However, one of the inherent limitations of this category of approximation is curse dimensionality associated with the approximation of uncertain matrix. There are three possible representations for the approximation of the uncertain matrix: Kronecker product, sparse matrices, and GL operator. Both Kronecker product and sparse matrices can grow exponentially with the dimension of the target matrix, whereas GL operator can grow linearly but without the use of conventional operations of matrices. In light of the above, this paper proposes a simple representation for the approximation of the uncertain matrix. The proposed representation is directly linear with respect to the dimension of the target matrix using the conventional operations of matrices. A comparative study is performed to all previously investigated representations, including the proposed representation in view of control law, adaptive law and the order of approximation for robotic manipulators in free space. Two case studies are simulated which are: two-link manipulator and 6-link biped robots during the single support phase. The results show that for low dimension robotic manipulators, all representations can be conducted equivalently. There is no large difference in view of simulation time, whereas for higher degrees of freedom robots the Gl operator and the proposed representation are superior in view of simulation time.

Approximation-based adaptive tracking of a class of uncertain nonlinear time-delay systems in nonstrict-feedback form

ABSTRACTThis paper investigates a predefined performance control problem for adaptive tracking of uncertain nonlinear time-delay systems in nonstrict-feedback form. Nonstrict-feedback nonlinearities, time-varying delays and external disturbances are assumed to be unknown. Based on the exponential decaying design functions denoting the preassigned bounds of transient and steady-state tracking errors, some variable separation lemmas are derived to design an approximation-based robust adaptive control scheme in the presence of nonstrict-feedback time-delayed nonlinearities. The proposed control system guarantees that a tracking error remains within a predesigned bound for all t ≥ 0 and converges to a preselected neighbourhood of the origin. Compared with the existing results in the literature, the main contribution of this paper is to provide a solution on the guaranteed performance control in the presence of unknown nonstrict-feedback nonlinearities related to all delayed state variables. Simulation results illustrate the effectiveness of the proposed methodology.

Composite Learning Fuzzy Control of Uncertain Nonlinear Systems

Function approximation accuracy and computational cost are two major concerns in approximation-based adaptive fuzzy control. In this paper, a model reference composite learning fuzzy control strategy is proposed for a class of affine nonlinear systems with functional uncertainties. In the proposed approach, a modified modeling error that utilizes data recorded online is defined as a prediction error, a linear filter is applied to estimate time derivatives of plant states, and both the tracking error and the prediction error are exploited to update parametric estimates. It is proven that the closed-loop system achieves semiglobal practical exponential stability by an interval-excitation condition which is much weaker than a persistent-excitation condition. Compared with a concurrent learning approach that has the same aim as this study, the computational cost of the proposed approach is significantly reduced for the guarantee of accurate function approximation. An illustrative example of aircraft wing rock control has been provided to verify effectiveness of the proposed control strategy.

Neural Approximation-Based Adaptive Control for a Class of Nonlinear Nonstrict Feedback Discrete-Time Systems.

In this paper, an adaptive control approach-based neural approximation is developed for a class of uncertain nonlinear discrete-time (DT) systems. The main characteristic of the considered systems is that they can be viewed as a class of multi-input multioutput systems in the nonstrict feedback structure. The similar control problem of this class of systems has been addressed in the past, but it focused on the continuous-time systems. Due to the complicacies of the system structure, it will become more difficult for the controller design and the stability analysis. To stabilize this class of systems, a new recursive procedure is developed, and the effect caused by the noncausal problem in the nonstrict feedback DT structure can be solved using a semirecurrent neural approximation. Based on the Lyapunov difference approach, it is proved that all the signals of the closed-loop system are semiglobal, ultimately uniformly bounded, and a good tracking performance can be guaranteed. The feasibility of the proposed controllers can be validated by setting a simulation example.

Approximation-based adaptive neural output feedback control for a class of uncertain switched stochastic nonlinear systems with average dwell time condition

This paper studies the problem of adaptive neural output feedback controller design for a class of uncertain switched stochastic nonlinear systems in strict-feedback form. In the design procedure, a common coordinate transformation for all subsystems is constructed to overcome the design difficulty caused by adoption of different coordinate transformation for different subsystems. Then, by using switched state observer to estimate the unmeasured states and different update laws for different subsystems, a novel neural output-feedback controller is designed via backstepping approach. Furthermore, based on the Lyapunov method and the average dwell time condition, the stability of the resulting closed-loop system can be achieved. It is shown that all the signals of the closed-loop system are bounded under a class of switching signals with average dwell time. Finally, simulation results are included for validating the advantages of the proposed approaches.

Hybrid feedback feedforward: An efficient design of adaptive neural network control

This paper presents an efficient hybrid feedback feedforward (HFF) adaptive approximation-based control (AAC) strategy for a class of uncertain Euler–Lagrange systems. The control structure includes a proportional–derivative (PD) control term in the feedback loop and a radial-basis-function (RBF) neural network (NN) in the feedforward loop, which mimics the human motor learning control mechanism. At the presence of discontinuous friction, a sigmoid-jump-function NN is incorporated to improve control performance. The major difference of the proposed HFF-AAC design from the traditional feedback AAC (FB-AAC) design is that only desired outputs, rather than both tracking errors and desired outputs, are applied as RBF-NN inputs. Yet, such a slight modification leads to several attractive properties of HFF-AAC, including the convenient choice of an approximation domain, the decrease of the number of RBF-NN inputs, and semiglobal practical asymptotic stability dominated by control gains. Compared with previous HFF-AAC approaches, the proposed approach possesses the following two distinctive features: (i) all above attractive properties are achieved by a much simpler control scheme; (ii) the bounds of plant uncertainties are not required to be known. Consequently, the proposed approach guarantees a minimum configuration of the control structure and a minimum requirement of plant knowledge for the AAC design, which leads to a sharp decrease of implementation cost in terms of hardware selection, algorithm realization and system debugging. Simulation results have demonstrated that the proposed HFF-AAC can perform as good as or even better than the traditional FB-AAC under much simpler control synthesis and much lower computational cost.