Adaptive Control Of Nonlinear Systems Research Articles

Stochastic optimisation algorithm for optimisation of controller parameters for control of dissolved oxygen in wastewater treatment plant

Wastewater treatment plants (WWTPs) are very important facilities for mankind. They enable the removal and neutralisation of man-made pollutants. Therefore, it is important for wastewater treatment plants to operate as efficiently as possible so that the level of pollutants in the treated wastewater meets specific requirements. This paper concerns the design of a hierarchical nonlinear adaptive control system for dissolved oxygen (DO) concentration in wastewater for a biological Sequential Batch Reactor (SBR). The parameters of the control system used are optimised to ensure the best possible control quality and low energy consumption at the same time. Based on data collected from a case study WWTP, an Activated Sludge Model 2d (ASM2d) of the biological processes and a model of the aeration system are applied. The Coyote Optimization Algorithm (COA) is used to optimize the adaptive controller parameters. A Proportional-Integral-Derivative (PID) control system is also developed to compare the control results. The results obtained from simulation studies for both control systems are presented. As a result of optimised parameters, higher wastewater treatment efficiency and reduced electricity consumption are achieved.

Event-Triggered Adaptive Control of Nonlinear Systems With Dynamic Uncertainties: The Switching Threshold Case

This brief considers the adaptive tracking problem for a class of uncertain nonlinear systems. First, the disturbance observer (DO) is established, and the neural network (NN) technique is adopted to deal with unmeasured disturbances and system dynamic uncertainties. Then, the switching threshold event-triggered mechanism is utilized, and the adaptive tracking controller is further designed based on backstepping techniques. We show that the tracking errors simultaneously converge to an adjustable compact set of origin, and all the closed-loop signals are semi-globally uniformly bounded. Finally, the practicability and effectiveness of the proposed control approach are well illustrated by a simulation case.

Finite-time performance guaranteed event-triggered adaptive control for nonlinear systems with unknown control direction

This paper studies the issue of finite-time performance guaranteed event-triggered (ET) adaptive neural tracking control for strict-feedback nonlinear systems with unknown control direction. A novel finite-time performance function is first constructed to describe the prescribed tracking performance, and then a new lemma is given to show the differentiability and boundedness of the performance function, which is important for the verification of the closed-loop system stability. Furthermore, with the help of the error transformation technique, the origin constrained tracking error is transformed into an equivalent unconstrained one. By utilizing the first-order sliding mode differentiator, the issue of “explosion of complexity” caused by the backstepping design is adequately addressed. Subsequently, an ingenious adaptive updated law is given to co-design the controller and the ET mechanism by the combination of the Nussbaum-type function, thus effectively handling the influences of the measurement error resulted from the ET mechanism and the challenge of the controller design caused by the unknown control direction. The presented event-triggered control scheme can not only guarantee the prescribed tracking performance, but also alleviate the communication burden simultaneously. Finally, numerical and practical examples are provided to demonstrate the validity of the proposed control strategy.

A New Adaptive Controller for Nonlinear Systems with Uncertain Virtual Control Gains

This paper addresses the adaptive asymptotic tracking control problem for nonlinear systems whose virtual control gains are unknown nonlinear functions of system states. Only in the first step, the Nussbaum gain technique is utilized to handle the uncertain virtual control gain. In the remaining steps, virtual control gains are dealt with by constructing novel control laws without the approximation of the uncertain nonlinear functions and external disturbances by neural networks or fuzzy logic. New adaptive laws are defined to compensate for unknown virtual control gains, uncertain parameters, and external disturbances. Finally, an adaptive tracking controller is designed and applied to the control of a 3‐order robot system, which guarantees the boundedness of all the signals in the closed‐loop system and asymptotic stability of the tracking error.

Incremental Adaptive Control of a Class of Nonlinear Nonaffine Systems

As a class of familiar nonlinear systems, nonaffine systems are frequently encountered in practical applications. Currently, in the context of learning control, there is a lack of research results about such general class of nonlinear systems, especially for the case of performing infinite interval tasks. This article focuses on the incremental adaptive control for nonlinear systems in nonaffine form, without requiring periodicity or repeatability. Instead of using the integral adaptation, incremental adaptive mechanisms are developed and the corresponding control schemes are presented, by which the numerical integration for implementation can be avoided. With the proposed incremental adaptation, the implicit function theorem is introduced to solve the intractability problem of the nonaffine structure. The robustness (robust convergence) of the tracking error is characterized, with the aid of a proposed key lemma, while the boundedness of all the variables is examined. Numerical results are presented to verify the effectiveness of the proposed control design.

Hybrid adaptive control of nonlinear systems with non-Lipschitz nonlinearities

In this paper, a hybrid adaptive control method is proposed for a class of discrete-time multiple-inputs-multiple-outputs (MIMO) systems with non-Lipschitz nonlinearities by introducing a novel Riemann sum operator with variable step size. Firstly, for the first order approximation of the original nonlinear system, a linear adaptive controller is developed to assure essential boundedness of all the signals but with unsatisfactory performance. Secondly, an artificial neural network (ANN)-based nonlinear adaptive controller is designed for the original system to improve response performance, nevertheless, may lead to instability. Thirdly, switching mechanism between the linear adaptive controller and the nonlinear one is suitably designed to achieve stability and improved output tracking performance simultaneously. Finally, a numerical example is provided to verify the effectiveness of the proposed method.

Direct adaptive control for nonlinear systems using a TSK fuzzy echo state network based on fractional-order learning algorithm

This paper presents a new Takagi-Sugeno-Kang fuzzy Echo State Neural Network (TSKFESN) structure to design a direct adaptive control for uncertain SISO nonlinear systems. The proposed TSKFESN structure is based on the echo state neural network framework containing multiple sub-reservoirs. Each sub-reservoir is weighted with a TSK fuzzy rule. The adaptive law of the TSKFESN-based direct adaptive controller is derived by using a fractional-order sliding mode learning algorithm. Moreover, the Lyapunov stability criterion is employed to verify the convergence of the fractional-order adaptive law of the controller parameters. The evaluation of the proposed direct adaptive control scheme is verified using two case studies, the regulation problem of a torsional pendulum and the speed control of a direct current (DC) machine as a real-time application. The simulation and the experimental results show the effectiveness of the proposed control scheme.

Neural-based adaptive control for nonlinear systems with quantized input and the output constraint

This study reports adaptive neural network tracking control problem for a class of uncertain strict-feedback nonlinear systems with quantized input and the output constraint. To successfully overcome the obstacle caused by quantized input and the output constraint, the disintegration of hysteresis quantizer and a log-type Barrier Lyapunov function are exploited. During the control design, uncertain nonlinearities are approximated by radial basis function neural networks. Moreover, the number of adaptive law is only one, thereby reducing the computational burden. Under the proposed quantized tracking control scheme, the boundedness of all signals in the closed-loop system is validated and the output tracking error converges to an arbitrarily small domain of origin. At the same time, it can be ensured that the output constraint isn’t violated. Finally, two simulation examples are provided to verify the effectiveness of the control scheme.

Finite-time command filtered adaptive control for nonlinear systems via immersion and invariance

Finite-time command filtered adaptive control for nonlinear systems via immersion and invariance

Finite‐time adaptive control for nonlinear systems with uncertain parameters based on the command filters

SummaryThe trajectory tracking control problem for a class of nonlinear systems with uncertain parameters is considered in this article. A new adaptive finite‐time tracking control is designed based on the adaptive backstepping method via the command filters. The command filter mechanism can avoid the calculation of partial derivatives and solve the “explosion of complexity” in the backstepping design. The compensation signals are introduced to eliminate errors produced by the command filters. The proposed adaptive backstepping control can guarantee the tracking error remains in a small neighborhood of the origin in finite time, while the practical finite‐time stability of the control systems with uncertain parameters is proven by the stability criterion. The effectiveness of the proposed scheme is verified by some simulation results.

Modeling and Nonlinear Adaptive Control for Omnidirectional Mobile Robot

This study presents a complete model for RobotinoMD an omnidirectional mobile robot. This model includes the kinematics and dynamics. It is used for the simulation and design of an adaptive nonlinear control system. The hierarchical control system that is proposed has three levels. The level-one which is the inner loop is used to control the DC motors that drive the robot wheels. A control design method combining an adaptive feedback linearization technique and the Backstepping approach is used to find the controller equation. The adaptation module that is included in the control system maintains the performance of the system in the presence of uncertainties on the inertia, weight and other parameters in the robot dynamics. The level-one controller receives its reference signal from the level-two controller which converts the linear and rotational speeds into desired speeds. This level-two controller receives its reference signal from the level-three controller which is the outer loop controller. The level-three controller equation is found so that the robot can follow a desired path described in a Cartesian space. The proposed control system is evaluated in simulation in the MATLAB-SIMULINK environment. It is compared to a PID controller. Simulation results show that the nonlinear adaptive controller has better performances.

Fuzzy Adaptive Control of Nonlinear Systems with Odd System Powers, Complex Dynamics, and Uncertain Control Coefficients

The adaptive stabilization issue for complicated nonlinear systems is investigated in this work. The discussed problem is comparatively challenging since the system owns non-triangular structure and involves unknown coefficients, unknown parameters, and complex dynamics. By proposing an improved fuzzy-based adaptive control approach, a new stable control law is designed to make semi-globally uniformly ultimately bounded (SUUB). The presented method is validated with a simulation example.

Novel fuzzy event-triggered adaptive control for nonlinear systems with input hysteresis

Novel fuzzy event-triggered adaptive control for nonlinear systems with input hysteresis

Implicit Regularization and Momentum Algorithms in Nonlinearly Parameterized Adaptive Control and Prediction.

Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear systems revolves around a few key algorithms. By exploiting strong connections between classical adaptive nonlinear control techniques and recent progress in optimization and machine learning, we show that there exists considerable untapped potential in algorithm development for both adaptive nonlinear control and adaptive dynamics prediction. We begin by introducing first-order adaptation laws inspired by natural gradient descent and mirror descent. We prove that when there are multiple dynamics consistent with the data, these non-Euclidean adaptation laws implicitly regularize the learned model. Local geometry imposed during learning thus may be used to select parameter vectors-out of the many that will achieve perfect tracking or prediction-for desired properties such as sparsity. We apply this result to regularized dynamics predictor and observer design, and as concrete examples, we consider Hamiltonian systems, Lagrangian systems, and recurrent neural networks. We subsequently develop a variational formalism based on the Bregman Lagrangian. We show that its Euler Lagrange equations lead to natural gradient and mirror descent-like adaptation laws with momentum, and we recover their first-order analogues in the infinite friction limit. We illustrate our analyses with simulations demonstrating our theoretical results.

Adaptive control of nonlinear systems with severe uncertainties in the input powers

Adaptive control of nonlinear systems with severe uncertainties in the input powers

Neural Network–Based Event-Triggered Adaptive Control Algorithms for Uncertain Nonlinear Systems with Actuator Failures

The adaptive control for strict-feedback nonlinear systems has drawn a lot of attention in various communities. Since neural network is a useful universal-approximator to approximate unknown plant model, the neural network–based adaptive control for nonlinear systems has attracted substantial interest over decades. Furthermore, to reduce the controller updating and save the control resource, the event-triggered mechanism has been widely applied. In this paper, the RBF neural network is applied to construct the state and composite disturbance observers and the back-stepping and Lyapunov-like method are applied to design the event-triggered adaptive controller. The theoretical framework of adaptive fault-tolerant control issue for strict-feedback nonlinear system that suffer from both unknown mismatched disturbance and actuator failures is formulated. This paper comes up with a novel event-triggered control strategy to guarantee that the tracking issue is resolved with better desired performance. In this study, a unified theoretical mechanism is developed to tackle the case where some factors consisting of unknown state variables, unknown mismatched disturbance, and actuator failures as well as event-triggered effects are merged together. We expect to extend the proposed method for the self-triggered case.

Higher-order tracking properties of nonlinear adaptive control systems

While the asymptotic output tracking property has been proven for many nonlinear adaptive control systems, their higher-order output tracking property has not been reported. In this paper, the higher-order derivative convergence of the output tracking error e ( t ) is studied for nonlinear adaptive control systems using the feedback linearization design. It is proven that not only each error component e j ( t ) from e ( t ) = [ e 1 ( t ) , e 2 ( t ) , … , e m ( t ) ] T converges to zero asymptotically but also its up to k th-order time-derivative e j ( k ) ( t ) converges to zero, for k = 1 , 2 , … , ρ j , where ρ j , j = 1 , 2 , … , m , are the control relative degrees of the nonlinear system with m inputs.

Multi-dimensional Taylor network-based adaptive control for nonlinear systems with unknown parameters

This paper presents an adaptive multi-dimensional Taylor network (MTN) control approach for a class of nonlinear systems with unknown parameters. MTN is employed to identify unknown nonlinear characteristics existing in the system, and then a novel adaptive MTN tracking control method is proposed, via backstepping technique. In the controller design, double adaptive laws are designed and appropriate Lyapunov functions are chosen to overcome the difficulties caused by the unknown parameters. The designed controller can guarantee that all the variables in the closed-loop systems are bounded and the tracking error can be arbitrarily small. Finally, simulation results are presented to verify the effectiveness of the proposed approach.

Adaptive Control Using Neural Networks and Approximate Models for Nonlinear Dynamic Systems

In this research, a comparative study of two recurrent neural networks, nonlinear autoregressive with exogenous input (NARX) neural network and nonlinear autoregressive moving average (NARMA-L2), and a feedforward neural network (FFNN) is performed for their ability to provide adaptive control of nonlinear systems. Three dynamical nonlinear systems of different complexity are considered. The aim of this work is to make the output of the plant follow the desired reference trajectory. The problem becomes more challenging when the dynamics of the plants are assumed to be unknown, and to tackle this problem, a multilayer neural network-based approximate model is set up which will work in parallel to the plant and the control scheme. The network parameters are updated using the dynamic backpropagation (BP) algorithm.

Neural network adaptive control of nonlinear systems preceded by hysteresis

Neural network adaptive control is proposed for a class of nonlinear system preceded by hysteresis. A novel model is developed to represent the hysteresis characteristics in explicit form. Furthermore, the auxiliary variable of the proposed model is proved to be bounded, which is essential for controller design. Then, neural network adaptive controller is directly applied to mitigate the influence of the hysteresis without constructing the hysteresis inverse. The updated law and control law of the controllers are derived from Lyapunov stability theorem, so that the boundedness of the close-loop system is guaranteed. Finally, the experimental tests are carried out to validate the effectiveness of the proposed approach.