Robust Control Of Nonlinear Systems Research Articles

An Introduction to Nonlinear Robust Control for Unmanned Quadrotor Aircraft: How to Design Control Algorithms for Quadrotors Using Sliding Mode Control and Adaptive Control Techniques [Focus on Education

Quadrotor aircraft are drawing considerable attention for their high mobility and capacity to perform tasks with complete autonomy, while minimizing the costs and risks involved with the direct intervention of human operators. Moreover, several limitations characterizing these rotary-wing unmanned aerial systems (UASs), such as their underactuation, make quadrotors ideal testbeds for innovative theoretical approaches to the problem of controlling mechanical systems. Designing autopilots for autonomous quadrotors is a challenging task, which involves multiple interconnected aspects. Numerous researchers are currently addressing the problem of designing autonomous guidance systems, navigation systems, and control systems for quadrotors. The primary goal of this article is to present an analysis and synthesis of several nonlinear robust control systems for quadrotors, as discussed in “Summary.” First, the article presents and analyzes the equations of motion of quadrotors under three sets of progressively restrictive modeling assumptions: 1) the vehicle’s inertial properties (such as the mass and matrix of inertia) vary in time, 2) the quadrotor’s main frame is a rigid body and the propellers are thin spinning discs, and 3) the pitch and roll angles are small.

Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

SummaryWithout any prior knowledge of the physical bounds of unknown parameters and uncertain nonlinearities, an indirect adaptive robust controller is constructed for uncertain nonlinear time‐varying systems in a strict‐feedback form. Firstly, an adaptive strong robust controller is derived based on the command filtered adaptive backstepping approach. This controller not only can guarantee the boundedness of the closed‐loop system signals in the presence of time‐varying (TV) parameters and uncertain nonlinearities but also obviate the need to compute analytic derivatives of virtual control functions. Thus, the problem of “explosion of terms” in the standard adaptive backstepping technique is avoided. Through introduction of a simple adaptation law on the upper bound of uncertainties, a smooth robust control term is used to realize the disturbance attenuation. Afterwards, based on the nonlinear X‐swapping techniques, a modular approach in which the controller and the identifier can be designed separately is exploited. A novel algorithm is proposed to estimate the TV parameters accurately. By adopting the variation trend of the covariance matrix as an indicator of the driving signals' persistent excitation level, this online parameter estimation law is switched between a modified least‐squares algorithm and a gradient algorithm based on fixed σ‐modification. Finally, a series of properties on the asymptotic stability and the global uniform ultimate boundedness of the closed‐loop system is established. Simulation results verify the effectiveness of the suggested method.

Adaptive Critic Designs for Event-Triggered Robust Control of Nonlinear Systems With Unknown Dynamics.

This paper develops a novel event-triggered robust control strategy for continuous-time nonlinear systems with unknown dynamics. To begin with, the event-triggered robust nonlinear control problem is transformed into an event-triggered nonlinear optimal control problem by introducing an infinite-horizon integral cost for the nominal system. Then, a recurrent neural network (RNN) and adaptive critic designs (ACDs) are employed to solve the derived event-triggered nonlinear optimal control problem. The RNN is applied to reconstruct the system dynamics based on collected system data. After acquiring the knowledge of system dynamics, a unique critic network is proposed to obtain the approximate solution of the event-triggered Hamilton-Jacobi-Bellman equation within the framework of ACDs. The critic network is updated by using simultaneously historical and instantaneous state data. An advantage of the present critic network update law is that it can relax the persistence of excitation condition. Meanwhile, under a newly developed event-triggering condition, the proposed critic network tuning rule not only guarantees the critic network weights to converge to optimums but also ensures nominal system states to be uniformly ultimately bounded. Moreover, by using Lyapunov method, it is proved that the derived optimal event-triggered control (ETC) guarantees uniform ultimate boundedness of all the signals in the original system. Finally, a nonlinear oscillator and an unstable power system are provided to validate the developed robust ETC scheme.

An adaptive critic approach to event‐triggered robust control of nonlinear systems with unmatched uncertainties

SummaryIn this paper, we develop a novel event‐triggered robust control strategy for continuous‐time nonlinear systems with unmatched uncertainties. First, we build a relationship to show that the event‐triggered robust control can be obtained by solving an event‐triggered nonlinear optimal control problem of the auxiliary system. Then, within the framework of reinforcement learning, we propose an adaptive critic approach to solve the event‐triggered nonlinear optimal control problem. Unlike typical actor‐critic dual approximators used in reinforcement learning, we employ a unique critic approximator to derive the solution of the event‐triggered Hamilton‐Jacobi‐Bellman equation arising in the nonlinear optimal control problem. The critic approximator is updated via the gradient descent method, and the persistence of excitation condition is necessary. Meanwhile, under a newly proposed event‐triggering condition, we prove that the developed critic approximator update rule guarantees all signals in the auxiliary closed‐loop system to be uniformly ultimately bounded. Moreover, we demonstrate that the obtained event‐triggered optimal control can ensure the original system to be stable in the sense of uniform ultimate boundedness. Finally, a F‐16 aircraft plant and a nonlinear system are provided to validate the present event‐triggered robust control scheme.

Robust Control of Nonlinear System with Input and Output Nonlinear Constraints

With the development of modern technology, actuators and sensors composed of smart materials, such as piezoceramic and magnetostrictive materials, have been widely used in practice owing to their various advantages. However, in the working process of a smart material based actuator and sensor, non-smooth nonlinear constraints in their output responses may induce inaccuracies and oscillations, which severely degrade system performance. Therefore, input and output nonlinear constraints brought about by actuators and sensors should be considered. Generally, the output nonlinear constraint, namely, non-smooth effects from sensors, has been ignored. Therefore, in this paper, a robust control for a system with an output constraint as well as with both input and output constraints will be considered. Firstly, the generalized Prandtl-Ishlinskii (PI) hysteresis model is used for describing the input and output nonlinearities owing to its excellent characteristics, the model has proved suitable in theoretical operator based settings. Further, a robust control for a nonlinear system with an output nonlinear constraint is considered by using operator based robust right coprime factorization approach. Here, operator based robust stability is considered, and the control system structure including feedforward and feedback controllers is presented with a derivation of sufficient conditions for stable controller operation. Based on the proposed conditions, the influence from an output nonlinear constraint is rejected, the systems are robustly stable, and output tracking performance can be realized. Moreover, robust stability and output tracking performance for a nonlinear system with both input and output nonlinear constraints are also analyzed.

Nonlinear robust control system for an unsteady nonaffine dynamic plant with a delay

A problem of design of a robust controller for an unsteady nonaffine (in terms of the input) a priori uncertain dynamic plant is considered. The quality of the designed control system performance is illustrated through simulations.

A Miniature Pneumatic Bending Rubber Actuator Controlled by Using the PSO-SVR-Based Motion Estimation Method with the Generalized Gaussian Kernel

Soft actuators have been employed in various fields recently. A miniature pneumatic bending rubber actuator is one of the soft actuators. This actuator will be used for medical and biological fields. Its flexibility and high safety are suitable for fragile objects. However, its modeling is difficult due to its nonlinearity. There are no suitable sensors to measure the output of this actuator. In this paper, the particle swarm optimization-support vector regression (PSO-SVR)-based estimation method with the generalized Gaussian kernel is proposed. An experimental result with the operator-based robust nonlinear control system is employed to verify the effectiveness of the proposed method.

Nonlinear robust state feedback control system design for nonlinear uncertain systems

SummaryThis paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd.

Robust market-based control method for nonlinear structure

For a nonlinear control system, there are many uncertainties, such as the structural model, controlled parameters and external loads. Although the significant progress has been achieved on the robust control of nonlinear systems through some researches on this issue, there are still some limitations, for instance, the complicated solving process, weak conservatism of system, involuted structures and high order of controllers. In this study, the computational structural mechanics and optimal control theory are adopted to address above problems. The induced norm is the eigenvalue problem in structural mechanics, i.e., the elastic stable Euler critical force or eigenfrequency of structural system. The segment mixed energy is introduced with a precise integration and an extended Wittrick-Williams (W-W) induced norm calculation method. This is then incorporated in the market-based control (MBC) theory and combined with the force analogy method (FAM) to solve the MBC robust strategy (R-MBC) of nonlinear systems. Finally, a single-degree-of-freedom (SDOF) system and a 9-stories steel frame structure are analyzed. The results are compared with those calculated by the <TEX>$H{\infty}$</TEX>-robust (R-<TEX>$H{\infty}$</TEX>) algorithm, and show the induced norm leads to the infinite control output as soon as it reaches the critical value. The R-MBC strategy has a better control effect than the R-<TEX>$H{\infty}$</TEX> algorithm and has the advantage of strong strain capacity and short online computation time. Thus, it can be applied to large complex structures.

Robust Control for Nonlinear Systems with Nonlinear Characteristics

본 연에서는 미지의 데드존을 갖는 시 연속 비선형 동적 시스템에 대해서 견실한 적응제어 법칙을 제안하였다. 액츄에터의 비선형특성은 제어 시스템에서 흔하게 존재하게 된다. 이러한 여러 비선형 특성은 데드존, 백래쉬, 히스테리시스, 또는 피이스와이스 선형에 대해서 부드럽지 않은(넌 스무스)한 특성을 가지게 된다. 이러한 비선형특성을 갖는 제어 시스템에 대해서 많은 연구가들이 제안한 제어법칙들은 대부분 역 데드존을 활용해서 제어법칙들을 제안하였다. 본 연구에서 제안하는 견실한 적응제어 법칙은 역 데드존을 사용하지 않고 제안하였으며, 데드존에 대해서 직관과 수학적인 관점에서의 모델을 활용하였다. 제안된 법칙에 대해서 리아프노프 정리를 활용하여 대역적 안정도에 대해서 증명을 통해서 제시 하였다. 제안된 제어기에 대해서 수치적 예를 통한 결과로부터 제안된 알고리즘의 타당성을 검증 하였다.

Design and Simulation of Sliding Mode Fuzzy Controller for Nonlinear System

Sliding Mode Controller (SMC) is a simple method and powerful technique to design a robust controller for nonlinear systems. It is an effective tool with acceptable performance. The major drawback is a classical Sliding Mode controller suffers from the chattering phenomenon which causes undesirable zigzag motion along the sliding surface. To overcome the snag of this classical approach, many methods were proposed and implemented. In this work, a Fuzzy controller was added to classical Sliding Mode controller in order to reduce the impact chattering problem. The new structure is called Sliding Mode Fuzzy controller (SMFC) which will also improve the properties and performance of the classical Sliding Mode controller. A single inverted pendulum has been utilized for testing the design of the proposed controller. Programming and Simulink by Matlab have been used for the simulation results.&#x0D; &#x0D;

Distributed robust control for nonlinear systems using wireless neural control

This paper is concerned with the synthesis of a class of nonlinear system over the wireless neural control network (WNCN) which refers to a group of neuron nodes interacting with each other by radio connection. The nonlinear system is modeled by a standard neural network model (SNNM) which is the interconnection of a linear dynamic system and bounded static nonlinear operators. The WNCN treats itself as a fully distributed nonlinear dynamic controller. The unreliable wireless communication links within WNCN are modeled by fading channels. By constructing appropriate discretetime Lyapunov function, the global asymptotic stability of the closed-loop system is discussed in particular for the cases with stochastic perturbations induced by packet losses. The connection weights among the neuron nodes that guarantee stability of the system can be obtained by solving a convex optimization problem with some linear matrix inequality (LMI) constraints. A numerical example is given to illustrate the correctness and effectiveness of the theoretical results.

Robust Adaptive Control of Nonlinear Systems with Uncertainties

This paper proposes a robust adaptive robust controller for nonlinear systems represented by input-output models with unmodeled dynamics. Under the circumstances that the output of the system is bounded, the proposed controller can guarantee that all the variables of the system are bounded in the presence of unmodeled dynamics and time-varying disturbances. The scheme does not need to generate an additional dynamic signal to dominate the effects of the unmodeled dynamics. It is shown that the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately.

Compensation on the Uncertain Nonlinear Plants Preceded by Uncertain Backlash

In this paper, a nonlinear control system considering the uncertainties of the backlash of nonlinear plants is proposed. The uncertainties of the backlash of nonlinear plants are included in thresholds of backlash. Firstly, a backlash model with uncertain thresholds is proposed. Secondly, a robust nonlinear control system is designed. Finally, the effectiveness of the proposed system is confirmed by simulations.

Digital self-triggered robust control of nonlinear systems

In this paper, we develop novel results on self-triggered control of nonlinear systems, subject to perturbations, and sensing/computation/actuation delays. First, considering an unperturbed nonlinear system with bounded delays, we provide conditions that guarantee the existence of a self-triggered control strategy stabilizing the closed-loop system. Then, considering parameter uncertainties, disturbances and bounded delays, we provide conditions guaranteeing the existence of a self-triggered strategy that keeps the state arbitrarily close to the equilibrium point. In both cases, we provide a methodology for the computation of the next execution time. We show on an example the relevant benefits obtained with this approach in terms of energy consumption with respect to control algorithms based on a constant sampling with a sensible reduction of the average sampling time.

Set membership inversion and robust control from data of nonlinear systems

SUMMARYA set membership method for right inversion of nonlinear systems from data is proposed in the paper. Both the cases where the system to invert is known or unknown and therefore identified from data are addressed. The method does not require the invertibility of the regression function describing the system and ensures tight bounds on the inversion error. In the case of unknown system, the method allows the derivation of a robust right‐inverse, guaranteeing the inversion error bound for all the systems belonging to the uncertainty set which can be defined from the available prior and experimental information. Based on such a set membership inversion, two methods for robust control of nonlinear systems from data are introduced: nonlinear feed‐forward control (NFFC) and nonlinear internal model control (NIMC). Both the design methods ensure robust stability and bounded tracking errors for all the systems belonging to the involved uncertainty set. Two applicative examples of robust control from data are presented: NFFC control of semi‐active suspension systems and NIMC control of vehicle lateral dynamics.Copyright © 2013 John Wiley &amp; Sons, Ltd.

A Design Method of Compensator to Minimize Model Error

The robust control design method has been studied in recent decades. A control system works well under the modeling errors and disturbances if controller design is based on the robust control method. However, it is well known that in control systems, generally, there exists a trade-off between control performance and robustness. To overcome the trade-off problem, this paper proposes an internal model type compensator structure that minimizes the modeling gap between the nominal model and actual plant dynamics. By using the proposed compensator, the dynamics of the compensated system closes to that of the nominal model. Then, a design method of the compensator parameters is also proposed for minimizing a set of plant dynamics. The proposed design method is reduced to the standard µ design control problem. If we use the proposed compensator for control systems instead of the plant itself, the output performance might be better despite plant uncertainty. Given that the proposed compensator can be used for the control of not only linear but also nonlinear plants, we can easily achieve robust control of nonlinear systems. The effectiveness of the proposed method is shown by numerical examples.

Receding Horizon Robust Control for Nonlinear Systems Based on Linear Differential Inclusion of Neural Networks

In this paper, we present a new receding horizon neural robust control scheme for a class of nonlinear systems based on the linear differential inclusion (LDI) representation of neural networks. First, we propose a linear matrix inequality (LMI) condition on the terminal weighting matrix for a receding horizon neural robust control scheme. This condition guarantees the nonincreasing monotonicity of the saddle point value of the finite horizon dynamic game. We then propose a receding horizon neural robust control scheme for nonlinear systems, which ensures the infinite horizon robust performance and the internal stability of closed-loop systems. Since the proposed control scheme can effectively deal with input and state constraints in an optimization problem, it does not cause the instability problem or give the poor performance associated with the existing neural robust control schemes.

Robust control for nonlinear systems with unknown perturbations using simplified robust right coprime factorisation

This article is concerned with operator-based robust control for nonlinear feedback system with unknown perturbations with simplified robust right coprime factorisation method. By the designed simplified robust controllers, the Bezout identity for the nominal nonlinear system and the perturbed nonlinear system are guaranteed to be simply satisfied, which means that not only the nonlinear system with nominal plant but also that with perturbed plant can be stabilised. Moreover, the plant output can be guaranteed to asymptotically track the reference output. The effectiveness of the proposed design scheme is verified by the simulation results.

Authors' Reply to “Comments on ‘Chattering Free Robust Control for Nonlinear Systems’”

The following paper is a reply to the comment note titled, "Comments on 'Chattering Free Robust Control for Nonlinear Systems'," by P. Potluri. The purpose of this reply is to: 1) agree with the comment 2) discuss the potential benefit of the controller in terms of the chattering mitigation instead of chattering free; and 3) correct two typos in the original paper titled, "Chattering free robust control for nonlinear systems".