Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form

The dynamic surface control (DSC) technique was developed recently by Swaroop et al. This technique simplified the backstepping design for the control of nonlinear systems in strict-feedback form by overcoming the problem of "explosion of complexity." It was later extended to adaptive backstepping design for nonlinear systems with linearly parameterized uncertainty. In this paper, by incorporating this design technique into a neural network based adaptive control design framework, we have developed a backstepping based control design for a class of nonlinear systems in strict-feedback form with arbitrary uncertainty. Our development is able to eliminate the problem of "explosion of complexity" inherent in the existing method. In addition, a stability analysis is given which shows that our control law can guarantee the uniformly ultimate boundedness of the solution of the closed-loop system, and make the tracking error arbitrarily small.     

Model reference robust control of a class of SISO systems

A new control design technique, model reference robust control (MRRC), is introduced for a class of SISO systems which contain unknown parameters, possible nonlinear uncertainties, and additive bounded disturbances. The design methodology is a natural, nontrivial extension of model reference adaptive control (MRAC) which is essential to achieving robust stability and performance for linear time-invariant systems. The methodology also represents an important step toward achieving robust stability for time-varying and nonlinear systems. MRRC requires only input and output measurements of the system, rather than the full state feedback and structural conditions on uncertainties required by existing robust control results. MRRC is developed from existing model reference control (MRC) in a manner similar to MRAC. An intermediate result gives conditions under which MRRC yields exponentially asymptotic stability. The general result yielding uniformly ultimately bounded stability is then developed. A scalar example provides intuition into why the control works against a wide class of uncertainties and reveals the implicit learning capability of MRRC     

A Sum-of-Squares Approach to Modeling and Control of Nonlinear Dynamical Systems With Polynomial Fuzzy Systems

This paper presents a sum of squares (SOS) approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi--Sugeno (T--S) fuzzy modeling and control. First, we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well-known T--S fuzzy modeling and control. Secondly, we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing LMI-based approaches to T--S fuzzy modeling and control. Moreover, the derived stability and stabilizability conditions are represented in terms of SOS and can be numerically (partially symbolically) solved via the recently developed SOSTOOLS. To illustrate the validity and applicability of the proposed approach, a number of analysis and design examples are provided. The first example shows that the SOS approach renders more relaxed stability results than those of both the LMI-based approaches and a polynomial system approach. The second example presents an extensive application of the SOS approach in comparison with a piecewise Lyapunov function approach. The last example is a design exercise that demonstrates the viability of the SOS-based approach to synthesizing a stabilizing controller.      

一类纯反馈力学系统的自适应模糊动态面控制

针对一类纯反馈形式的不稳定力学系统,提出自适应模糊动态面控制方法。在一般动态面控制的设计框架下,引入模糊系统逼近模型的未知函数,设计自适应律在线估计模糊系统权参数和模型未知参数,通过Lyapunov方法证明得出闭环系统半全局稳定。该策略避免了传统反演设计存在的“微分爆炸”现象,并且解决了纯反馈系统控制设计中通常存在的循环设计问题。仿真结果表明,控制系统能够克服不确定性,且能够简单有效地实现跟踪控制。     

网络稳定性与控制的小增益原理:回顾与近期进展

小增益定理是现代控制理论中极为重要的基本工具之一,它在关联系统和不确定系统的鲁棒稳定性分析以及鲁棒控制器设计的许多工作中都发挥着极大的作用.基于输入到状态稳定性的概念,笔者于1994年首次提出了广义非线性小增益定理.与之前的小增益定理不同,这一结果为同时刻画关联系统的内部稳定性和外部稳定性提供了一个统一的框架.从镇定与鲁棒自适应控制到分散式或分布式控制以及输出调节(抗干扰渐近跟踪),基于非线性小增益定理已经发展出一系列的鲁棒非线性控制器设计新工具.在过去10年间,复杂非线性大系统已成为研究热点,驱动着小增益定理向更加完备的网络小增益定理方向发展,以期解决网络稳定性与控制中的新问题.对此,针对非线性小增益理论的一些最新研究进展及其在通讯和计算约束下的网络化控制和事件驱动控制应用结果进行综述,并对该理论的未来研究方向给出一些建议.     

Analysis of stability and robust stability of polynomial fuzzy model-based control systems using a sum-of-squares approach

The well known Takagi–Sugeno (T–S) fuzzy model can be extended in different ways including the polynomial fuzzy model, whose consequent parts are polynomial sub-systems. Compared with the traditional T–S fuzzy model, the polynomial fuzzy model can represent a nonlinear system more accurately with a smaller number of fuzzy logic rules. It is worth emphasizing that the stability analysis and controller design of polynomial fuzzy model-based (PFMB) control systems are not based on the linear matrix inequalities but the recently developed sum-of-squares decompositions. In this paper, based on an existing result for traditional fuzzy control systems, we propose a new stability condition for the stability analysis of PFMB control systems. Furthermore, the stability of PFMB control systems with parameter uncertainties is investigated. The popular inverted pendulum and an unstable nonlinear system are employed to demonstrate the quality of the proposed stability conditions.     

Neural network‐based adaptive dynamic surface control of uncertain nonlinear pure‐feedback systems

In this paper, by incorporating the dynamic surface control technique into a neural network‐based adaptive control design framework, we have developed a backstepping‐based control design for a class of nonlinear systems in pure‐feedback form with arbitrary uncertainty. The circular design problem which may exist in pure‐feedback systems is overcome. In addition, our development is able to eliminate the problem of ‘explosion of complexity’ inherent in the existing backstepping‐based methods. A stability analysis is given, which shows that our control law can guarantee the semi‐global uniformly ultimate boundedness of the solution of the closed‐loop system, and makes the tracking error arbitrarily small. Moreover, the proposed control design scheme can also be directly applied to the strict‐feedback nonlinear systems with arbitrary uncertainty. Copyright © 2010 John Wiley & Sons, Ltd.     

A general U-block model-based design procedure for nonlinear polynomial control systems

The proposition of U-model concept (in terms of ‘providing concise and applicable solutions for complex problems’) and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work – using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.     

Robust design of stochastic controllers for nonlinear systems

The previous results are generalized on the stabilizing property of a control scheme designed for a class of discrete-time nonlinear stochastic systems. First, the existing controller is made more robust with a prescribed degree of stability by proper modifications. Next, the inherent robustness is illustrated by a design utilizing erroneous noise characteristics. Reconsideration of the stability analysis used allows one to treat a larger class of nonlinear stochastic systems with more general structures     

Nonlinear Control Method for Nonlinear Systems with Unknown Perturbations by Combining Left and Right Factorization

In this paper, nonlinear control design scheme for a class of nonlinear systems is proposed based on operator coprime factorization theory. In detail, two stable controllers are provided to design a Bezout identity by combining left factorization (not coprime) with right factorization. Based on the proposed design method, a realization approach to left coprime factorization for the nonlinear system is obtained, which provides an effective framework for constructing left coprime factorization. Meanwhile, internal‐output stability of the nonlinear system is guaranteed. After that, based on the obtained left coprime factorization, the cases of the nonlinear systems with perturbations are discussed for guaranteeing robust stability for the perturbed systems. For the perturbations, two different cases, known bounded perturbations and unknown bounded perturbations, are investigated from different viewpoints to analyze robust stability issue for the perturbed systems. Finally, a simulation example is given to confirm the effectiveness of the proposed design method.     

The science and education of mechatronics engineering

We try to get to the heart of multidisciplinary engineering, of which mechatronics is an excellent example, and point out how the integration of disciplines leads to new degrees of freedom in design and corresponding research directions that otherwise would not have been investigated. This is the major contribution achieved by a multidisciplinary approach to engineering science; it leads to a new important research field and at the same time helps to push research in related fields into new fruitful directions. We point to a number of areas that have benefited from the interdisciplinary perspective and a focus on interactions between disciplines including: engineering curriculum; mechatronics research; control of nonlinear mechanical systems; real time control systems modelling; and time varying control systems     

Multi-agent compositional stability exploiting system symmetries

This paper considers nonlinear symmetric control systems. By exploiting the symmetric structure of the system, stability results are derived that are independent of the number of components in the system. This work contributes to the fields of research directed toward compositionality and composability of large-scale system in that a system can be “built-up” by adding components while maintaining system stability. The modeling framework developed in this paper is a generalization of many existing results which focus on interconnected systems with specific dynamics. The main utility of the stability result is one of scalability or compositionality. If the system is stable for a given number of components, under appropriate conditions stability is then guaranteed for a larger system composed of the same type of components which are interconnected in a manner consistent with the smaller system. The results are general and applicable to a wide class of problems. The examples in this paper focus on the formation control problems for multi-agent robotic systems.     

Fractional-order Generalized Principle of Self-support (FOGPSS) in Control System Design

This paper reviews research that studies the principle of self-support (PSS) in some control systems and proposes a fractional-order generalized PSS framework for the first time. The existing PSS approach focuses on practical tracking problem of integer-order systems including robotic dynamics, high precision linear motor system, multi-axis high precision positioning system with unmeasurable variables, imprecise sensor information, uncertain parameters and external disturbances. More generally, by formulating the fractional PSS concept as a new generalized framework, we will focus on the possible fields of the fractional-order control problems such as practical tracking, -tracking, etc. of robot systems, multiple mobile agents, discrete dynamical systems, time delay systems and other uncertain nonlinear systems. Finally, the practical tracking of a first-order uncertain model of automobile is considered as a simple example to demonstrate the efficiency of the fractional-order generalized principle of self-support (FOGPSS) control strategy.      

Decentralised disturbance-observer-based adaptive tracking in the presence of unmatched nonlinear time-delayed interactions and disturbances

This paper proposes an approximation-based nonlinear disturbance observer (NDO) approach for decentralised adaptive tracking of uncertain interconnected pure-feedback nonlinear systems with unmatched time-delayed nonlinear interactions and external disturbances. Compared with the existing approximation-based NDO approach for uncertain interconnected nonlinear systems where the centralised design framework was proposed, the main contribution of this paper is to develop a decentralised and memoryless NDO-based adaptive control scheme in the presence of unknown time-varying delayed interactions and disturbances unmatched in the control inputs. The recursive design methodology is derived to construct the decentralised NDO and controller where the function approximators used in the decentralised NDO are employed to design the decentralised adaptive controller. From the Lyapunov stability theorem using Lyapunov--Krasovskii functionals, it is shown that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors converge to an adjustable neighbourhood of the origin.     

FAME: A UML-based framework for modeling fuzzy self-adaptive software

Context: Software Fuzzy Self-Adaptation (SFSA) is a fuzzy control-based software self-adaptation paradigm proposed to deal with the fuzzy uncertainty existing in self-adaptive software. However, as many software engineers lack fuzzy control knowledge, it is difficult for them to design and model this kind of fuzzy self-adaptive software (F-SAS). Therefore, efficient and effective modeling technologies and tools are needed for the SFSA framework.Objective: This paper aims to identify modeling requirements of F-SAS and to provide a modeling framework to specify, design and model F-SAS systems. Such a framework can simplify modeling process of F-SAS and improve the accessibility of software engineers to the SFSA paradigm.Method: This study proposes a modeling framework called Fuzzy self-Adaptation ModEling (FAME). By extending UML, FAME creates three types of modeling views. An analysis view called Fuzzy Case Diagram is created to specify the fuzzy self-adaptation goal and the realization processes of this goal. A structure view called Fuzzy Class Diagram is created to describe the fuzzy concepts and structural characteristics of F-SAS. A behavior view called Fuzzy Sequence Diagram is created to depict the dynamic behaviors of the F-SAS systems. The framework is implemented as a plug-in of Enterprise Architect.Results: We demonstrate the effectiveness and efficiency of the proposed approach by carrying out a subject-based empirical evaluation. The results show that FAME framework can improve modeling quality of F-SAS systems by 44.38% and shorten modeling time of F-SAS systems by 38.41% in comparison with traditional UML. Thus, FAME can considerably ease the modeling process of F-SAS systems.Conclusion: FAME framework incorporates the SFSA concepts into standard UML. Therefore, it provides a direct support to model SFSA characteristics and improves the accessibility of software engineers to the SFSA paradigm. Furthermore, it behaves a good example and provides good references for modeling domain-specific software systems.     

On Maximum Stability Margin Design of Nonlinear Uncertain Systems: Fuzzy Control Approach

This paper studies the maximum stability margin design for nonlinear uncertain systems using fuzzy control. First, the Takagi and Sugeno fuzzy model is employed to approximate a nonlinear uncertain system. Next, based on the fuzzy model, the maximum stability margin for a nonlinear uncertain system is studied to achieve as much tolerance of plant uncertainties as possible using a fuzzy control method. In the proposed fuzzy control method, the maximum stability margin design problem is parameterized in terms of a corresponding generalized eigenvalue problem (GEVP). For the case where state variables are unavailable, a fuzzy observer‐based control scheme is also proposed to deal with the maximum stability margin for nonlinear uncertain systems. Using a suboptimal approach, we characterize the maximum stability margin via fuzzy observer‐based control in terms of a linear matrix inequality problem (LMIP). The GEVP and LMIP can be solved very efficiently via convex optimization techniques. Simulation examples are given to illustrate the design procedure of the proposed method.     

Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems

In this paper, finite-time stabilization is considered for a class of nonlinear systems dominated by a lower-triangular model with a time-varying gain. Based on the finite-time Lyapunov stability theorem and dynamic gain control design approach, state feedback finite-time stabilization controllers are proposed with gains being tuned online by two dynamic equations. Different from many existing finite-time control designs for lower-triangular nonlinear systems, the celebrated backstepping method is not utilized here. It is observed that our design procedure is much simpler, and the resulting control gains are in general not as high as those provided by the backstepping method. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Robust optimization of nonlinear dynamic systems with application to a jacketed tubular reactor

We present robust optimization techniques for dynamic systems which are affected by time-varying uncertainties. After reviewing existing techniques from the field of reachability analysis and ellipsoidal calculus, we discuss how to over-estimate the influence of uncertainty in nonlinear dynamic systems. The corresponding strategies lead to a framework which can be used to solve min–max optimal control problems in a conservative approximation. The technique is illustrated by applying it to a robust optimal control problem for a nonlinear jacketed tubular reactor. Inside this reactor a highly nonlinear and exothermic chemical reaction takes place which is uncertain due to fouling at the reactor wall. We regard safety constraints on the temperature which must be satisfied for all possible scenarios.     

On uniform asymptotic stability of time-varying parameterized discrete-time cascades

Recently, a framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been proposed in the literature. In this paper, we develop novel tools that can be used within this framework and that are useful for tracking problems. In particular, results for stability analysis of parameterized time-varying discrete-time cascaded systems are given. This class of models arises naturally when one uses an approximate discrete-time model to design a stabilizing or tracking controller for a sampled-data plant. While some of our results parallel their continuous-time counterparts, the stability properties that are considered, the conditions that are imposed, and the the proof techniques that are used, are tailored for approximate discrete-time systems and are technically different from those in the continuous-time context. A result on constructing strict Lyapunov functions from nonstrict ones that is of independent interest, is also presented. We illustrate the utility of our results in the case study of the tracking control of a mobile robot. This application is fairly illustrative of the technical differences and obstacles encountered in the analysis of discrete-time parameterized systems.     

A general framework for tackling the output regulation problem

Output regulation aims to achieve, in addition to closed-loop stability, asymptotic tracking and disturbance rejection for a class of reference inputs and disturbances. Thus, it poses a more challenging problem than stabilization. For over a decade, the nonlinear output regulation problem has been one of the focuses in nonlinear control research, and active research on this problem has generated many fruitful results. Nevertheless, there are two hurdles that impede the further progress of the research on the output regulation problem. The first one is the assumption that the solution or the partial solution of the regulator equations is polynomial. The second one is the lack of a systematic mechanism to handle the global robust output regulation problem. We establish a general framework that systematically converts the robust output regulation problem for a general nonlinear system into a robust stabilization problem for an appropriately augmented system. This general framework, on one hand, relaxes the polynomial assumption, and on the other hand, offers a greater flexibility to incorporate recent new stabilization techniques, thus setting a stage for systematically tackling the robust output regulation with global stability.