A class of predefined-time stabilizing controllers for nonholonomic system

The design of a class of predefined-time stabilizing controller for a class uncertain nonholonomic systems in chained form is investigated in this paper. First, some modifications to the classical fixed-time algorithms for first and second order systems are introduced. These modified algorithms, which are developed under the concept of predefined-time stability, reduce the settling time overestimation drawback suffered by the classical fixed-time algorithm. Unlike current finite-time and fixed-time schemes, an upper bound of the settling time is easily tunable through a simple selection of the parameters of the controllers. Then, based on the developed first and second-order algorithms, a switching control strategy is designed to guarantee the predefined-time stability of the chained-form nonholonomic system. Finally, a simulation example is presented to show the effectiveness of the proposed method.ITESO, A.C

Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control

Nondeterministic hybrid dynamical systems

This thesis is concerned with the analysis, control and identification of hybrid dynamical systems. The main focus is on a particular class of hybrid systems consisting of linear subsystems. The discrete dynamic, i.e., the change between subsystems, is unknown or nondeterministic and cannot be influenced, i.e. controlled, directly. However changes in the discrete dynamic can be detected immediately, such that the current dynamic (subsystem) is known. In order to motivate the study of hybrid systems and show the merits of hybrid control theory, an example is given. It is shown that real world systems like Anti Locking Brakes (ABS) are naturally modelled by such a class of linear hybrids systems. It is shown that purely continuous feedback is not suitable since it cannot achieve maximum braking performance. A hybrid control strategy, which overcomes this problem, is presented. For this class of linear hybrid system with unknown discrete dynamic, a framework for robust control is established. The analysis methodology developed gives a robustness radius such that the stability under parameter variations can be analysed. The controller synthesis procedure is illustrated in a practical example where the control for an active suspension of a car is designed. Optimal control for this class of hybrid system is introduced. It is shows how a control law is obtained which minimises a quadratic performance index. The synthesis procedure is stated in terms of a convex optimisation problem using linear matrix inequalities (LMI). The solution of the LMI not only returns the controller but also the performance bound. Since the proposed controller structures require knowledge of the continuous state, an observer design is proposed. It is shown that the estimation error converges quadratically while minimising the covariance of the estimation error. This is similar to the Kalman filter for discrete or continuous time systems. Further, we show that the synthesis of the observer can be cast into an LMI, which conveniently solves the synthesis problem

On Continuous Full-Order Integral-Terminal Sliding Mode Control with Unknown Apriori Bound on Uncertainty

This study aims at providing a solution to the problem of designing a continuous and finite-time control for a class of nonlinear systems in the presence of matched uncertainty with an unknown apriori bound. First, we propose a Full-Order Integral-Terminal Sliding Manifold (FOITSM) with a conventional (discontinuous) sliding mode to show that it provides the combined attributes of the nonsingular terminal and integral sliding mode algorithms. Secondly, an Adaptive Disturbance Observer (ADO) has been designed to alleviate the effect of the uncertainty acting on the system. On application of the ADO-based Full-Order Integral-Terminal Sliding Mode Control (FOITSMC), the chattering phenomenon in control input has been reduced substantially in the presence of conditionally known matched disturbances. Moreover, the adaptive gains of ADO are updated non-monotonically without over-bounding the acting disturbance, yet sustain the global boundedness of state trajectories within a specific bound. %Finally, an application of the proposed algorithm for attitude stabilization of a rigid spacecraft has been successively shown.Comment: 14 pages, 9 figure

Generalised regular form based SMC for nonlinear systems with application to a WMR

In this paper, a generalised regular form is proposed to facilitate sliding mode control (SMC) design for a class of nonlinear systems. A novel nonlinear sliding surface is designed using implicit function theory such that the resulting sliding motion is globally asymptotically stable. Sliding mode controllers are proposed to drive the system to the sliding surface and maintain a sliding mo-tion thereafter. Tracking control of a two-wheeled mobile robot is considered to underpin the developed theoretical results. Model-based tracking control of a wheeled mobile robot (WMR) is first transferred to a stabilisation problem for the corresponding tracking error system, and then the developed theoretical results are applied to show that the tracking error system is globally asymptotically stable even in the presence of matched and mismatched uncertainties. Both experimental and simulation results demonstrate that the developed results are practicable and effective

State Feedback Sliding Mode Control of Complex Systems with Applications

This thesis concerns the development of robust nonlinear control design for complex systems including nonholonomic systems and large-scale systems using sliding mode control (SMC) techniques under the assumption that all system state variables are accessible for design. The main developments in this thesis include: 1). The concept of generalised regular form and design of a novel sliding function. The mathematical definition of generalised regular form is proposed for the first time. It is an extension of the classical regular form, which makes SMC applicable to a wider class of nonlinear systems. A novel sliding function design, which is based on the global implicit function theorem, is proposed to guarantee unique sliding mode dynamics. 2). The development of decentralised SMC for large-scale interconnected systems. For systems with uncertain interconnections which possess the superposition property, a decentralised control scheme is presented to counteract the effect of the uncertainty by using bounds on uncertainties and interconnections. The bounds used in the design are nonlinear functions instead of constant, linear or polynomial functions. The design strategy has also been expanded to a fully nonlinear case for interconnected systems in the generalised regular form. 3). Robust decentralised SMC for a class of nonlinear systems with uncertainties in input distribution. A system with uncertainties in input distribution is full of challenges. A novel method is proposed to deal with such uncertainties for a class of nonlinear interconnected systems. The designed decentralised SMC enhances the robustness of the controlled systems. This thesis also provides case studies of three applications for the proposed approaches. The existence of the generalised regular form is verified in the trajectory tracking control of a wheeled mobile robot (WMR) system. Both simulations and experiments on the WMR are given to demonstrate the validity and effectiveness of the generalised regular form-based SMC design. A continuous stirred tank reactor (CSTR) system and a longitudinal vehicle-following system are used to test the proposed decentralised SMC schemes. An expanded vehicle-following system with both longitudinal and lateral controllers has been developed to demonstrate the robust control design for system with uncertainties in input distribution

An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination

This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations

A stability-theory perspective to synchronisation of heterogeneous networks

Dans ce mémoire, nous faisons une présentation de nos recherches dans le domaine de la synchronisation des systèmes dynamiques interconnectés en réseau. Une des originalités de nos travaux est qu'ils portent sur les réseaux hétérogènes, c'est à dire, des systèmes à dynamiques diverses. Au centre du cadre d'analyse que nous proposons, nous introduisons le concept de dynamique émergente. Il s'agit d'une dynamique "moyennée'' propre au réseau lui-même. Sous l'hypothèse qu'il existe un attracteur pour cette dynamique, nous montrons que le problème de synchronisation se divise en deux problèmes duaux : la stabilité de l'attracteur et la convergence des trajectoires de chaque système vers celles générées par la dynamique émergente. Nous étudions aussi le cas particulier des oscillateurs de Stuart-Landau