Lyapunov stabilization of discrete-time feedforward dynamics

The paper discusses stabilization of nonlinear discrete-time dynamics in feedforward form. First it is shown how to define a Lyapunov function for the uncontrolled dynamics via the construction of a suitable cross-term. Then, stabilization is achieved in terms of u-average passivity. Several constructive cases are analyzed

Stability, observer design and control of networks using Lyapunov methods

We investigate different aspects of the analysis and control of interconnected systems. Different tools, based on Lyapunov methods, are provided to analyze such systems in view of stability, to design observers and to control systems subject to stabilization. All the different tools presented in this work can be used for many applications and extend the analysis toolbox of networks. Considering systems with inputs, the stability property input-to-state dynamical stability (ISDS) has some advantages over input-to-state stability (ISS). We introduce the ISDS property for interconnected systems and provide an ISDS small-gain theorem with a construction of an ISDS-Lyapunov function and the rate and the gains of the ISDS estimation for the whole system. This result is applied to observer design for single and interconnected systems. Observers are used in many applications where the measurement of the state is not possible or disturbed due to physical reasons or the measurement is uneconomical. By the help of error Lyapunov functions we design observers, which have a so-called quasi ISS or quasi-ISDS property to guarantee that the dynamics of the estimation error of the systems state has the ISS or ISDS property, respectively. This is applied to quantized feedback stabilization. In many applications, there occur time-delays and/or instantaneous jumps of the systems state. At first, we provide tools to check whether a network of time-delay systems has the ISS property using ISS-Lyapunov-Razumikhin functions and ISS-Lyapunov-Krasovskii functionals. Then, these approaches are also used for interconnected impulsive systems with time-delays using exponential Lyapunov-Razumikhin functions and exponential Lyapunov-Krasovskii functionals. We derive conditions to assure ISS of an impulsive network with time-delays. Controlling a system in a desired and optimal way under given constraints is a challenging task. One approach to handle such problems is model predictive control (MPC). In this thesis, we introduce the ISDS property for MPC of single and interconnected systems. We provide conditions to assure the ISDS property of systems using MPC, where the previous result of this thesis, the ISDS small-gain theorem, is applied. Furthermore, we investigate the ISS property for MPC of time-delay systems using the Lyapunov-Krasovskii approach. We prove theorems, which guarantee ISS for single and interconnected systems using MPC

Stabilization of cascaded nonlinear systems under sampling and delays

Over the last decades, the methodologies of dynamical systems and control theory have been playing an increasingly relevant role in a lot of situations of practical interest. Though, a lot of theoretical problem still remain unsolved. Among all, the ones concerning stability and stabilization are of paramount importance. In order to stabilize a physical (or not) system, it is necessary to acquire and interpret heterogeneous information on its behavior in order to correctly intervene on it. In general, those information are not available through a continuous flow but are provided in a synchronous or asynchronous way. This issue has to be unavoidably taken into account for the design of the control action. In a very natural way, all those heterogeneities define an hybrid system characterized by both continuous and discrete dynamics. This thesis is contextualized in this framework and aimed at proposing new methodologies for the stabilization of sampled-data nonlinear systems with focus toward the stabilization of cascade dynamics. In doing so, we shall propose a small number of tools for constructing sampled-data feedback laws stabilizing the origin of sampled-data nonlinear systems admitting cascade interconnection representations. To this end, we shall investigate on the effect of sampling on the properties of the continuous-time system while enhancing design procedures requiring no extra assumptions over the sampled-data equivalent model. Finally, we shall show the way sampling positively affects nonlinear retarded dynamics affected by a fixed and known time-delay over the input signal by enforcing on the implicit cascade representation the sampling process induces onto the retarded system

Decentralized control of uncertain interconnected time-delay systems

In this thesis, novel stability analysis and control synthesis methodologies are proposed for uncertain interconnected time-delay systems. It is known that numerous real-world systems such as multi-vehicle flight formation, automated highway systems, communication networks and power systems can be modeled as the interconnection of a number of subsystems. Due to the complex and distributed structure of this type of systems, they are subject to propagation and processing delays, which cannot be ignored in the modeling process. On the other hand, in a practical environment the parameters of the system are not known exactly, and usually the nominal model is used for controller design. It is important, however, to ensure that robust stability and performance are achieved, that is, the overall closed-loop system remains stable and performs satisfactorily in the presence of uncertainty. To address the underlying problem, the notion of decentralized fixed modes is extended to the class of linear time-invariant (LTI) time-delay systems, and a necessary and sufficient condition is proposed for stabilizability of this type of systems by means of a finite-dimensional decentralized LTI output feedback controller. A near-optimal decentralized servomechanism control design method and a cooperative predictive control scheme are then presented for uncertain LTI hierarchical interconnected systems. A H {592} decentralized overlapping control design technique is provided consequently which guarantees closed-loop stability and disturbance attenuation in the presence of delay. In particular, for the case of highly uncertain time-delay systems, an adaptive switching control methodology is proposed to achieve output tracking and disturbance rejection. Simulation results are provided throughout the thesis to support the theoretical finding

Curve Tracking Control Under State Constraints and Uncertainties

We study a class of steering control problems for free-moving particles tracking a curve in the plane and also in a three-dimensional environment, which are central problems in robotics. In the two-dimensional case, we provide adaptive controllers for curve tracking under unknown curvatures and control uncertainty. The system dynamics include a nonlinear dependence on the curvature, and are coupled with an estimator for the unknown curvature to form the augmented error dynamics. This nonlinear dependence puts our curvature identification objective outside the scope of existing adaptive tracking and parameter identification results that were limited to cases where the unknown parameters enter the system in an affine way. We prove input-to-state stability of the augmented error dynamics under polygonal state constraints and under suitable known bounds on the curvature and on the control uncertainty. When the uncertainty is zero, this ensures tracking of the curve and convergence of the curvature estimate to the unknown curvature. In the three-dimensional setting, we provide a new method to achieve curve tracking, identify unknown control gains, and maintain robust forward invariance of compact regions in the state space, under arbitrarily large perturbation bounds. Our new technique entails scaling certain control components

On Resilient Control for Secure Connected Vehicles: A Hybrid Systems Approach

According to the Internet of Things Forecast conducted by Ericsson, connected devices will be around 29 billion by 2022. This technological revolution enables the concept of Cyber-Physical Systems (CPSs) that will transform many applications, including power-grid, transportation, smart buildings, and manufacturing. Manufacturers and institutions are relying on technologies related to CPSs to improve the efficiency and performances of their products and services. However, the higher the number of connected devices, the higher the exposure to cybersecurity threats. In the case of CPSs, successful cyber-attacks can potentially hamper the economy and endanger human lives. Therefore, it is of paramount importance to develop and adopt resilient technologies that can complement the existing security tools to make CPSs more resilient to cyber-attacks. By exploiting the intrinsically present physical characteristics of CPSs, this dissertation employs dynamical and control systems theory to improve the CPS resiliency to cyber-attacks. In particular, we consider CPSs as Networked Control Systems (NCSs), which are control systems where plant and controller share sensing and actuating information through networks. This dissertation proposes novel design procedures that maximize the resiliency of NCSs to network imperfections (i.e., sampling, packet dropping, and network delays) and denial of service (DoS) attacks. We model CPSs from a general point of view to generate design procedures that have a vast spectrum of applicability while creating computationally affordable algorithms capable of real-time performances. Indeed, the findings of this research aspire to be easily applied to several CPSs applications, e.g., power grid, transportation systems, and remote surgery. However, this dissertation focuses on applying its theoretical outcomes to connected and automated vehicle (CAV) systems where vehicles are capable of sharing information via a wireless communication network. In the first part of the dissertation, we propose a set of LMI-based constructive Lyapunov-based tools for the analysis of the resiliency of NCSs, and we propose a design approach that maximizes the resiliency. In the second part of the thesis, we deal with the design of DOS-resilient control systems for connected vehicle applications. In particular, we focus on the Cooperative Adaptive Cruise Control (CACC), which is one of the most popular and promising applications involving CAVs

Switched dynamical systems: Transition model, qualitative theory, and advanced control

Ph.DDOCTOR OF PHILOSOPH

Hybrid dynamics in large-scale logistics networks

We study stability properties of interconnected hybrid systems with application to large-scale logistics networks. Hybrid systems are dynamical systems that combine two types of dynamics: continuous and discrete. Such behaviour occurs in wide range of applications. Logistics networks are one of such applications, where the continuous dynamics occurs in the production and processing of material and the discrete one in the picking up and delivering of material. Stability of logistics networks characterizes their robustness to the changes occurring in the network. However, the hybrid dynamics and the large size of the network lead to complexity of the stability analysis. In this thesis we show how the behaviour of a logistics networks can be described by interconnected hybrid systems. Then we recall the small gain conditions used in the stability analysis of continuous and discrete systems and extend them to establish input-to-state stability (ISS) of interconnected hybrid systems. We give the mixed small gain condition in a matrix form, where one matrix describes the interconnection structure of the system and the other diagonal matrix takes into account whether ISS condition for a subsystem is formulated in the maximization or the summation sense. The small gain condition is sufficient for ISS of an interconnected hybrid system and can be applied to an interconnection of an arbitrary finite number of ISS subsystems. We also show an application of this condition to particular subclasses of hybrid systems: impulsive systems, comparison systems and the systems with stability of only a part of the state. Furthermore, we introduce an approach for structure-preserving model reduction for large-scale logistics networks. This approach supposes to aggregate typical interconnection patterns (motifs) of the network graph. Such reduction allows to decrease the number of computations needed to verify the small gain condition