Continuous-time Part Research Articles

Finite-time stabilization of state dependent impulsive dynamical linear systems

The problem of finite-time stabilizing control design for state-dependent impulsive dynamical linear systems (SD-IDLS) is tackled in this paper. Such systems are characterized by continuous-time, linear, possibly time-varying, dynamics coupled with discrete-time, linear, possibly time-varying, dynamics. The continuous-time part determines the system evolution in any time interval between two consecutive resetting events, while the discrete-time part governs its instantaneous state jump whenever the system trajectory intersects a resetting set, i.e. a region of the state space assumed to be time-independent. By making use of a quadratic control Lyapunov function, the finite-time stabilization of SD-IDLS through a static output feedback control design is specifically discussed in this paper. A sufficient and constructive result is provided based on the conical hulls of the resetting set subregions and on some cone copositivity properties of the chosen control Lyapunov function. Such a result is based on the solution of a feasibility problem that involves a set of coupled Difference/Differential Linear Matrix Inequalities (D/DLMI), which is shown to be less conservative and more numerically amenable with respect to other results available in the literature. An example illustrates the effectiveness of the proposed approach.

Distributed Dynamic Event-Triggered Power Management Strategy for Global Economic Operation in High-Power Hybrid AC/DC Microgrids

With the increasing integration of distributed generators (DGs), renewable energy sources (RESs), and energy storage systems (ESSs) in the hybrid AC/DC microgrid (HMG), the paralleled bidirectional interlinking converters (BILCs) play a significant role in the economic power interaction (EPI) between AC and DC subgrids. This paper proposes a distributed dynamic event-triggered control (ETC) strategy for the HMG to realize the global economic operation. In each subgrid, economic power sharing (EPS) among DGs can be achieved by economic droop controllers with no global information. The proposed distributed dynamic ETC includes a continuous-time part and a discrete-time part, where the former part realizes the EPI between two subgrids, while the latter part ensures the proportional power sharing between BILCs. Thus, a particular over-stressed BILC can be avoided, and system reliability and scalability are significantly improved. Additionally, only data from neighboring BILCs at the event-triggered times are involved, which greatly minimizes the communication burden and costamong BILCs. Furthermore, the asymptotic stability of the closed-loop system dynamics and the communication time delay stability are proven. Finally, the hardware-in-loop experimental results are conducted to demonstrate the effectiveness of the proposed control strategy.

On finite-time stability and stabilization of nonlinear hybrid dynamical systems

<abstract> Finite time stability involving dynamical systems whose trajectories converge to a Lyapunov stable equilibrium state in finite time have been studied for both continuous-time and discrete-time systems. For continuous-time systems, finite time stability is defined for equilibria of continuous but non-Lipschitzian nonlinear dynamics, whereas discrete-time systems can exhibit finite time stability even when the system dynamics are linear, and hence, Lipschitz continuous. Alternatively, for impulsive dynamical systems it may be possible to reset the system states to an equilibrium state achieving finite time stability without requiring a non-Lipschitz condition for the continuous-time part of the hybrid system dynamics. In this paper, we develop sufficient Lyapunov conditions for finite time stability of impulsive dynamical systems using both a scalar differential Lyapunov inequality on the continuous-time dynamics as well as a scalar difference Lyapunov inequality on the discrete-time resetting dynamics. Furthermore, using our proposed finite time stability results, we design universal hybrid finite time stabilizing control laws for impulsive dynamical systems. Finally, we present several numerical examples for finite time stabilization of network impulsive dynamical systems. </abstract>

Orbital stability of periodic solutions of an impulsive system with a linear continuous-time part

An impulsive system with a linear continuous-time part and a nonlinear discrete-time part is considered. A criterion for exponential orbital stability of its periodic solutions is obtained. The proof is based on linearization by the first approximation of an auxiliary discrete-time system. The formulation of the criterion depends significantly on a number of impulses per period of the solution. The paper provides a mathematical rationale for some results previously examined in mathematical biology by computer simulations.

Distributed Hybrid Secondary Control for a DC Microgrid via Discrete-Time Interaction

This paper studies the current sharing problem of a dc microgrid using the hybrid dynamic control method. The hybrid dynamic controller framework is established including a continuous-time part and a discrete-time part, where the former part eliminates the voltage deviation of the dc bus and the latter part ensures the current sharing accuracy of the dc microgrid. The proposed distributed hybrid secondary controller not only guarantees a high accuracy of current sharing but also maintains the voltage regulation at the dc bus. Different from most existing methods, it only utilizes the sampling output current information of neighbors at the discrete time instants, which greatly reduces the communication burden. Under the framework of stability analysis on the closed-loop system, the proposed hybrid dynamic controller achieves both current sharing and voltage regulation if the average interacted interval of the discrete time interaction satisfies a bounded constraint. Besides, a detailed parameter design of the controller is provided. Finally, simulation and experimental tests are presented to demonstrate the effectiveness of the proposed method.

Integrating continuous-time and discrete-event concepts in modelling and simulation of manufacturing machines

Using simulation models for the development and testing of control systems can have significant advantages over using real machines. This paper demonstrates the suitability of the χ language for modelling, simulation and control of manufacturing machines. The language integrates a small number of powerful orthogonal continuous-time and discrete-event concepts. The continuous-time part of χ is based on DAEs; the discrete-event part is based on a CSP-like concurrent programming language. Models are specified in a symbolic mathematical notation. A case study is presented of a transport system consisting of conveyor belts.

Design of Discrete Controllers for Continuous Systems Using Hybrid Chi

Controllers of continuous systems are usually discrete, because of the sampling required by computer implementations. The controlled physical systems are often nonlinear. It is therefore important that tools and languages for control system design provide adequate support for dealing with these phenomena. The χ language, presented in this paper, provides such support. It is suited to specification and simulation of control systems of a continuous-time, discrete-event or discrete-time nature. Such control systems may range from stand-alone controllers to interacting plant-wide control systems. The language integrates a small number of orthogonal continuous-time and discrete-event concepts. The continuous-time part of χ is based on differential algebraic equations; the discrete-event part is based on a CSP-like concurrent programming language. A case study is presented of a tank level control system. Several control strategies are modelled, including a PI controller with antiwindup.

A hybrid state-space approach to sampled-data feedback control

This paper develops a state-space theory for the study of linear shift-invariant finite-dimensional hybrid dynamical systems. By hybrid systems, we mean an input-output operator relating hybrid signals, that is, signals which consist of two parts: a continuous-time part and a discrete-time part. We first introduce the hybrid state-space model and show the closedness properties under the fundamental operations. We next investigate the standard basic issues associated with this formalism: reachability, observability, and internal stability. We define the notion of H 2-norm of the hybrid system and show how to evaluate it. Since the analysis result can be applied to any hybrid system with the proposed hybrid state-space model, we apply the analysis result to the optimal digital control problem for standard four-block configuration with H 2-norm performance measure. The solution, with computational algorithm, is derived for the time-delay case.