Electrical and Electronic Engineering - Research Publications

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    Averaging in singularly perturbed hybrid systems with hybrid boundary layer systems
    Wang, W ; Teel, AR ; Nesic, D (IEEE, 2012-01-01)
    We analyze a class of singularly perturbed hybrid systems based on two auxiliary hybrid systems: the averaged system, which approximates the slow dynamics, and the boundary layer system, which approximates the fast dynamics. The average system is generated by averaging the solutions of the boundary layer system. The novelty of this work is that the boundary layer system is a hybrid system rather than a continuous-time system. This extends available results to cover new classes of hybrid systems. We illustrate how to apply our results through an example that is a power converter system under hybrid feedbacks implemented by pulse-width modulation (PWM).
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    On the uniform global pre-asymptotic stability of closed sets for switched hybrid systems
    Wang, W ; Postoyan, R ; Nesic, D (IEEE, 2013-01-01)
    We investigate the stability of a class of dynamical systems that switch among a given finite family of hybrid systems. We propose sufficient conditions tailored to this particular type of hybrid systems which guarantee the uniform global pre-asymptotic stability (UGpAS) of a given closed set. We first assume this set to be UGpAS for each system of the family. A slow switching condition is then presented to maintain this property for the overall system. We introduce for this purpose the concept of hybrid dwell time which characterizes the length of the hybrid time intervals between two successive switching instants.
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    Design of observers implemented over FlexRay networks
    Wang, W ; Nesic, D ; Postoyan, R (IEEE, 2014-01-01)
    We investigate the observer design for nonlinear systems whose measurements are sent over a network governed by FlexRay. FlexRay is a communication protocol used in the automotive industry which has the feature to switch between two scheduling rules associated with the two segments of its communication cycles. The objective of this paper is to generalize existing works on emulated observers for networked control systems (NCS) to be applicable to NCS with FlexRay. We propose for that purpose a novel hybrid model and guarantee the observer convergence provided that, for each segment, the scheduling rules are uniformly globally exponentially stable and the maximal allowable transmission intervals satisfy given explicit bounds. The analysis relies on the use of an hybrid Lyapunov function we recently constructed to investigate the stabilization of NCS with FlexRay. We finally apply the approach to a class of globally Lipschitz systems, which includes linear time-invariant systems as a particular case.
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    Diagonal stability for a class of graphs with connected circles
    Wang, W ; Nesic, D (IEEE, 2012)
    Diagonal stability for a class of matrices having strongly connected graphs is considered, in which each pair of distinct simple circles have at most one common edge or a common vertex. We apply the obtained results to analyze stability of a class of nonlinear dynamical networked systems, for which each subsystem is output strictly passive and the storage function is available. We show that diagonal stability of the dissipativity matrix that includes the information of interconnection structure of subsystems implies that the sum of weighted storage functions is a storage Lyapunov function for this class of networks.
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    Emulated controller design for networked control systems implemented on FlexRay
    Wang, W ; Nesic, D ; Postoyan, R (IEEE, 2014-01-01)
    We design stabilizing controllers for nonlinear networked control systems (NCS) whose transmissions are scheduled by FlexRay. FlexRay protocol has been developed by the automotive industry to provide high bandwidth and deterministic communications. It works with communication cycles which consist of a static segment and a dynamic segment during which different scheduling rules are employed. We generalize existing emulated controller designs to be applicable to NCS with FlexRay. We start from a feedback law which stabilizes the origin of the plant when there is no network. We then present a novel hybrid model of the closed-loop system when the controller is implemented over a network scheduled by FlexRay. Afterwards, we provide conditions on the network under which the stability of the NCS is ensured. In particular, we consider segments of arbitrary lengths and we provide segment-dependent maximal allowable transmission interval bounds. The analysis relies on the construction of a new hybrid Lyapunov function. We believe that this work demonstrates the flexibility of the emulation approach and that it can be used to investigate other control problems for NCS with switched protocols.
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    Stabilization of nonlinear systems using state-feedback periodic event-triggered controllers
    Wang, W ; Postoyan, R ; Nešić, D ; Heemels, WPMH (IEEE, 2016)
    We investigate the scenario where a controller communicates with a plant at discrete time instants generated by an event-triggering mechanism. In particular, the latter collects sampled data from the plant and the controller at each sampling instant, and then decides whether the control input needs to be updated, leading to periodic event-triggered control (PETC). In this paper, we propose a systematic design procedure for PETC that stabilize general nonlinear systems. The design is based on the existence of a continuous-time state-feedback controller, which stabilizes the system in the absence of communication constraints. We then take into account the sampling and we design an event-triggering condition, which is only updated at some of the sampling instants, to preserve stability. An explicit bound on the maximum sampling period with which the triggering rule is evaluated is provided. We show that there exists a trade-off between the latter and a parameter used to define the triggering condition. The results are applied to a van de Pol oscillator as an illustration.
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    Periodic event-triggered output feedback control of nonlinear systems
    Wang, W ; Postoyan, R ; Nesic, D ; Heemels, WPMH (IEEE, 2018-01-01)
    We investigate the stabilization of perturbed nonlinear systems using output-based periodic event-triggered controllers. Thus, the communication between the plant and the controller is triggered by a mechanism, which evaluates an output- and input-dependent rule at given sampling instants. We address the problem by emulation. Hence, we assume the knowledge of a continuous-time output feedback controller, which robustly stabilizes the system in the absence of network. We then implement the controller over the network and model the overall system as a hybrid system. We design the event-triggered mechanism to ensure an input-to-state stability property. An explicit bound on the maximum allowable sampling period at which the triggering rule is evaluated is provided. The analysis relies on the construction of a novel hybrid Lyapunov function. The results are applied to a class of Lipschitz nonlinear systems, for which we formulate the required conditions as linear matrix inequalities. The effectiveness of the scheme is illustrated via simulations of a nonlinear example.
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    Periodic event-triggered supervisory control of nonlinear systems: dwell-time switching logic
    Wang, W ; Nesic, D ; Shames, I (IEEE, 2018-01-01)
    We consider supervisory control of nonlinear systems which are implemented on digital networks. In particular, two candidate controllers are orchestrated by a supervisor to stabilize the origin of the plant by following a dwell time logic, i.e. evaluating a control-mode switching rule at instants which are at least spaced by some dwell time interval. The plant, the controllers and the supervisor communicate via a network and the transmissions are triggered by a mechanism at the discrete sampling instants, which leads to periodic event-triggered control. Thus, there are possibly two kinds of events generated at the sampling instants: the control-mode switching event to activate another control law and the transmission event to update the control input. We propose a systematic design procedure for periodic event-triggered supervisory control for nonlinear systems. We start from a supervisory control scheme which robustly stabilizes the system in the absence of the network. We then implement it over the network and design event-triggering rules to preserve its stability properties. In particular, for each candidate controller, we provide a lower bound for the control-mode dwell time, design criterion to generate transmission events and present an explicit bound on the maximum sampling period with which the triggering rules are evaluated, to ensure stability of the whole system. We show that there exist relationships among the control-mode dwell time, a parameter used to define the transmission event-triggering condition and the bound of the sampling period. An example is given to illustrate the results.