We synthesize robust output-based event-triggered controllers for a class of nonlinear systems subject to external disturbances and noises in both the plant measurement and the control input. We follow an emulation approach to this purpose: we first assume that we know a robust feedback law in continuous time, we then take into account the sampling and we explain how to construct the triggering condition to preserve stability. The triggering strategy enforces a minimum time between two consecutive transmissions by combining ideas from event-triggered control and periodic sampled-data control. The closed-loop system is shown to satisfy an input-to-state stability (ISS) property with respect to the external disturbances, the noises as well as their time-derivatives. The analysis reveals a tradeoff between the enforced minimum inter-transmission time and the magnitude of the ISS gains. The results are also new in the particular case where the triggering condition is only time-dependent as in traditional sampled-data control.

We synthesize robust output-based event-triggered controllers for a class of nonlinear systems subject to external disturbances and noises in both the plant measurement and the control input. We follow an emulation approach to this purpose: we first assume that we know a robust feedback law in continuous time, we then take into account the sampling and we explain how to construct the triggering condition to preserve stability. The triggering strategy enforces a minimum time between two consecutive transmissions by combining ideas from event-triggered control and periodic sampled-data control. The closed-loop system is shown to satisfy an input-to-state stability (ISS) property with respect to the external disturbances, the noises as well as their time-derivatives. The analysis reveals a tradeoff between the enforced minimum inter-transmission time and the magnitude of the ISS gains. The results are also new in the particular case where the triggering condition is only time-dependent as in traditional sampled-data control.

The performance of any fuzzy logic controller (FLC) is greatly dependent on its inference rules. In most cases, the closed-loop control performance and stability are enhanced if more rules are added to the rule base of the FLC. However, a large set of rules requires more on-line computational time and more parameters need to be adjusted. In this paper, a robust PD-type FLC is driven for a class of MIMO second order nonlinear systems with application to robotic manipulators. The rule base consists of only four rules per each degree of freedom (DOF). The approach implements fuzzy partition to the state variables based on Lyapunov synthesis. The resulting control law is stable and able to exploit the dynamic variables of the system in a linguistic manner. The presented methodology enables the designer to systematically derive the rule base of the control. Furthermore, the controller is decoupled and the procedure is simplified leading to a computationally efficient FLC. The methodology is model free approach and does not require any information about the system nonlinearities, uncertainties, time varying parameters, etc. Here, we present experimental results for the following controllers: the conventional PD controller, computed torque controller (CTC), sliding mode controller (SMC) and the proposed FLC. The four controllers are tested and compared with respect to ease of design, implementation, and performance of the closed-loop system. Results show that the proposed FLC has outperformed the other controllers.

The performance of any fuzzy logic controller (FLC) is greatly dependent on its inference rules. In most cases, the closed-loop control performance and stability are enhanced if more rules are added to the rule base of the FLC. However, a large set of rules requires more on-line computational time and more parameters need to be adjusted. In this paper, a robust PD-type FLC is driven for a class of MIMO second order nonlinear systems with application to robotic manipulators. The rule base consists of only four rules per each degree of freedom (DOF). The approach implements fuzzy partition to the state variables based on Lyapunov synthesis. The resulting control law is stable and able to exploit the dynamic variables of the system in a linguistic manner. The presented methodology enables the designer to systematically derive the rule base of the control. Furthermore, the controller is decoupled and the procedure is simplified leading to a computationally efficient FLC. The methodology is model free approach and does not require any information about the system nonlinearities, uncertainties, time varying parameters, etc. Here, we present experimental results for the following controllers: the conventional PD controller, computed torque controller (CTC), sliding mode controller (SMC) and the proposed FLC. The four controllers are tested and compared with respect to ease of design, implementation, and performance of the closed-loop system. Results show that the proposed FLC has outperformed the other controllers.

The performance of any fuzzy logic controller (FLC) is greatly dependent on its inference rules. In most cases, the closed-loop control performance and stability are enhanced if more rules are added to the rule base of the FLC. However, a large set of rules requires more on-line computational time and more parameters need to be adjusted. In this paper, a robust PD-type FLC is driven for a class of MIMO second order nonlinear systems with application to robotic manipulators. The rule base consists of only four rules per each degree of freedom (DOF). The approach implements fuzzy partition to the state variables based on Lyapunov synthesis. The resulting control law is stable and able to exploit the dynamic variables of the system in a linguistic manner. The presented methodology enables the designer to systematically derive the rule base of the control. Furthermore, the controller is decoupled and the procedure is simplified leading to a computationally efficient FLC. The methodology is model free approach and does not require any information about the system nonlinearities, uncertainties, time varying parameters, etc. Here, we present experimental results for the following controllers: the conventional PD controller, computed torque controller (CTC), sliding mode controller (SMC) and the proposed FLC. The four controllers are tested and compared with respect to ease of design, implementation, and performance of the closed-loop system. Results show that the proposed FLC has outperformed the other controllers.

Controllers are often designed based on a reduced or simplified model of the plant dynamics. In this context, we investigate whether it is possible to synthesize a stabilizing event-triggered feedback law for networked control systems (NCS) which have two time-scales, based only on an approximate model of the slow dynamics. We follow an emulation-like approach as we assume that we know how to solve the problem in the absence of sampling and then we study how to design the event-triggering rule under communication constraints. The NCS is modeled as a hybrid singularly perturbed system which exhibits the feature to generate jumps for both the fast variable and the error variable induced by the sampling. The first conclusion is that a triggering law which guarantees the stability and the existence of a uniform minimum amount of time between two transmissions for the slow model may not ensure the existence of such a time for the overall system, which makes the controller not implementable in practice. The objective of this contribution is twofold. We first show that existing event-triggering conditions can be adapted to singularly perturbed systems and semiglobal practical stability can be ensured in this case. Second, we propose another technique that combines event-triggered and time-triggered results in the sense that transmissions are only allowed after a predefined amount of time has elapsed since the last transmission. This technique has the advantage, under an additional assumption, to ensure a global asymptotic stability property and to allow the user to directly tune the minimum inter-transmission interval. We believe that this technique is of its own interest independently of the two-time scale nature of the addressed problem. The results are shown to be applicable to a class of globally Lipschitz systems.

In this paper, we are interested in the stabilization of a linear plant based on output measurements that are subject to dynamic quantization. Moreover, to save communication resources, these measurements are transmitted to the controller using an output-based event-triggering condition. The proposed event-triggering mechanism and the dynamic quantization strategy ensure an input-to-state stability (ISS) property of a set around the origin with respect to the external disturbances. The existence of a strictly positive lower bound is ensured on both the inter-transmission times and the inter-zoom times in order to prevent the occurrence of Zeno behaviour. The chattering between zoom-in and zoom-out actions is avoided, and the zoom variable of the dynamic quantizer is guaranteed to be bounded. We characterize the inherent tradeoff between transmissions and quantization in terms of design parameters that can be tuned by the user. The effectiveness of the approach is illustrated on a numerical example.

The objective is to design output feedback event-triggered controllers to stabilize a class of nonlinear systems. One of the main difficulties of the problem is to ensure the existence of a minimum amount of time between two consecutive transmissions, which is essential in practice. We solve this issue by combining techniques from event-triggered and time-triggered control. The idea is to turn on the event-triggering mechanism only after a fixed amount of time has elapsed since the last transmission. This time is computed based on results on the stabilization of time-driven sampled-data systems. The overall strategy ensures an asymptotic stability property for the closed-loop system. The results are proved to be applicable to linear time-invariant (LTI) systems as a particular case.

We address the robust stabilization of nonlinear systems subject to exogenous inputs using event-triggered output feedback laws. The plant dynamics is affected by external disturbances, while the output measurement and the control input are corrupted by noises. The communication between the plant and the controller is ensured by a digital channel. The feedback law is constructed in continuous-time, meaning that we ignore the communication network at this step. We then design the sampling rule to preserve stability. Two implementation scenarios are investigated. We first consider the case where the sampling of the plant measurements and of the control input are generated by the same rule, which leads to synchronous transmissions. We then study the scenario where two different laws are used to sample the measurements on the one hand, and the control input on the other hand, thus leading to asynchronous transmissions. In both cases, the transmission conditions consist in waiting a fixed amount of time after each sampling instant and then in checking a state-dependent criterion: when the latter is violated, a transmission occurs. In that way, Zeno phenomenon is a fortiori excluded. The proposed hybrid controllers are shown to ensure either an input-to-state stability property or an Lp stability property, depending on the assumptions. The results are applied to linear time-invariant systems as a particular case, for which the assumptions are formulated as linear matrix inequalities. The proposed strategy encompasses time-driven (and so periodic) sampling as a particular case, for which the results are new. The effectiveness of the approach is illustrated on simulations for a physical system.

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