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Register a new userDynamic self-triggered control for nonlinear systems based on hybrid Lyapunov functions
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Self-triggered control (STC) is a well-established technique to reduce the amount of samples for sampled-data systems, and is hence particularly useful for Networked Control Systems. At each sampling instant, an STC mechanism determines not only an updated control input but also when the next sample should be taken. In this paper, a dynamic STC mechanism for nonlinear systems is proposed. The mechanism incorporates a dynamic variable for determining the next sampling instant. Such a dynamic variable for the trigger decision has been proven to be a powerful tool for increasing sampling intervals in the closely related concept of event-triggered control, but was so far not exploited for STC. This gap is closed in this paper. For the proposed mechanism, the dynamic variable is chosen to be the filtered values of the Lyapunov function at past sampling instants. The next sampling instant is, based on the dynamic variable and on hybrid Lyapunov function techniques, chosen such that an average decrease of the Lyapunov function is ensured. The proposed mechanism is illustrated with a numerical example from the literature. For this example, the obtained sampling intervals are significantly larger than for existing static STC mechanisms. This paper is the accepted version of [1], containing also proofs of the main results.
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It has been shown that self-triggered control has the ability to reduce computational loads and deal with the cases with constrained resources by properly setting up the rules for updating the system control when necessary. In this paper, self-triggered stabilization of Boolean control networks (BCNs), including deterministic BCNs, probabilistic BCNs and Markovian switching BCNs, is first investigated via semi-tensor product of matrices and Lyapunov theory of Boolean networks. The self-triggered mechanism with the aim to determine when the controller should be updated is given based on the decrease of the corresponding Lyapunov functions between two successive sampling times. We show that the self-triggered controllers can be chosen as the conventional controllers without sampling, and also can be optimally constructed based on the triggering conditions.
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