Characterizing Boundedness in Chase Variants

Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions.

Finite-Time Boundedness Control for Nonlinear Networked Systems with Randomly Occurring Multi-Distributed Delays and Missing Measurements

This paper investigates the stochastic finite-time H∞ boundedness problem for nonlinear discrete time networked systems with randomly occurring multi-distributed delays and missing measurements. The randomly occurring multi-distributed delays and missing measurements are described as Bernoulli distributed white noise sequence. The goal of this paper is to design a full-order output-feedback controller to guarantee that the corresponding closed-loop system is stochastic finite-time H∞ bounded and with desired H∞ performance. By constructing a new Lyapunov-Krasovskii functional, sufficient conditions for the existence of output-feedback are established. The desired full-order output-feedback controller is designed in terms of the solution to linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the validity of the designed method.

Finite-Time Boundedness and H∞ Control for Affine Switched Systems

For affine switched systems, the existence of multiple equilibria is related to subsystems owing to the affine terms, which makes asymptotic and finite-time stability analysis nontrivial. In this paper, the problems of finite-time boundedness (FTB) analysis and stabilization are addressed for affine switched systems, and several definitions and sufficient conditions are proposed to study FTB and H∞ performance. At first, the definition of FTB for affine switched systems is improved concerning the affine terms and multiple equilibria. Based on the FTB definition, sufficient conditions ensuring finite-time boundedness for affine switched systems under a prespecified state boundary are given. Then the results are extended to solve H∞ finite-time boundedness problem, in which the H∞ controllers are designed to guarantee the finite-time boundedness of affine switched system with H∞ performance. In our investigation, average dwell-time approach is employed to study the time-dependent constrained switching case. Finally, several numerical examples are given to illustrate the effectiveness of the proposed results.

Finite-Time Bounded Tracking Control for Linear Discrete-Time Systems

A finite-time bounded tracking control problem for a class of linear discrete-time systems subject to disturbances is investigated. Firstly, by applying a difference method to constructing the error system, the problem is transformed into a finite-time boundedness problem of the output vector of the error system. In fact, this is a finite-time boundedness problem with respect to the partial variables. Secondly, based on the partial stability theory and the research methods of finite-time boundedness problem, a state feedback controller formulated in form of linear matrix inequality is proposed. Based on this, a finite-time bounded tracking controller of the original system is obtained. Finally, a numerical example is presented to illustrate the effectiveness of the controller.

Adaptive nonlinear generalized predictive control for hypersonic vehicle with unknown parameters and control constraints

In this article, an adaptive nonlinear generalized predictive controller is developed for the hypersonic vehicle with unknown parameter uncertainties and control surface constraints. A nominal controller based on generalized predictive control is first developed for the nominal longitudinal model. Considering the complicated practical flying environment and outer unknown disturbances, a parametric longitudinal dynamics model of the hypersonic vehicle is constructed. Then, an adaptive parameter estimation method is proposed to update the unknown controller parameters and parameter projection is applied to solve the control singularity and the parameter boundedness problem. Control surface is restricted to deflect in a range. To satisfy the above constraint, the predictive time should be selected appropriately. Through a large number of simulation experiments, the suitable ranges of the predictive time under different commands are given. All closed-loop signals are guaranteed to be bounded. And simulation results verify the effectiveness of the proposed controller.