Nonlinear \boldsymbol{\mathcal{H}}_{\boldsymbol\infty} Control of UAVs for Collision Avoidance in Gusty Environments

This paper proposes a nonlinear $\mathcal{H}_{\infty}$ controller for stabilization of velocities, attitudes and angular rates of a fixed-wing unmanned aerial vehicle (UAV) in a windy environment. The suggested controller aims to achieve a steady-state flight condition in the presence of wind gusts such that the host UAV can be maneuvered to avoid collision with other UAVs during cruise flight with safety guarantees. This paper begins with building a proper model capturing flight aerodynamics of UAVs. Then a nonlinear controller is developed with gust attenuation and rapid response properties. Simulations are conducted for the Shadow UAV to verify performance of the proposed controller. Comparative studies with the proportional-integral-derivative (PID) controllers demonstrate that the proposed controller exhibits great performance improvement in a gusty environment, making it suitable for integration into the design of flight control systems for cruise flight of UAVs.     

Integrated damping parameter and control design in structural systems for \bf{\mathcal{H}^2} and {\mathcal{H}^{\infty}} specifications

The paper presents a linear matrix inequality (LMI)-based approach for the simultaneous optimal design of output feedback control gains and damping parameters in structural systems with collocated actuators and sensors. The proposed integrated design is based on simplified $\mathcal{H}^2$ and $\mathcal{H}^{\infty}$ norm upper bound calculations for collocated structural systems. Using these upper bound results, the combined design of the damping parameters of the structural system and the output feedback controller to satisfy closed-loop $\mathcal{H}^2$ or $\mathcal{H}^{\infty}$ performance specifications is formulated as an LMI optimization problem with respect to the unknown damping coefficients and feedback gains. Numerical examples motivated from structural and aerospace engineering applications demonstrate the advantages and computational efficiency of the proposed technique for integrated structural and control design. The effectiveness of the proposed integrated design becomes apparent, especially in very large scale structural systems where the use of classical methods for solving Lyapunov and Riccati equations associated with $\mathcal{H}^2$ and $\mathcal{H}^{\infty}$ designs are time-consuming or intractable.     

Design and Validation of an ${\mathcal{L}}_{1}$ Adaptive Controller for Mini-UAV Autopilot

The dynamics of Unmanned Aerial Vehicles (UAVs) is nonlinear and subject to external disturbances. The scope of this paper is the test of an \({\mathcal{L}_1}\) adaptive controller as autopilot inner loop controller candidate. The selected controller is based on piecewise constant adaptive laws and is applied to a mini-UAV. Navigation outer loop parameters are regulated via PID control. The main contribution of this paper is to demonstrate that the proposed control design can stabilize the nonlinear system, even if the controller parameters are selected starting from a decoupled linear model. The main advantages of this technique are: (1) the controller can be implemented for both linear and nonlinear systems without parameter adjustment or tuning procedure, (2) the controller is robust to unmodeled dynamics and parametric model uncertainties. The design scheme of a customized autopilot is illustrated and different configurations (in terms of mass, inertia and airspeed variations) are analyzed to validate the presented approach.     

Parallel {\mathcal {H}}-matrix arithmetic on distributed-memory systems

In the last decade, the hierarchical matrix technique was introduced to deal with dense matrices in an efficient way. It provides a data-sparse format and allows an approximate matrix algebra of nearly optimal complexity. This paper is concerned with utilizing multiple processors to gain further speedup for the ${\mathcal {H}}$ -matrix algebra, namely matrix truncation, matrix–vector multiplication, matrix–matrix multiplication, and inversion. One of the most cost-effective solution for large-scale computation is distributed computing. Distribute-memory architectures provide an inexpensive way for an organization to obtain parallel capabilities as they are increasingly popular. In this paper, we introduce a new distribution scheme for ${\mathcal {H}}$ -matrices based on the corresponding index set. Numerical experiments applied to a BEM model will complement our complexity analysis.     

An algebraic approach for $${\mathcal{H}}$$-matrix preconditioners

Hierarchical matrices ( -matrices) approximate matrices in a data-sparse way, and the approximate arithmetic for -matrices is almost optimal. In this paper we present an algebraic approach for constructing -matrices which combines multilevel clustering methods with -matrix arithmetic to compute the -inverse, -LU, and the -Cholesky factors of a matrix. Then the -inverse, -LU or -Cholesky factors can be used as preconditioners in iterative methods to solve systems of linear equations. The numerical results show that this method is efficient and greatly speeds up convergence compared to other approaches, such as JOR or AMG, for solving some large, sparse linear systems, and is comparable to other -matrix constructions based on Nested Dissection.     

A Dynamic Logic of Agency II: Deterministic $${\mathcal{DLA}}$$ , Coalition Logic,and Game Theory

We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are first-class citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called DDLA{\mathcal{DDLA}} (Deterministic Dynamic logic of Agency) which supports reasoning about actions and joint actions of agents and coalitions, and agentive and coalitional capabilities. In DDLA{\mathcal{DDLA}} it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess DDLA{\mathcal{DDLA}} we prove that it embeds Coalition Logic. We then extend DDLA{\mathcal{DDLA}} with modal operators for agents’ preferences, and show that the resulting logic is sufficiently expressive to capture the game-theoretic concepts of best response and Nash equilibrium.     

Infimal Convolution Regularisation Functionals of BV and $$\varvec{\mathrm {L}}^{\varvec{p}}$$ Spaces

We study a general class of infimal convolution type regularisation functionals suitable for applications in image processing. These functionals incorporate a combination of the total variation seminorm and \(\mathrm {L}^{p}\) norms. A unified well-posedness analysis is presented and a detailed study of the one-dimensional model is performed, by computing exact solutions for the corresponding denoising problem and the case \(p=2\). Furthermore, the dependency of the regularisation properties of this infimal convolution approach to the choice of p is studied. It turns out that in the case \(p=2\) this regulariser is equivalent to the Huber-type variant of total variation regularisation. We provide numerical examples for image decomposition as well as for image denoising. We show that our model is capable of eliminating the staircasing effect, a well-known disadvantage of total variation regularisation. Moreover as p increases we obtain almost piecewise affine reconstructions, leading also to a better preservation of hat-like structures.     

Mutually unbiased special entangled bases with Schmidt number 2 in $${\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}$$

A way of constructing special entangled basis with fixed Schmidt number 2 (SEB2) in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k\in z^+,3\not \mid k)\) is proposed, and the conditions mutually unbiased SEB2s (MUSEB2s) satisfy are discussed. In addition, a very easy way of constructing MUSEB2s in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k=2^l)\) is presented. We first establish the concrete construction of SEB2 and MUSEB2s in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4}\) and \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{8}\), respectively, and then generalize them into \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k\in z^+,3\not \mid k)\) and display the condition that MUSEB2s satisfy; we also give general form of two MUSEB2s as examples in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k=2^l)\).     

Top-$\boldsymbol{k}$ query processing over uncertain data in distributed environments

Although top-k queries over uncertain data in centralized databases have been studied widely in recent years, it is still a challenging issue in distributed environments. In distributed environments, such as Peer-to-Peer (P2P) systems and sensor networks, there exists an inherent uncertainty on the data objects due to imprecise measurements and network delays. Therefore, it is necessary to study the problem of how to efficiently retrieve top-k uncertain data objects over distributed environments with minimum network overhead. In this paper, we propose a novel approach of processing uncertain top-k queries in large-scale P2P networks, where datasets are horizontally partitioned over peers. In our approach, each peer constructs an Uncertain Quad-Tree (UQ-Tree) index for its local uncertain data, while the P2P network constructs a global index by summarizing the local indexes. Based on the global index, we propose a spatial-pruning algorithm to reduce communication costs and a distributed-pruning algorithm to reduce computation costs. Extensive experiments are conducted to verify the effectiveness and efficiency of the proposed methods in terms of communication costs and response time.     

Branching Time Logics \mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha } with Operations Until and Since Based on Bundles of Integer Numbers, Logical Consecutions, Deciding Algorithms

This paper is intended as an attempt to describe logical consequence in branching time logics. We study temporal branching time logics $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ which use the standard operations Until and Next and dual operations Since and Previous (LTL, as standard, uses only Until and Next). Temporal logics $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ are generated by semantics based on Kripke/Hinttikka structures with linear frames of integer numbers $\mathcal {Z}$ with a single node (glued zeros). For $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ , the permissible branching of the node is limited by α (where 1≤α≤ω). We prove that any logic $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ is decidable w.r.t. admissible consecutions (inference rules), i.e. we find an algorithm recognizing consecutions admissible in $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ . As a consequence, it implies that $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ itself is decidable and solves the satisfiability problem.     

Engineering and verifying agent-oriented requirements augmented by business constraints with $${\mathcal{B}}$$-Tropos

We propose B{\mathcal{B}}-Tropos as a modeling framework to support agent-oriented systems engineering, from high-level requirements elicitation down to execution-level tasks. In particular, we show how B{\mathcal{B}}-Tropos extends the Tropos methodology by means of declarative business constraints, inspired by the ConDec graphical language. We demonstrate the functioning of B{\mathcal{B}}-Tropos using a running example inspired by a real-world industrial scenario, and we describe how B{\mathcal{B}}-Tropos models can be automatically formalized in computational logic, discussing formal properties of the resulting framework and its verification capabilities.     

描述逻辑ALC中关于伪子概念极小改变的R-演算

AGM公设是用于信念修正的（被一个单一信念修正）,而DP公设是用于迭代修正的（被一个有限的信念序列修正）.李未给出了对于R-构型（configuration）△|Γ的R-演算,其中,△是一个原子公式或原子公式否定的集合,而Γ是一个有限的公式集合.为了在修正过程中能够保留断言中尽可能多的信息,将考虑一种新的极小改变的定义：伪子概念极小改变（≤-极小改变）,其中,≤是一种伪子概念的关系;之后,在此基础上给出一种新的R-演算T^DL,它是关于≤-极小改变可靠和完备的,使得△|Γ在T^DL中可以被约减为一个理论△∪Θ（记作├_T^DL △|Γ⇒△,Θ）当且仅当Θ是Γ关于△的一个≤-极小改变.     

Construction of a discrete divergence-free basis through orthogonal factorization in $${\mathcal{H}}$$ -arithmetic

Summary  In computational fluid dynamics, linear constraints on the fluid velocity lead to challenging indefinite linear systems of equations. In this paper, we propose to compute an approximation to the constrained linear space of divergence-free functions using hierarchical matrix techniques. This approach will yield a data-sparse, well-conditioned basis of the desired subspace in almost optimal computational complexity which is confirmed by numerical tests. The novelty of this paper lies in the application of hierarchical matrix techniques to orthogonal factorization as well as the construction of an explicit approximation to the subspace basis.