An original Nyquist-based frequency domain robust decentralized controller (DC) design technique for robust stability and guaranteed nominal performance is proposed, applicable for continuous-time uncertain systems described by a set of transfer function matrices. To provide nominal performance, interactions are included in individual design using one selected characteristic locus of the interaction matrix, used to reshape frequency responses of decoupled subsystems; such modified subsystems are termed "equivalent subsystems". Local controllers of equivalent subsystems independently tuned for stability and specified feasible performance constitute the decentralized controller guaranteeing specified performance of the full system. To guarantee robust stability, the M−Δ stability conditions are derived. Unlike standard robust approaches, the proposed technique considers full nominal model, thus reducing conservativeness of resulting robust stability conditions. The developed frequency domain design procedure is graphical, interactive and insightful. A case study providing a step-by-step robust DC design for the Quadruple Tank Process [K.H. Johansson: Interaction bounds in multivariable control systems. Automatica 38 (2002), 1045-1051] is included.
This paper proposes a new quantum particle swarm optimization algorithm with local attracting (LAQPSO), which is based on quantum-inspired evolutionary algorithm (QEA) and particle swarm optimization algorithm (PSO). In the proposed LAQPSO, a novel quantum bit expression mechanism called quantum angle is employed to encode the solution onto particle, and a new local attractor is proposed to determine the rotation angle of quantum rotation gate automatically. During the process of seeking the global solution, the magnitude of rotation angle is adjusted by an important parameter called contraction coefficient, which can quantitatively determine the tradeoff between exploration ability and exploitation ability. The simulation results for different contraction coeffcients are helpful for selecting the key parameter. A set of benchmark functions are used to evaluate the performance of LAQPSO, QEA and QBPSO, and the results show that the proposed algorithm has a fast convergence rate and can effectively avoid premature convergence.
Embedding approaches can be used for solving non linear programs \emph{P}. The idea is to define a one-parametric problem such that for some value of the parameter the corresponding problem is equivalent to \emph{P}. A particular case is the multipliers embedding, where the solutions of the corresponding parametric problem can be interpreted as the points computed by the multipliers method on \emph{P}. However, in the known cases, either path-following methods can not be applied or the necessary conditions for its convergence are fulfilled under very restrictive hypothesis. In this paper, we present a new multipliers embedding such that the objective function and the constraints of P(t) are C3 differentiable functions. We prove that the parametric problem satisfies the \emph{JJT}-regularity generically, a necessary condition for the success of the path-following method.
In the article a new sparse low-rank matrix decomposition model is proposed based on the smoothly clipped absolute deviation (SCAD) penalty. In order to overcome the computational hurdle we generalize the alternating direction method of multipliers (ADMM) algorithm to develop an alternative algorithm to solve the model. The algorithm we designed alternatively renew the sparse matrix and low-rank matrix in terms of the closed form of SCAD penalty. Thus, the algorithm reduces the computational complexity while at the same time to keep the computational accuracy. A series of simulations have been designed to demonstrate the performances of the algorithm with comparing with the Augmented Lagrange Multiplier (ALM) algorithm. Ultimately, we apply the model to an on- board video background modeling problem. According to model the on-board video background, we can separate the video background and passenger's actions. Thus, the model can help us to identify the abnormal action of train passengers. The experiments show the background matrix we estimated is not only sparser, but the computational efficiency is also improved.
In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions $d\geq 3$.
Pseudo $\star $-autonomous lattices are non-commutative generalizations of $\star $-autonomous lattices. It is proved that the class of pseudo $\star $-autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo $\star $-autonomous lattices can be described as their normal ideals.
We prove a non-archimedean Dugundji extension theorem for the spaces $C^{\ast }(X,\mathbb {K})$ of continuous bounded functions on an ultranormal space $X$ with values in a non-archimedean non-trivially valued complete field $\mathbb {K}$. Assuming that $\mathbb {K}$ is discretely valued and $Y$ is a closed subspace of $X$ we show that there exists an isometric linear extender $T\colon C^{\ast }(Y,\mathbb {K})\rightarrow C^{\ast }(X,\mathbb {K})$ if $X$ is collectionwise normal or $Y$ is Lindelöf or $\mathbb {K}$ is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace $Y$ of an ultraregular space $X$ is a retract of $X$.