Controller synthesis offers a correct-by-construction methodology to ensure the correctness and reliability of safety-critical cyber-physical systems (CPS). Controllers are classified based on the types of controls th...
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Controller synthesis offers a correct-by-construction methodology to ensure the correctness and reliability of safety-critical cyber-physical systems (CPS). Controllers are classified based on the types of controls they employ, which include reset controllers, feedback controllers and switching logic controllers. Reset controllers steer the behavior of a CPS to achieve system objectives by restricting its initial set and redefining its reset map associated with discrete jumps. Although the synthesis of feedback controllers and switching logic controllers has received considerable attention, research on reset controller synthesis is still in its early stages, despite its theoretical and practical significance. This paper outlines our recent efforts to address this gap. Our approach reduces the problem to computing differential invariants and reach-avoid sets. For polynomial CPS, the resulting problems can be solved by further reduction to convex optimizations. Moreover, considering the inevitable presence of time delays in CPS design, we further consider synthesizing reset controllers for CPS that incorporate delays.
In wireless sensor networks, the problem of sensor node location is a very important indicator. The accuracy of localization depends on the elimination of errors. Based on Euclidean distance, an optimization algorithm...
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In wireless sensor networks, the problem of sensor node location is a very important indicator. The accuracy of localization depends on the elimination of errors. Based on Euclidean distance, an optimization algorithm for semidefiniteprogramming(SDP) is proposed in this paper. Combining the effective anchor node position selection and ratio range setting, the SDP algorithm was used to relax the non-convex constraints, and effectively reduced the impact of errors and get the actual position of measurement nodes. This algorithm effectively solved the problem of inaccurate estimation of nodes outside the convex hull of the anchor node. The numerical results show that the proposed SDP algorithm achieves high accuracy in the location estimation of unknown nodes.
We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given...
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We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box or an ellipsoid, we provide a method to compute certified outer approximations of the reachable set. The proposed method consists of building a hierarchy of relaxations for an infinite-dimensional moment problem. Under certain assumptions, the optimal value of this problem is the volume of the reachable set and the optimum solution is the restriction of the Lebesgue measure on this set. Then, one can outer approximate the reachable set as closely as desired with a hierarchy of super level sets of increasing degree polynomials. For each fixed degree, finding the coefficients of the polynomial boils down to computing the optimal solution of a convex semidefinite program. When the degree of the polynomial approximation tends to infinity, we provide strong convergence guarantees of the super level sets to the reachable set. We also present some application examples together with numerical results.
作者：
Ye, DanLi, XiehuanNortheastern Univ
Coll Informat Sci & Engn State Key Lab Synthet Automat Proc Ind Shenyang 110189 Liaoning Peoples R China Northeastern Univ
Coll Informat Sci & Engn Shenyang 110189 Liaoning Peoples R China
This paper mainly investigates the state feedback controller design and the stability analysis for the general polynomial-fuzzy-model-based systems with time-varying delay. A Lyapunov-Krasovskii (L-K) function with th...
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This paper mainly investigates the state feedback controller design and the stability analysis for the general polynomial-fuzzy-model-based systems with time-varying delay. A Lyapunov-Krasovskii (L-K) function with the delay information in integral parts is used in the stability analysis process, and the time-delay terms are solved by an introduced lemma. Here, the assumption that the input matrices and the delay matrices have zero rows at the same time is not needed. A novel square of sum (SOS) optimization method successfully solves the non-convex problem by transforming the nonlinear terms and the time-varying delay matrix items into indices, which are optimized to zero by a semi-definite programming. The resultant SOS conditions are delay dependent, and more flexible stability conditions are obtained by introducing the slack matrices. Numerical simulation proves the effectiveness of the method.
In this paper we consider polynomial conic optimization problems, where the feasible set is defined by constraints in the form of given polynomial vectors belonging to given nonempty closed convex cones, and we assume...
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In this paper we consider polynomial conic optimization problems, where the feasible set is defined by constraints in the form of given polynomial vectors belonging to given nonempty closed convex cones, and we assume that all the feasible solutions are non-negative. This family of problems captures in particular polynomial optimization problems (POPs), polynomial semi-definite polynomial optimization problems (PSDPs) and polynomial second-order cone-optimization problems (PSOCPs). We propose a new general hierarchy of linear conic optimization relaxations inspired by an extension of Polya's Positivstellensatz for homogeneous polynomials being positive over a basic semi-algebraic cone contained in the non-negative orthant, introduced in Dickinson and Povh (J Glob Optim 61(4):615-625, 2015). We prove that based on some classic assumptions, these relaxations converge monotonically to the optimal value of the original problem. Adding a redundant polynomial positive semi-definite constraint to the original problem drastically improves the bounds produced by our method. We provide an extensive list of numerical examples that clearly indicate the advantages and disadvantages of our hierarchy. In particular, in comparison to the classic approach of sum-of-squares, our new method provides reasonable bounds on the optimal value for POPs, and strong bounds for PSDPs and PSOCPs, even outperforming the sum-of-squares approach in these latter two cases.
This paper presents an efficient optimization technique for gridless 2-D line spectrum estimation, named decoupled atomic norm minimization (D-ANM). The framework of atomic norm minimization (ANM) is considered, which...
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This paper presents an efficient optimization technique for gridless 2-D line spectrum estimation, named decoupled atomic norm minimization (D-ANM). The framework of atomic norm minimization (ANM) is considered, which has been successfully applied in 1-D problems to allow super-resolution frequency estimation for correlated sources even when the number of snapshots is highly limited. The state-of-the-art 2-D ANM approach vectorizes the 2-D measurements to their 1-D equivalence, which incurs huge computational cost and may become too costly for practical applications. We develop a novel decoupled approach of 2-D ANM via semi-definite programming (SDP), which introduces a new matrix-form atom set to naturally decouple the joint observations in both dimensions without loss of optimality. Accordingly, the original large-scale 2-D problem is equivalently reformulated via two decoupled one-level Toeplitz matrices, which can be solved by simple 1-D frequency estimation with pairing. Compared with the conventional vectorized approach, the proposed D-ANM technique reduces the computational complexity by several orders of magnitude with respect to the problem size, at no loss of optimality. It also retains the benefits of ANM in terms of precise signal recovery, small number of required measurements, and robustness to source correlation. The complexity benefits are particularly attractive for large-scale antenna systems such as massive MIMO, radar signal processing and radio astronomy. (C) 2019 Elsevier B.V. All rights reserved.
We derive a procedure for computing an upper bound on the number of equiangular lines in various Euclidean vector spaces by generalizing the classical pillar decomposition developed by Lemmens and Seidel;namely, we us...
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We derive a procedure for computing an upper bound on the number of equiangular lines in various Euclidean vector spaces by generalizing the classical pillar decomposition developed by Lemmens and Seidel;namely, we use linear algebra and combinatorial arguments to bound the number of vectors within an equiangular set which have inner products of certain signs with a negative clique. After projection and rescaling, such sets are also certain spherical two-distance sets, and semidefiniteprogramming techniques may be used to bound the size of the set. Applying our method, we prove new relative bounds for the angle arccos(1/5). Experiments show that our relative bounds for all possible angles are considerably smaller than the known semidefiniteprogramming bounds for a range of larger dimensions. Our computational results also show an explicit bound on the size of a set of equiangular lines in R-r regardless of angle, which is strictly less than the well-known Gerzon's bound if r + 2 is not a square of an odd number.
CVX-based numerical algorithms are widely and freely available for solving convex optimization problems but their applications to solve optimal design problems are limited. Using the CVX programs in MATLAB, we demonst...
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CVX-based numerical algorithms are widely and freely available for solving convex optimization problems but their applications to solve optimal design problems are limited. Using the CVX programs in MATLAB, we demonstrate their utility and flexibility over traditional algorithms in statistics for finding different types of optimal approximate designs under a convex criterion for nonlinear models. They are generally fast and easy to implement for any model and any convex optimality criterion. We derive theoretical properties of the algorithms and use them to generate new A-, c-, D- and E-optimal designs for various nonlinear models, including multi-stage and multi-objective optimal designs. We report properties of the optimal designs and provide sample CVX program codes for some of our examples that users can amend to find tailored optimal designs for their problems. The Canadian Journal of Statistics 47: 374-391;2019 (c) 2019 Statistical Society of Canada
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this paper, this problem is tackled by minimizing the sum of a nonconvex least-squares fit criterion and a penalty term. We ...
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Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this paper, this problem is tackled by minimizing the sum of a nonconvex least-squares fit criterion and a penalty term. We assume that the nonlinearity of the model can be accounted for by a rational function. In addition, we suppose that the signal to be sought is sparse and a rational approximation of the l(0) pseudonorm thus constitutes a suitable penalization. The resulting composite cost function belongs to the broad class of semialgebraic functions. To find a globally optimal solution to such an optimization problem, it can be transformed into a generalized moment problem, for which a hierarchy of semidefiniteprogramming relaxations can be built. Global optimality comes at the expense of an increased dimension and to overcome computational limitations concerning the number of involved variables, the structure of the problem has to be carefully addressed. A situation of practical interest is when the nonlinear model consists of a convolutive transform followed by a componentwise nonlinear rational saturation. We then propose to use a sparse relaxation able to deal with up to several hundreds of optimized variables. In contrast with the naive approach consisting of linearizing the model, our experiments show that the proposed approach offers good performance.
The existing dynamic models assume the technology is unchanged in which the same factor should have the same multiplier, no matter which process it is associated with. The internal network structures embedded in a mul...
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The existing dynamic models assume the technology is unchanged in which the same factor should have the same multiplier, no matter which process it is associated with. The internal network structures embedded in a multi-period system are ignored in the literature. The current paper considers that the technology is changed in the dynamic system The same factor may have different multipliers in different periods, except for the variables of intermediate measures connecting two stages in one period and flows connecting two consecutive periods. An additive aggregation dynamic network data envelopment analysis is developed to measure the multi-period systems with a two-stage process embedded in each period. The system efficiency, overall efficiency and stage efficiencies of each period can be derived, and the relationship between the system efficiency and period efficiencies can be identified. The newly developed dynamic network model is nonlinear, and can be transformed to a semi-definite programming problem. A case of high-tech industry in China is illustrated to the approach.
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