scholarly journals Stability of 1-Bit Compressed Sensing in Sparse Data Reconstruction

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yuefang Lian ◽  
Jinchuan Zhou ◽  
Jingyong Tang ◽  
Zhongfeng Sun
Keyword(s):  
Optimization Problems ◽  
Inequality Constraints ◽  
Necessary Condition ◽  
Sensing Matrix ◽  
Quadratic Constraint ◽  
Linear Equality ◽  
Equality And Inequality Constraints ◽  
Measurement Vector ◽  
The Stability ◽  
Sufficient And Necessary Condition

1-bit compressing sensing (CS) is an important class of sparse optimization problems. This paper focuses on the stability theory for 1-bit CS with quadratic constraint. The model is rebuilt by reformulating sign measurements by linear equality and inequality constraints, and the quadratic constraint with noise is approximated by polytopes to any level of accuracy. A new concept called restricted weak RSP of a transposed sensing matrix with respect to the measurement vector is introduced. Our results show that this concept is a sufficient and necessary condition for the stability of 1-bit CS without noise and is a sufficient condition if the noise is available.

scholarly journals A QP Solver Implementation for Embedded Systems Applied to Control Allocation

Computation ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 88
Author(s):  
Christina Schreppel ◽  
Jonathan Brembeck
Keyword(s):  
Embedded Systems ◽  
Simulation Experiment ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Control Allocation ◽  
Control Engineering ◽  
Linear Equality ◽  
Equality And Inequality Constraints ◽  
Quadratic Programming Problems ◽  
Function Matrix

Quadratic programming problems (QPs) frequently appear in control engineering. For use on embedded platforms, a QP solver implementation is required in the programming language C. A new solver for quadratic optimization problems, EmbQP, is described, which was implemented in well readable C code. The algorithm is based on the dual method of Goldfarb and Idnani and solves strictly convex QPs with a positive definite objective function matrix and linear equality and inequality constraints. The algorithm is outlined and some details for an efficient implementation in C are shown, with regard to the requirements of embedded systems. The newly implemented QP solver is demonstrated in the context of control allocation of an over-actuated vehicle as application example. Its performance is assessed in a simulation experiment.

Consensus Problem of Singular Multi-Agent Systems with Continuous-Time and Fixed Topology

2013 ◽  
Vol 278-280 ◽  
pp. 1687-1691
Author(s):  
Tong Qiang Jiang ◽  
Jia Wei He ◽  
Yan Ping Gao
Keyword(s):  
Continuous Time ◽  
Spanning Tree ◽  
Undirected Graph ◽  
Necessary Condition ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Fixed Topology ◽  
The Stability ◽  
Sufficient And Necessary Condition

The consensus problems of two situations for singular multi-agent systems with fixed topology are discussed: directed graph without spanning tree and the disconnected undirected graph. A sufficient and necessary condition is obtained by applying the stability theory and the system is reachable asymptotically. But for normal systems, this can’t occur in upper two situations. Finally a simulation example is provided to verify the effectiveness of our theoretical result.

scholarly journals Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications

2021 ◽  
Vol Volume 2 (Original research articles>) ◽  
Author(s):  
Lisa C. Hegerhorst-Schultchen ◽  
Christian Kirches ◽  
Marc C. Steinbach
Keyword(s):  
Normal Form ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
First Order ◽  
Nonlinear Programs ◽  
Mathematical Programs ◽  
Ongoing Effort ◽  
Equality And Inequality Constraints ◽  
Smooth Optimization

This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie's and Guignard's kink qualification and prove relations to MPCC-ACQ and MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a specific slack reformulation suggested in [10], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. We also prove the weaker result that equivalence of Guginard's (and Abadie's) constraint qualifications for all branch problems hold, while the question of GCQ preservation remains open. Finally, we introduce M-stationarity and B-stationarity concepts for abs-normal NLPs and prove first order optimality conditions corresponding to MPCC counterpart formulations.

A Simplified Stability Criterion for Nonconservative Systems

1979 ◽  
Vol 46 (2) ◽  
pp. 423-426 ◽  
Author(s):  
I. Fawzy
Keyword(s):  
Dynamic Stability ◽  
Stability Criterion ◽  
Degrees Of Freedom ◽  
Necessary Condition ◽  
Matrix Methods ◽  
Nonconservative System ◽  
Nonconservative Systems ◽  
The Stability ◽  
Lyapunov’S Theorem ◽  
Sufficient And Necessary Condition

Dynamic stability of a general nonconservative system of n degrees of freedom is investigated. A sufficient and necessary condition for the stability of such a system is developed. It represents a simplified criterion based on the famous Lyapunov’s theorem which is proved afresh using λ-matrix methods only. When this criterion is adopted, it reduces the number of equations in Lyapunov’s method to less than half. A systematic procedure is then suggested for the stability investigation and its use is illustrated through a numerical example at the end of the paper.

Coning motion stability of spinning missiles with strapdown seekers

2016 ◽  
Vol 120 (1232) ◽  
pp. 1566-1577 ◽  
Author(s):  
S. He ◽  
D. Lin ◽  
J. Wang
Keyword(s):  
Stability Analysis ◽  
Scaling Factor ◽  
Guidance System ◽  
Necessary Condition ◽  
Stability Conditions ◽  
Motion Stability ◽  
Model Derivation ◽  
The Stability ◽  
Stability Issues ◽  
Sufficient And Necessary Condition

ABSTRACTThis paper investigates the problem of coning motion stability of spinning missiles equipped with strapdown seekers. During model derivation, it is found that the scaling factor error between the strapdown seeker and the onboard gyro introduces an undesired parasitic loop in the guidance system and, therefore, results in stability issues. Through stability analysis, a sufficient and necessary condition for the stability of spinning missiles with strapdown seekers is proposed analytically. Theoretical and numerical results reveal that the scaling factor error, spinning rate and navigation ratio play important roles in stable regions of the guidance system. Consequently, autopilot gains must be checked carefully to satisfy the stability conditions.

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