scholarly journals Robust LCEKF for Mismatched Nonlinear Systems with Non-Additive Noise/Inputs and Its Application to Robust Vehicle Navigation

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 2086
Author(s):  
Rayen Ben Ben Abdallah ◽  
Jordi Vilà-Valls ◽  
Gaël Pagès ◽  
Damien Vivet ◽  
Eric Chaumette
Keyword(s):  
Additive Noise ◽  
Real Life ◽  
Linear Constraints ◽  
Robust Tracking ◽  
Navigation Problem ◽  
Model Mismatch ◽  
Perfect System ◽  
Linearly Constrained ◽  
Robust Filters ◽  
Noise Statistics

It is well known that the standard state estimation technique performance is particularly sensitive to perfect system knowledge, where the underlying assumptions are: (i) Process and measurement functions and parameters are known, (ii) inputs are known, and (iii) noise statistics are known. These are rather strong assumptions in real-life applications; therefore, a robust filtering solution must be designed to cope with model misspecifications. A possible way to design robust filters is to exploit linear constraints (LCs) within the filter formulation. In this contribution we further explore the use of LCs, derive a linearly constrained extended Kalman filter (LCEKF) for systems affected by non-additive noise and system inputs, and discuss its use for model mismatch mitigation. Numerical results for a robust tracking and navigation problem are provided to show the performance improvement of the proposed LCEKF, with respect to state-of-the-art techniques, that is, a benchmark EKF without mismatch and a misspecified EKF not accounting for the mismatch.

scholarly journals Art of Formulating LPs and IPs from Real Life Problems

2013 ◽  
Vol 61 (2) ◽  
pp. 185-191
Author(s):  
Md Hasib Uddin Molla ◽  
M Babul Hasan
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Real Life ◽  
Linear Constraints ◽  
Decision Problems ◽  
System Of Equations ◽  
Present Formulation ◽  
Real Life Problem ◽  
Life Problems ◽  
Life Decision

Formulation of LPs and IPs is a technique to convert real life decision problems into a mathematical model. This model consists of a linear objective function and a set of linear constraints expressed in the form of a system of equations or inequalities. In this paper, we present formulation from real life problem as an art. We discuss formulation through real life example and solve them using computer techniques AMPL and LINDO. DOI: http://dx.doi.org/10.3329/dujs.v61i2.17068 Dhaka Univ. J. Sci. 61(2): 185-191, 2013 (July)

scholarly journals Automated handling of complex chemical structures in Z-matrix coordinates - the chemcoord library

2021 ◽  
Author(s):  
Oskar Weser ◽  
Björn Hein Hanke ◽  
Ricardo Mata
Keyword(s):  
Structural Changes ◽  
Molecular System ◽  
Linear Constraints ◽  
Analytical Geometry ◽  
Cartesian Coordinates ◽  
Chemical Structures ◽  
Automated Method ◽  
Non Linear ◽  
Linearly Constrained ◽  
Automated Handling

In this work, we present a fully automated method for the construction of chemically meaningful sets of non-redundant internal coordinates (also commonly denoted as Z-matrices) from the cartesian coordinates of a molecular system. Particular focus is placed on avoiding ill-definitions of angles and dihedrals due to linear arrangements of atoms, to consistently guarantee a well-defined transformation to cartesian coordinates, even after structural changes. The representations thus obtained are particularly well suited for pathway construction in double-ended methods for transition state search and optimisations with non-linear constraints. Analytical gradients for the transformation between the coordinate systems were derived for the first time, which allows analytical geometry optimizations purely in Z-matrix coordinates. The geometry optimisation was coupled with a Symbolic Algebra package to support arbitrary non-linear constraints in Z-matrix coordinates, while retaining analytical energy gradient conversion. Sample applications are provided for a number of common chemical reactions and illustrative examples where these new algorithms can be used to automatically produce chemically reasonable structure interpolations, or to perform non-linearly constrained optimisations of molecules.

Modified proximal symmetric ADMMs for multi-block separable convex optimization with linear constraints

2021 ◽  
pp. 1-28
Author(s):  
Yuan Shen ◽  
Yannian Zuo ◽  
Liming Sun ◽  
Xiayang Zhang
Keyword(s):  
Convex Optimization ◽  
Splitting Method ◽  
Principal Component ◽  
Convergence Result ◽  
Linear Constraints ◽  
Convex Optimization Problem ◽  
Separable Convex Programming ◽  
Separable Convex Optimization ◽  
Linearly Constrained ◽  
Correction Step

We consider the linearly constrained separable convex optimization problem whose objective function is separable with respect to [Formula: see text] blocks of variables. A bunch of methods have been proposed and extensively studied in the past decade. Specifically, a modified strictly contractive Peaceman–Rachford splitting method (SC-PRCM) [S. H. Jiang and M. Li, A modified strictly contractive Peaceman–Rachford splitting method for multi-block separable convex programming, J. Ind. Manag. Optim. 14(1) (2018) 397-412] has been well studied in the literature for the special case of [Formula: see text]. Based on the modified SC-PRCM, we present modified proximal symmetric ADMMs (MPSADMMs) to solve the multi-block problem. In MPSADMMs, all subproblems but the first one are attached with a simple proximal term, and the multipliers are updated twice. At the end of each iteration, the output is corrected via a simple correction step. Without stringent assumptions, we establish the global convergence result and the [Formula: see text] convergence rate in the ergodic sense for the new algorithms. Preliminary numerical results show that our proposed algorithms are effective for solving the linearly constrained quadratic programming and the robust principal component analysis problems.

Behavioral Study of Drosophila Fruit Fly and Its Modeling for Soft Computing Application

2016 ◽  
pp. 32-84 ◽  
Author(s):  
Tapan Kumar Singh ◽  
Kedar Nath Das
Keyword(s):  
Real Life ◽  
Optimal Solution ◽  
Fruit Fly ◽  
Linear Constraints ◽  
Behavioral Study ◽  
Search Optimization ◽  
Life Problems ◽  
Decision Variables ◽  
Wide Range ◽  
Real Life Situation

Most of the problems arise in real-life situation are complex natured. The level of the complexity increases due to the presence of highly non-linear constraints and increased number of decision variables. Finding the global solution for such complex problems is a greater challenge to the researchers. Fortunately, most of the time, bio-inspired techniques at least provide some near optimal solution, where the traditional methods become even completely handicapped. In this chapter, the behavioral study of a fly namely ‘Drosophila' has been presented. It is worth noting that, Drosophila uses it optimized behavior, particularly, when searches its food in the nature. Its behavior is modeled in to optimization and software is designed called Drosophila Food Search Optimization (DFO).The performance, DFO has been used to solve a wide range of both unconstrained and constrained benchmark function along with some of the real life problems. It is observed from the numerical results and analysis that DFO outperform the state of the art evolutionary techniques with faster convergence rate.

scholarly journals Randomized sketch descent methods for non-separable linearly constrained optimization

2020 ◽  
Author(s):  
Ion Necoara ◽  
Martin Takáč
Keyword(s):  
Objective Function ◽  
Large Scale ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Linear Constraints ◽  
Descent Methods ◽  
Constrained Problems ◽  
Special Cases ◽  
Linearly Constrained

Abstract In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first investigate necessary and sufficient conditions for the sketch sampling to have well-defined algorithms. Based on these sampling conditions we develop new sketch descent methods for solving general smooth linearly constrained problems, in particular, random sketch descent (RSD) and accelerated random sketch descent (A-RSD) methods. To our knowledge, this is the first convergence analysis of RSD algorithms for optimization problems with multiple non-separable linear constraints. For the general case, when the objective function is smooth and non-convex, we prove for the non-accelerated variant sublinear rate in expectation for an appropriate optimality measure. In the smooth convex case, we derive for both algorithms, non-accelerated and A-RSD, sublinear convergence rates in the expected values of the objective function. Additionally, if the objective function satisfies a strong convexity type condition, both algorithms converge linearly in expectation. In special cases, where complexity bounds are known for some particular sketching algorithms, such as coordinate descent methods for optimization problems with a single linear coupled constraint, our theory recovers the best known bounds. Finally, we present several numerical examples to illustrate the performances of our new algorithms.

scholarly journals Convergence Analysis on an Accelerated Proximal Point Algorithm for Linearly Constrained Optimization Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Sha Lu ◽  
Zengxin Wei
Keyword(s):  
Machine Learning ◽  
Linear Programming ◽  
Proximal Point Algorithm ◽  
Original Problem ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Proximal Point ◽  
Constrained Optimization Problems ◽  
Linearly Constrained ◽  
Linear Programming Problems

Proximal point algorithm is a type of method widely used in solving optimization problems and some practical problems such as machine learning in recent years. In this paper, a framework of accelerated proximal point algorithm is presented for convex minimization with linear constraints. The algorithm can be seen as an extension to G u ¨ ler’s methods for unconstrained optimization and linear programming problems. We prove that the sequence generated by the algorithm converges to a KKT solution of the original problem under appropriate conditions with the convergence rate of O 1 / k 2 .

scholarly journals Creating Better Collision-Free Trajectory for Robot Motion Planning by Linearly Constrained Quadratic Programming

2021 ◽  
Vol 15 ◽  
Author(s):  
Yizhou Liu ◽  
Fusheng Zha ◽  
Mantian Li ◽  
Wei Guo ◽  
Yunxin Jia ◽  
...  
Keyword(s):  
Quadratic Programming ◽  
Motion Planning ◽  
Trajectory Optimization ◽  
Optimization Technique ◽  
Optimization Methods ◽  
Linear Constraints ◽  
Task Constraints ◽  
Probabilistic Sampling ◽  
Smooth Path ◽  
Linearly Constrained

Many algorithms in probabilistic sampling-based motion planning have been proposed to create a path for a robot in an environment with obstacles. Due to the randomness of sampling, they can efficiently compute the collision-free paths made of segments lying in the configuration space with probabilistic completeness. However, this property also makes the trajectories have some unnecessary redundant or jerky motions, which need to be optimized. For most robotics applications, the trajectories should be short, smooth and keep away from obstacles. This paper proposes a new trajectory optimization technique which transforms a polygon collision-free path into a smooth path, and can deal with trajectories which contain various task constraints. The technique removes redundant motions by quadratic programming in the parameter space of trajectory, and converts collision avoidance conditions to linear constraints to ensure absolute safety of trajectories. Furthermore, the technique uses a projection operator to realize the optimization of trajectories which are subject to some hard kinematic constraints, like keeping a glass of water upright or coordinating operation with dual robots. The experimental results proved the feasibility and effectiveness of the proposed method, when it is compared with other trajectory optimization methods.

scholarly journals A General Self-Adaptive Relaxed-PPA Method for Convex Programming with Linear Constraints

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaoling Fu
Keyword(s):  
Convex Programming ◽  
State Of The Art ◽  
Adaptive Strategies ◽  
Linear Constraints ◽  
Proximal Point ◽  
Mild Conditions ◽  
Linearly Constrained Convex Programming ◽  
Linearly Constrained ◽  
Algorithmic Framework ◽  
Self Adaptive

We present an efficient method for solving linearly constrained convex programming. Our algorithmic framework employs an implementable proximal step by a slight relaxation to the subproblem of proximal point algorithm (PPA). In particular, the stepsize choice condition of our algorithm is weaker than some elegant PPA-type methods. This condition is flexible and effective. Self-adaptive strategies are proposed to improve the convergence in practice. We theoretically show under mild conditions that our method converges in a global sense. Finally, we discuss applications and perform numerical experiments which confirm the efficiency of the proposed method. Comparisons of our method with some state-of-the-art algorithms are also provided.

THE PROGRAM SYSTEM FOR SOLVING OPTIMAL CONTROL PROBLEMS WITH PHASE CONSTRAINTS

1993 ◽  
Vol 03 (04) ◽  
pp. 487-497 ◽  
Author(s):  
A.I. TYATUSHKIN ◽  
A.I. ZHOLUDEV ◽  
N.M. ERINCHEK
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Lagrange Function ◽  
Main Idea ◽  
Linear Constraints ◽  
Control Problems ◽  
Program System ◽  
Control Functions ◽  
Phase Constraints ◽  
Linearly Constrained

In this paper, we present a program system for solving optimal control problems with phase constraints. The main idea of the method realized in the program system consists in successive solving auxiliary problems, which minimizes a special constructed Lagrange function, subject to linearized phase constraints. The linearly constrained auxiliary problems are more simple than the original ones because linear constraints can be easily processed. We shall discuss different aspects connected with approximating control problems and using the program system for solving them. We shall then pay attention to optimal control problems with constraints on inertia of control functions. For illustrations, two control problems will be solved using the proposed software.

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