Nonlinear programming

About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.

Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator

Abstract: Highlights? Multiobjective optimization finds a set of solutions called non-dominated solutions. ? The NSGA-II approach is evaluated. ? This algorithm is tested in PID tuning using a robotic manipulator of two-degree-of-freedom. Most controllers optimization and design problems are multiobjective in nature, since they normally have several (possibly conflicting) objectives that must be satisfied at the same time. Instead of aiming at finding a single solution, the multiobjective optimization methods try to produce a set of good trade-off solutions from which the decision maker may select one. Several methods have been devised for solving multiobjective optimization problems in control systems field. Traditionally, classical optimization algorithms based on nonlinear programming or optimal control theories are applied to obtain the solution of such problems. The presence of multiple objectives in a problem usually gives rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Recently, Multiobjective Evolutionary Algorithms (MOEAs) have been applied to control systems problems. Compared with mathematical programming, MOEAs are very suitable to solve multiobjective optimization problems, because they deal simultaneously with a set of solutions and find a number of Pareto optimal solutions in a single run of algorithm. Starting from a set of initial solutions, MOEAs use iteratively improving optimization techniques to find the optimal solutions. In every iterative progress, MOEAs favor population-based Pareto dominance as a measure of fitness. In the MOEAs context, the Non-dominated Sorting Genetic Algorithm (NSGA-II) has been successfully applied to solving many multiobjective problems. This paper presents the design and the tuning of two PID (Proportional-Integral-Derivative) controllers through the NSGA-II approach. Simulation numerical results of multivariable PID control and convergence of the NSGA-II is presented and discussed with application in a robotic manipulator of two-degree-of-freedom. The proposed optimization method based on NSGA-II offers an effective way to implement simple but robust solutions providing a good reference tracking performance in closed loop.

Mathematical programming and control theory

Abstract: 1 Optimization problems introduction.- 1.1 Introduction.- 1.2 Transportation network.- 1.3 Production allocation model.- 1.4 Decentralized resource allocation.- 1.5 An inventory model.- 1.6 Control of a rocket.- 1.7 Mathematical formulation.- 1.8 Symbols and conventions.- 1.9 Differentiability.- 1.10 Abstract version of an optimal control problem.- References.- 2 Mathematical techniques.- 2.1 Convex geometry.- 2.2 Convex cones and separation theorems.- 2.3 Critical points.- 2.4 Convex functions.- 2.5 Alternative theorems.- 2.6 Local solvability and linearization.- References.- 3 Linear systems.- 3.1 Linear systems.- 3.2 Lagrangean and duality theory.- 3.3 The simplex method.- 3.4 Some extensions of the simplex method.- References.- 4 Lagrangean theory.- 4.1 Lagrangean theory and duality.- 4.2 Convex nondifferentiable problems.- 4.3 Some applications of convex duality theory.- 4.4 Differentiable problems.- 4.5 Sufficient Lagrangean conditions.- 4.6 Some applications of differentiable Lagrangean theory.- 4.7 Duality for differentiable problems.- 4.8 Converse duality.- References.- 5 Pontryagin theory.- 5.1 Introduction.- 5.2 Abstract Hamiltonian theory.- 5.3 Pointwise theorems.- 5.4 Problems with variable endpoint.- References.- 6 Fractional and complex programming.- 6.1 Fractional programming.- 6.2 Linear fractional programming.- 6.3 Nonlinear fractional programming.- 6.4 Algorithms for fractional programming.- 6.5 Optimization in complex spaces.- 6.6 Symmetric duality.- References.- 7 Some algorithms for nonlinear optimization.- 7.1 Introduction.- 7.2 Unconstrained minimization.- 7.3 Sequential unconstrained minimization.- 7.4 Feasible direction and projection methods.- 7.5 Lagrangean methods.- 7.6 Quadratic programming by Beale's method.- 7.7 Decomposition.- References.- Appendices.- A.1 Local solvability.- A.2 On separation and Farkas theorems.- A.3 A zero as a differentiable function.- A.4 Lagrangean conditions when the cone has empty interior.- A.5 On measurable functions.- A.6 Lagrangean theory with weaker derivatives.- A.7 On convex functions.

MINLPLib--A Collection of Test Models for Mixed-Integer Nonlinear Programming

Abstract: The paper describes a new computerized collection of test models for mixed-integer nonlinear programming. Because there is no standard format for nonlinear models, the model collection is augmented with a translation server that can transform the models from their basic GAMS format into other formats, including AMPL, BARON, LGO, LINGO, and MINOPT. The translation server can also be used to transform industrial models that contain confidential information. Such transformations allow many of these models to be distributed to the research community as highly relevant algorithmic test models.

Distributed Optimization for a Class of Nonlinear Multiagent Systems With Disturbance Rejection

Abstract: The paper studies the distributed optimization problem for a class of nonlinear multiagent systems in the presence of external disturbances. To solve the problem, we need to achieve the optimal multiagent consensus based on local cost function information and neighboring information and meanwhile to reject local disturbance signals modeled by an exogenous system. With convex analysis and the internal model approach, we propose a distributed optimization controller for heterogeneous and nonlinear agents in the form of continuous-time minimum-phase systems with unity relative degree. We prove that the proposed design can solve the exact optimization problem with rejecting disturbances.