Selecting appropriate weighting matrices for desired Linear Quadratic Regulator (LQR) controller design using evolutionary algorithms is presented in this paper. Obviously, it is not easy to determine the appropriate weighting matrices for an optimal control system and a suitable systematic method is not presented for this goal. In other words, there isn’t direct relationship between weighting matrices and control system characteristics and selecting these matrices is done using by trial and error based on designer’s experience. In this paper we use the Particle Swarm Optimization (PSO) method which is inspired by the social behavior of fish and birds in finding food sources to determine these matrices. Stable convergence characteristics and high calculation speed are advantages of the proposed method. Simulation results demonstrate that in comparison with Genetic Algorithms (GAs), the PSO method is very efficient and robust in designing of optimal LQR controller.
Introduction
In designing of many systems and solving the problems, we need to choose an answer between some possible answers as an optimal response. But because of the wide range of answers, all of them cannot be tested and then this test should be performed stochastically. On the other hand, this stochastic procedure should lead to the best answer [1].
Because of its simple implementation in engineering problems, it has been paid special attention on linear quadratic optimal control theory. Linear quadratic optimal control is significant for modern control theory and it can be implemented easily for engineering applications and it is the basic theory of other control techniques. However, in a special case which the cost function is a linear quadratic function, the o...
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A complex adaptive system is entity of networks and connections. It can “learn and adapt to change over time” which can change the “structure of the system” (Clancy, Effken, Pesut, 2008). It contains twelve elements: autopoesis or self-regenerization, open exchange, participation in networks, fractals, phase transition between order and chaos, search for fitness peaks, nonlinear dynamics, sensitive dependence, attractors that limit growth, strange attractors of emergence...
Abstract — Partially Observable Markov Decision Processes (POMDP) has been widely applied in fields including robot navigation, machine maintenance, marketing, Medical Diagnosis, and so on [1]. But its exact solution is inefficient in both space and time. This paper investigates Smooth Partially Observable Value Approximation (SPOVA) [2], which approximates belief values by a differentiable function and then use gradient descent to update belief values. This POMDP approximation algorithm is applied on pole-balancing problem with regulation. Simulation results turn out this regulated approach is capable of estimating state transition probabilities and improving its policy simultaneously.
Abstract—Most Independent System Operators (ISOs) adopt the Bid Cost Minimization (BCM) to select offers and their respective generation levels while minimizing the total bid cost. It was shown that the customer payment costs that result from selected offers can differ significantly from the customer payments resulting from the Payment Cost Minimization (PCM), under which payment costs are minimized directly. In order to solve the PCM in the dual space, the Lagrangian relaxation and surrogate optimization approach is frequently used. When standard optimization methods, such as branch-and-cut, become ineffective due to the large size of a problem, the Lagrangian relaxation and surrogate optimization approach provides a good feasible solution within a reasonable CPU time. The convergence of the standard Lagrangian relaxation and surrogate subgradient approach depends on the optimal dual value, which is usually unknown. Furthermore, when using the surrogate subgradient approach, the upper bound property is lost, so additional conditions are needed to ensure convergence. The main goal of this paper is to develop a convergent variation of the surrogate subgradient method without invoking the optimal dual value, and show the relevance and effectiveness of the new method for solving large constrained optimization problems, such as the PCM.
Synthesis problem: given a set of controllers with actuator limits and certain noise level, find one that maximize the operability enhancement.
Genetic Algorithms provide a holistic search process based on principles of natural genetics and survivals of the fittest……
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During the World War II, the main issue of extreme importance was to maximize the efficiency of resources. The projects related to World War II required attention and obviously spread resources thin. Therefore, linear programming was developed to address this issue. Programming was used in military at that time to deal with activities such as planning schedules efficiently or optimizing the deploying of men. In 1947, George Dantzig, a U.S. Air Force member at that time, developed the Simplex optimization method. The aim was to provide an efficient algorithm for solving programming problems that had linear structures. Since then, the theory behind linear programming and its applications have been extensively developed by experts from a variety of fields, particularly mathematics and economics [49].
Different objective functions generate different solutions even form the same evolutionary algorithm. Presuming also that the fitness could either be a minimization or a maximization function. Moreover, the algorithm could be formulated with one or with multi objective functions. To sum up, "choosing optimizati...
The mixed-integer nonlinear programming (MINLP) models can use some variables that can be integer, discrete, zero-one (binary) and continuous. In this study, we make mention of all the variables for the appropriate rotatable central composite design (CCD) using the MINLP model that is why classifying the variables are important to this research paper.
This paper focus on the study related to analysis and design of a control system for the
Un modelo de Optimización Matemática consiste en una función objetivo y un conjunto de restricciones en la forma de un sistema de ecuaciones o inecuaciones. Los modelos de optimización son usados en casi todas las áreas de toma de decisiones, como en ingeniería de diseño y selección de carteras financieras de inversión.
The fuzzy is basic set of rules which is based on system error and change in error which expert advice into automatic control condition for self adaptive controller. Fuzzy represents a sequence of control mechanism to adjust the effect of certain system stimulations. It reflects the expert conditions in to appropriate control design.
LINGO is a simples and powerful software that can be used to solve MIP optimization problems. This software can handle tens of thousands of variables and constraints with up to few thousand integer variables (Schrage, 2006). Wong et al. (2010) and Easa and Hossain (2008) used this software to solve MIP problems to find the global optimal solution.