Dynamic Optimization

We propose a new hierarchical approach to resolution scalable lossless and near-lossless (NLS) compression. It combines the adaptability of DPCM schemes with new hierarchical oriented predictors to provide resolution scalability with better compression performances than the usual hierarchical interpolation predictor or the wavelet transform. Because the proposed hierarchical oriented prediction (HOP) is not really efficient on smooth images, we also

An energy management strategy–torque distribution and charge sustaining control–for a parallel hybrid electric vehicle with continuously variable transmission is proposed in this study. The torque distribution control problem is formulated as a multi-objective nonlinear optimization problem. In order to facilitate the implementation of the proposed approach in real time, the aforementioned multi-objective nonlinear optimization problem is recast as a single objective linear optimization problem by linearization of the objective functions and ...

This is 'chapter 2' of the Lecture notes from my module on computational methods for Economists.

In this chapter we look at dynamic / intertemporal optimisation problems. This chapter focusses on (1) unconstrained optimization, (2) with and without future-discounting and (3) the conceptual differences between treating the resulting first-order conditions as boundary-value or initial-value problems.

The issues of stability, whether the extremization leads  to proper minima or maxima and how to handle constraints are left for the next week/chapter.

The approach to dynamic optimisation is the standard Euler-Lagrange variational calculus in continuous time. This week's notes do not go into 'Hamiltonian' type formalisms, discrete-time optimization or 'optimal control theory'.

The Modelica language, targeted at modeling of complex physical systems, has gained increased attention during the last decade. Modelica is about to establish itself as a de facto standard in the modeling community with strong support both within academia and industry. While there are several tools, both commercial and free, supporting simulation of Modelica models few efforts have been made

In this chapter we present a mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degree between the complementary slackness variables. The proposed model incorporates the state jumps via high-order distributions through the extension of Moreau’s sweeping process, which is a special type of differential inclusion. The time-discretization of these nonsmooth systems, which is non-trivial, is also presented. Applications of such high-order sweeping processes can be found in dynamic optimization under state constraints and electrical circuits with ideal diodes, where it may be helpful for a better understanding of the closed-loop dynamics induced by some feedback laws.

Numerical methods and software packages for solving dynamic optimization or optimal control problems require a suitable initial estimation of the solution. This paper focuses on problems that arise in chemical processes described by complex dynamics. We present a very simple method, based on Pontryagin’s Minimum Principle, to obtain an initial guess for the solution. Our method presents numerous advantages: it is very easy to programme, it allows a wide range of problems to be addressed, the computation time is very short, the initial guess is very close to the solution and is attracted to a global minimum.

In this chapter we present a mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degree between the complementary slackness variables. The proposed model incorporates the state jumps via high-order distributions through the extension of Moreau’s sweeping process, which is a special type of differential inclusion. The time-discretization of these nonsmooth systems, which is non-trivial, is also presented. Applications of such high-order sweeping processes can be found in dynamic optimization under state constraints and electrical circuits with ideal diodes, where it may be helpful for a better understanding of the closed-loop dynamics induced by some feedback laws.

Optimization is becoming a standard methodology in many engineering disciplines to im- prove products and processes. The need for optimization is driven by factors such as increased costs for raw materials and stricter environmental regulations as well as a general need to meet increased com- petition. As model-based design processes are being used increasingly in industry, the prerequisites for optimization

A strategy for adaptive control and energetic optimization of aerobic fermentors was implemented, with both air flow and agitation speed as manipulated variables. This strategy is separable in its components: control, optimization, estimation. We optimized parameter’s estimation (from the usual KLa correlation) using sinusoidal excitation of air flow and agitation speed. We have implemented parameter’s estimation trough recursive least squares algorithm with forgetting factor. We carried separate essays on control, optimization and estimation algorithms. We carried our essays using an original computational simulation environment, with noise and delay generating facilities for data sampling and filtering.

Our results show the convergence and robustness of the estimation algorithm used, improved with use of both forgetting factor and KLa dead-band facilities. Control algorithm used in our work compares favorably with PID using the integrated area criteria for deviation between oxygen molarity and critical molarity (set point). Optimization algorithm clearly reduces energetic consumption, respecting critical molarity. Integration of control, optimization and adaptive algorithms was implemented, but future work is needed for stability. Methods were defined and implemented for stability improvement. We have implemented data acquisition and computer manipulation of air flow and agitation speed for actual fermentors.

This work performs the dynamic optimization of semibatch vinyl acetate (VAc)/acrylic acid (AA) suspension copolymerizations. The proposed dynamic optimization strategy is based on a direct search Complex algorithm and is used to control the copolymer composition along the batch. First, a sequential optimization procedure is used to determine the optimum AA concentration and feed rate profiles, required to provide the specified copolymer composition. In the second step, a sequential optimization procedure is coupled with a predictive controller to guarantee that the manipulation of feed flow rates can allow for attainment of the desired copolymer compositions. The optimization strategy is validated through simulation, by assuming that reactions are subject to perturbations of the reaction temperature, initiator, and VAc concentrations. It is shown that the proposed optimization strategy can be used successfully both for design of monomer feed rate profiles and removal of process disturbances during semibatch suspension copolymerizations, to keep the copolymer composition constant throughout the batch. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

The SSPCO (See-See Particle Chicks Optimization) is a type of swarm intelligence algorithm derived from the behavior of See-See Partridge. Although efficiency of this algorithm has been proven for solving static optimization problems, it has not yet been tested to solve dynamic optimization problems. Due to the nature of NP-Hard dynamic problems, this algorithm alone is not able to solve such optimization problems. Therefore, to enable the algorithm to optimally track the variable in these problems, it is necessary to be provided solutions with this algorithm so that can increase the performance of this algorithm for dynamic environments. In this paper, two solutions for combining SSPCO are presented: (1) the multi-swarm method and (2) memory with Gaussian density estimation. The problem with most multi-swarm methods is that as the population increases uncontrollably, the speed and efficiency of the algorithm gradually decreases. The multi-swarm methods presented in this paper is adapted to the problem space, and whenever there is a need to increase the population, a population is created adaptively, and this reduces the problems of previous methods. One of the issues that is being addressed to solve uncertainty problems is prediction of near future using data of the near past. In this article, to preserve past data a new memory called Gaussian density estimation memory is used. This memory fixes standard memory defects and improves the performance of the proposed algorithm. To evaluate the efficiency of the proposed method, the well-known moving peak benchmark function, which simulates behavior of dynamic problems, is used. The proposed algorithm is compared with the 10 most popular dynamic optimization algorithms. According to the experimental results, the proposed method reduces offline error to a great extent compared to other methods and the error produced by the proposed method is very small.

In an effort to relieve peak hour congestion on freeways, various ramp metering algorithms have been employed to regulate the inputs to freeways from entry ramps. In this paper, we consider a freeway system comprised of a freeway section and its entry/exit ramps, and formulate the ramp control problem as a dynamic optimal process to minimize the total time spent in this system. Within this framework, we are able to show when ramp metering is beneficial to the system in terms of total time savings, and when it is not, under the restriction that the controlled freeway has to serve all of its ramp demand, and the traffic flow process follows the rules prescribed by the LWR theory with a triangular flow-density relationship. We also provide solution techniques to the problem and present some preliminary numerical results and empirical validation.

In this paper we investigate a Self-Adaptive Differential Evolution algorithm (jDE) where F and CR control parameters are self-adapted and a multi-population method with aging mechanism is used. The performance of the jDE algorithm is evaluated on the set of benchmark functions provided for the CEC 2009 special session on evolutionary computation in dynamic and uncertain environments.

This paper assesses the value of correlation dynamics in mean-variance asset allocation. A correlation-timing framework is deployed with state of the art models competing against industry correlation-updating rivals and static allocation strategies. We address the extent to which the superior statistical properties of multivariate conditional correlation models translate into enhanced investment performance. The success of the conditional correlation models is