Optimal Control Procedure Research Articles

Dynamic Programming Approach to Pension Funding: the Case of Incomplete State Information

AbstractHaberman and Sung (1994) have presented a dynamic model for a defined benefit occupational pension scheme which considered two types of risk: the “contribution rate” and the “solvency” risk. The current paper, extends this work by deriving optimal funding control procedures for determining the contribution rate for the case of a stochastic model with incomplete state information, making use of the separation principle. The stochastic inputs modelled are the investment returns and the benefit outgo.

Graduating dental students' perceptions of oral cancer education: results of an exit survey of seven dental schools.

A 22-question exit survey was administered on a voluntary basis to senior dental students at seven dental schools in order to evaluate perceptions regarding their knowledge and skills in oral cancer control. The questions encompassed prevention, role of tobacco, lesion recognition, diagnostic techniques, and patient management. The range of responses was broad between students as well as schools regarding didactic and clinical exposures, and confidence in abilities to manage oral cancer patients. Data from this survey showed a perceived lack of knowledge and skills among graduating dental students that may translate to a subsequent deficiency in incorporating optimal oral cancer control procedures in their practices.

MODAL OPTIMAL CONTROL PROCEDURE FOR NEAR DEFECTIVE SYSTEMS

This study discusses a modal optimal control procedure for defective systems with repeated eigenvalues. From the view point of mathematics, although near defective close eigenvalues are distinct, the characteristic of the system is also defective. Therefore, we have to transform near defective systems into the defective one, and then modal optimal control procedure for the defective systems can be extended to deal with the corresponding problems for near defective systems with close eigenvalues. Because of the defective characteristic of the system, we have to use an invariant sub-space recursive method with numerical stability to calculate the generalized modes of the defective and near defective systems. The Potter's approach is extended to solve the Riccati equations in the generalized model subspace of the defective system. Because the order of the Jordan block matrix of the defective eigenvalues, m, is much smaller than that of the state matrix, n, i.e.,m ⪡n, the present modal optimal control procedure is very simple and reduces the computing effort for the complex system with large number of degrees of freedom. A numerical example is given to illustrate and verify the validity of the procedure.

Quantum optimal control of multiple targets: Development of a monotonically convergent algorithm and application to intramolecular vibrational energy redistribution control

An optimal control procedure is presented to design a field that transfers a molecule into an objective state that is specified by the expectation values of multiple target operators. This procedure explicitly includes constraints on the time behavior of specified operators during the control period. To calculate the optimal control field, we develop a new monotonically and quadratically convergent algorithm by introducing a quadruple space that consists of a direct product of the double (Liouville) space. In the absence of the time-dependent constraints, the algorithm represented in the quadruple-space notation reduces to that of the double-space notation. This simplified formulation is applied to a two dimensional system which models intramolecular vibrational energy redistribution (IVR) processes in polyatomic molecules. An optimal pulse is calculated that exploits IVR to transfer a specific amount of population to an optically inactive state, while the other portion of the population remains in the initial state at a control time. Using trajectory plots in quantum-number space, we numerically analyze how the control pathway changes depending on the amount of the excited population.

Optimal control of a batch bioreactor for the production of xanthan gum

The application of an optimal control procedure to reduce the fermentation time necessary to produce a desired amount of xanthan gum is presented. This procedure computes the temperature operating policy for the culture based on the fermentation initial conditions and the desired (target) product concentration at the final time. For that purpose, it uses biomass and product growth models proposed previously in the literature, which are dependent on the medium temperature. Computational experiments show that the optimal fermentation time to produce 15 g of gum per l is 16.3% shorter than the necessary time when the usual constant temperature of 28°C is used, and 12% shorter than the necessary time when the two-temperature strategy of other authors is used. The results also show considerable energy savings. Rules to determine a near optimum temperature profile without applying the optimization procedure are outlined and some results are presented. These rules are based on the outcome of the optimal control procedure and only require the knowledge of the initial cell and the desired final gum concentrations.

EFFECTS OF SMALL TRAVEL SPEED VARIATIONS ON ACTIVE VIBRATION CONTROL IN MODERN VEHICLES

A stochastic optimal control procedure, based on a perturbation criterion, is developed to study effects of small travel speed variations on active suspensions of vehicles. The vehicle speed is regarded as an uncertain parameter that randomly varies around a measured (equilibrium) mean value. The approach here separates the active suspension forces into two control (laws) forces. The first force is termed steady (unperturbed) control force that isolates a vehicle body from a roadway disturbance and functions in large (mean) nominal speed variations starting from low to very high. The second force is termed a perturbation control force that accommodates changes in the steady force due to small speed variations. Eventually, after justifying the perturbation approach, it is shown how these two control forces could be combined to function only in terms of measured signals. The investigation is made of two different suspension structures for two levels of roadway roughness. Although the approach to the problem is approximate and needs perfect knowledge of all the state variables, the results show that there are noticeable variations to the steady control laws for even small deviations from nominal travel speed. In fact, the control procedure developed here as a design tool is meaningful since optimum vibration control problems are not easy to formulate when non-stationary random vibrations are considered. Also, it can be generalized with care to handle some parametric uncertainty problems.

Controlling Nonlinear Dynamics in a Two-Well Impact System.

To exploit all potentialities of the optimal control procedure, the analysis initiated in Part I focuses on the system response under one-side control, an excitation which furnishes high gain though, roughly, controlling only one part of the phase space. Many bifurcational and control items related to the unsymmetric and pulsed nature of the excitation are deeply investigated. A nonclassical kind of homoclinic bifurcation is identified and it is discussed how it may lead to major regularity. The system response is very rich, and the main local and global phenomena of the dynamics are analyzed in detail through combined use of bifurcation diagrams and attractor-basin phase portraits. Both the confinement of steady dynamics in the controlled potential well and their successive transition from confined to scattered are studied, and it is discussed how they are obtained through comparison with the case of harmonic excitation. It is shown that the two investigated optimal excitations permit to increase the amplitude level for confined to scattered dynamics and to regularize the steady dynamics, although in a different manner. The analysis shows the effectiveness — in "average" sense — of the proposed method for controlling nonlinear dynamics.

Vancomycin-resistant Staphylococcus aureus: infection control considerations.

The lessons of the antibiotic era are crystal clear: in the footrace between humans and microbes, the organisms' genetic repertoire and efficient response to environmental changes will win the day. New antibiotics are essential, but their shelf life will be enhanced only if used wisely and sparingly. The antibiotic era is continually threatened by inappropriate decisions regarding use, inappropriate choices, and unnecessary durations of treatment. In concert with improved prescribing habits, efforts to identify and isolate resistant organisms introduced from outside institutions are essential. Last, continual energy is needed to influence the behavior of health care professionals and to maintain optimal infection control policies and procedures. We remain optimistic about the ability of infectious diseases physicians to respond appropriately to continued microbial challenges with research, education, and wise practice.

An Approach to Determining Worst Case Platoon Behavior

SUMMARY This paper presents a method with which one can evaluate alternative platooning control strategies with respect to worst case behavior. The motivation is to provide platoon control designers with an objective means of evaluating robustness in the face of system uncertainties. The approach can be viewed as an extension of optimal control procedures and is applicable to complex, nonlinear systems. An arbitrary number of uncertain parameters, unmodeled components and inputs are allowed. The end result is a lower bound for the worst case platoon performance.

Control applications of the TRYM model

This paper outlines a control framework being developed for the TRYM model. The current procedure minimises a quadratic social loss function that targets non-steady-state settings for unemployment and inflation. The iterative technique is described in detail, and illustrated using the example of a temporary terms of trade shock. The effects of the shock on the model are compared for two separate policy regimes, one using the default TRYM policy reactions, and the other from the optimal control procedure. The limitations of using control techniques as an aid to the policy-formation process, and the benefits to be derived from implementing optimal control on a model like TRYM, are briefly discussed.

A nested, simultaneous approach for dynamic optimization problems—II: the outer problem

In a previous paper (Tanartkit, P. and Biegler, L. T. (1996) A nested, simultaneous approach for dynamic optimization problems - I. Comput. Chem. Eng. 20(6/7), 735–741), we introduced and demonstrated a general framework for solving dynamic optimization using bilevel programming. This framework decouples the element placement from the optimal control procedure and leads to a more robust algorithm. The optimization problem is replaced by two connected but simpler formulations, the inner and outer problems. The inner problem is essentially a dynamic optimization with fixed time steps. On the other hand, the outer problem adjusts the time step given the gradient information from the inner counterpart. By coupling a well-implemented collocation solver with reduced Hessian successive quadratic programming (SQP), we are able to tackle the inner part of the system in an efficient and stable fashion for both initial value and boundary value problems. However, the overall success of the algorithm still depends on robustness and performance of the outer problem. In this article this is achieved by combining a bundle underestimator with SQP. Also included in this article are different options of obtaining subgradients for the outer problem via sensitivity analysis and finite difference schemes. Here a decomposition is presented by taking advantage of the inner problem structure to reduce computational expense of the sensitivity evaluation. We will also address the limitations and properties involved in both schemes. In the final segment of the paper the focus is shifted to the issue of finite element addition. By utilizing insight from optimal control theory, we develop a systematic procedure for element addition with a rigorous stopping criterion. Finally, examples are given to illustrate the effectiveness and potential of the algorithm.

Uniqueness of the optimal control for a Lokta-Volterra control problem with a large crowding effect

Uniqueness of the optimal control is obtained by assuming certain conditions on the crowding effect of the species. Moreover, an approximation procedure for the unique optimal control is developed.

UNIK-OPT/NN Neural network based adaptive optimal controller on optimization models

When the future information for an optimization model is not complete, the model tends to incorporate such uncertainties as some assumptions on the coefficients. As time passes and more precise information is accumulated, the initial optimal solution may no longer be optimal, or even feasible. At this point, model builders want to modify the assumed and controllable coefficients to obtain the desired values of designated decision variables. To aid this process, a neural network could effectively be applied. So we develop a tool UNIK-OPT/NN which can support the construction and recall of the neural network model on top of the knowledge assisted optimization model formulator UNIK-OPT and the semantic neural network building aid UNIK-NEURO. By adopting a commonly interpretable semantic representation of optimization and neural network models, UNIK-OPT/NN can effectively automate most of the neural network construction and recall procedure for optimal control.

Control Applications of the TRYM Model

This paper outlines a control framework being developed for the TRYM model. The current procedure minimises a quadratic social loss function that targets non-steady state settings for unemployment and inflation. The iterative technique is described in detail and illustrated using the example of a temporary terms of trade shock. The effects of the shock on the model are compared for two seperate policy regimes, one using the default TRYM policy reactions and the other from the optimal control procedure. The limitations of using control techniques as an aid to the policy formation process and the benefits to be derived from implementing optimal control on a model like TRYM are breifly discussed.

Application of Markov decision processes to search problems

Many decision problems contain, in some form, a NP-hard combinatorial problem. Therefore decision support systems have to solve such combinatorial problems in a reasonable time. Many combinatorial problems can be solved by a search method. The search methods used in decision support systems have to be robust in the sense that they can handle a large variety of (user defined) constraints and that they allow user interaction, i.e. they allow a decision maker to control the search process manually. In this paper we show how Markov decision processes can be used to guide a random search process. We first formulate search problems as a special class of Markov decision processes such that the search space of a search problem is the state space of the Markov decision process. In general it is not possible to compute an optimal control procedure for these Markov decision processes in a reasonable time. We therefore, define several simplifications of the original problem that have much smaller state spaces. For these simplifications, decompositions and abstractions, we find optimal strategies and use the exact solutions of these simplified problems to guide a randomized search process. The search process selects states for further search at random with probabilities based on the optimal strategies of the simplified problems. This randomization is a substitute for explicit backtracking and avoids problems with local extrema. These randomized search procedures are repeated as long as we have time to solve the problem. The best solution of those generated during that time is accepted. We illustrate the approach with two examples: the N-puzzle and a job shop scheduling problem.

Active control of a circular plate to reduce transient noise transmission

Abstract An active control approach that reduces transient noise transmission through a plate in a circular duct is presented. Two circular pieces of piezoceramic material are used as actuators to induce a moment in the plate. A model for this configuration is developed and then used in an H 2 optimal control procedure to design a dynamic feedforward/feedback controller. In the experiment the forward travelling wave is estimated from the measurements of two microphones. This information is used as the feedforward signal, while the velocity of the center of the plate is measured with a laser vibrometer and used as the feedback signal. The discretized controller is implemented on a digital signal processor (DSP). A transient pressure pulse is used to excite the plate, and reductions of up to 15 dB are observed at a microphone placed downstream of the plate when the controller is active.

Stable Decomposition for Dynamic Optimization

Dynamic optimization problems are usually solved by transforming them to nonlinear programming (NLP) problems with either sequential or simultaneous approaches. However, both approaches can still be inefficient to tackle complex problems. In addition, many problems in chemical engineering have unstable components which lead to unstable intermediate profiles during the solution procedure. If the numerical algorithm chosen utilizes an initial value formulation, the error from decomposition or integration can accumulate and the Newton iterations then fail as a result of ill-conditioned constraint matrix. On the other hand, by using suitable decomposition, through multiple shooting or simultaneous collocation, the author's algorithm has favorable numerical characteristics for both stable and unstable problems; by exploiting the structure of the resulting system, a stable and efficient decomposition algorithm results. In the paper, the new algorithm for solving dynamic optimization is developed. This algorithm is based on the nonlinear programming (NLP) formulation coupled with a stable decomposition of the collocation equations. Solution of this NLP formulation is considered through a reduced Hessian successive quadratic programming (SQP) approach. The routine chosen for the decomposition of the system equations is COLDAE, in which the stable collocation scheme is implemented. To address the mesh selection, we will introduce a new bilevel framework that will decouple the element placement from the optimal control procedure. We also provide a proof for the connection of the algorithm and the calculus of variations

Successive approximation procedure for steady-state optimal control of bilinear systems

Successive approximation procedure for steady-state optimal control of bilinear systems

Successive approximation procedure for steady-state optimal control of bilinear systems

The optimum regulation problem of a bilinear system with a quadratic performance criterion is obtained in terms of a sequence of algebraic Lyapunov equations. The results are based on the method of successive approximations. The proof of convergence of the proposed scheme is given and the design procedure is illustrated by two examples.

Dynamic approaches to pension funding

The paper presents a dynamic model of pension funding for a defined benefit occupational pension scheme. Two types of risk are introduced concerned respectively with the stability and security of funding: the ‘ contribution rate’ risk and the ‘ solvency’ risk. An objective function is introduced to allow the simultaneous minimization of these two risks. The paper derives optimal funding control procedures for the contribution rate subject to specified constraints.