Open-loop Feedback Control Research Articles

Stochastic Control of Linear and Nonlinear Econometric Models: Some Computational Aspects

This paper considers the optimal control of small econometric models applying the OPTCON algorithm. OPTCON determines approximate numerical solutions to optimum control problems for nonlinear stochastic systems. These optimum control problems consist in minimizing a quadratic objective function for linear and nonlinear econometric models with additive and multiplicative (parameter) uncertainties. The algorithm was programmed in C# and in MATLAB and allows for stochastic control with open-loop and passive learning (open-loop feedback) information patterns. Here we compare the results of applying the OPTCON2 version of the algorithm to two macroeconomic models for Slovenia, the nonlinear model SLOVNL and the linear model SLOVL. The results for both models are similar, with open-loop feedback controls giving better results on average and less outliers than open-loop controls. The number of outliers is higher in the nonlinear case and especially under high parameter uncertainty.

Dynamic Portfolio Execution and Information Relaxations

We consider a portfolio execution problem where a possibly risk-averse agent needs to trade a fixed number of shares in multiple stocks over a short time horizon. Our price dynamics can capture linear but stochastic temporary and permanent price impacts as well as stochastic volatility. In general it is not possible to solve even numerically for the optimal policy in this model, however, and so we must instead search for good suboptimal policies. Our principal policy is a variant of an open-loop feedback control (OLFC) policy, and we show how the corresponding OLFC value function may be used to construct good primal and dual bounds on the optimal value function. The dual bound is constructed using the recently developed duality methods based on information relaxations. One of the contributions of this paper is the identification of sufficient conditions to guarantee convexity, and hence tractability, of the associated dual problem instances. That said, we do not claim that the only plausible models are th...

Optimal Structural Control under Stochastic Uncertainty: Robust Optimal Open-Loop Feedback Control

AbstractOptimal feedback controls of PD- or PID-type can be approximated very efficiently by optimal open-loop feedback controls based on optimal open-loop controls. Extending the standard construction, stochastic optimal open-loop feedback controls are constructed by taking into account still the random parameter variations in the control system. Hence, corresponding to the standard deterministic case, stochastic optimal open-loop feedback controls are obtained by computing first stochastic optimal open-loop controls on the remaining time intervals tb ≤ t ≤ tf with an arbitrary intermediate starting time point tb, t0 ≤ tb ≤ tf. Evaluating these controls at the corresponding intermediate starting time points tb only, a stochastic optimal open-loop feedback control law is obtained. Stochastic optimal open-loop controls are determined by using a stochastic Hamiltonian approach. Hence, after introducing the stochastic Hamiltonian of the control problem under stochastic uncertainty, the H-minimal controls are determined and the related two-point boundary value problem with random parameters is solved. In order to apply the solution technique in real-time for two-point boundary value problems developed in former papers, also to problems with a non constant system matrices, the occurring fundamental matrix is computed approximatively by appropriate approximations of the system matrix, as e.g. by i) constant system matrices, ii) piecewise constant system matrices, and iii) by discretization of the probability distribution in case of a random system matrix. Error estimates are given.

Optimal Pulse Strategies for Relative Orbit Transfer Along a Circular Orbit

This paper is concernedwith a fuel-optimal relative orbit transfer problem forHill–Clohessy–Wiltshire equations. The input is of the pulse type and the performance index is the total velocity change required for a transfer. For the in-plane motion, the existence of optimal three-pulse strategies is shown and the minimum total velocity change is explicitly given under the condition that the difference of orbit size is relatively larger than that of drift velocity. For the out-of-plane motion, the existence of optimal single-pulse strategies is shown. The orbit transfer problem covers formation reconfiguration problem as a special case. Midpoints of the optimal pulses coincide with those points at which the velocity along the radial direction is zero. Using this information and null controllability with vanishing energy of the Hill–Clohessy–Wiltshire equations, suboptimal feedback controllers are designed. Simulation results with optimal open-loop strategies and feedback controls are given for two formation reconfiguration problems.

On the Response of Different Particle State Sensors to Deliberate Process Variations

Deliberate particle state variations were performed using atmospheric plasma spray (APS) and high-velocity oxy-fuel flame spraying (HVOF) to create a set of first-order process maps. Particle states were measured simultaneously using five in-flight particle sensors: DPV-2000, Accuraspray, SprayWatch, TDS, and SprayCam. While the sensors use similar methods for calculating particle characteristics, absolute values of temperature and velocity were considerably different. Process map trends among sensors are in agreement for the HVOF process, but differ when using plasma spray at high total gas flow conditions. After understanding the stochastic nature of particle detection, an open loop feedback control algorithm was implemented to achieve similar particle states with different hydrogen gas flow rates. The resulting particle state window measured by three different sensors under select fixed hydrogen flow rates was significantly narrowed.

General unifying features of controlled quantum phenomena

Many proposals have been put forth for controlling quantum phenomena, including open-loop, adaptive feedback, and real-time feedback control. Each of these approaches has been viewed as operationally, and even physically, distinct from the others. This work shows that all such scenarios inherently share the same fundamental control features residing in the topology of the landscape relating the target physical observable to the applied controls. This unified foundation may provide a basis for development of hybrid control schemes that would combine the advantages of the existing approaches to achieve the best overall performance.

Stochastic programming for off-line adaptive radiotherapy

In intensity-modulated radiotherapy (IMRT), a treatment is designed to deliver high radiation doses to tumors, while avoiding the healthy tissue. Optimization-based treatment planning often produces sharp dose gradients between tumors and healthy tissue. Random shifts during treatment can cause significant differences between the dose in the “optimized” plan and the actual dose delivered to a patient. An IMRT treatment plan is delivered as a series of small daily dosages, or fractions, over a period of time (typically 35 days). It has recently become technically possible to measure variations in patient setup and the delivered doses after each fraction. We develop an optimization framework, which exploits the dynamic nature of radiotherapy and information gathering by adapting the treatment plan in response to temporal variations measured during the treatment course of a individual patient. The resulting (suboptimal) control policies, which re-optimize before each fraction, include two approximate dynamic programming schemes: certainty equivalent control (CEC) and open-loop feedback control (OLFC). Computational experiments show that resulting individualized adaptive radiotherapy plans promise to provide a considerable improvement compared to non-adaptive treatment plans, while remaining computationally feasible to implement.

Is measurement-based feedback still better for quantum control systems?

In this paper, we put forward a fundamental question concerning feedback control of quantum systems: Is measurement-based feedback control still better than open-loop control? In contrast to the classical control theory, the answer is far from obvious. This is because measurement-based feedback needs measurement to reduce the system uncertainty, whereas the measurement on a quantum system will inevitably increase the system uncertainty in turn. In fact, there is a complicated tradeoff between the uncertainty introduced and the information gained by the measurement on a quantum system. To investigate this fundamental problem, we will only focus on a typical model of coherent control mode with and without the decoherence term in the paper. By establishing some fundamental limits on the performances of both the open-loop and measurement-based feedback controls, we will demonstrate via simulation that the measurement-based feedback control of quantum systems is still superior to the open-loop control in some sense for the typical model under consideration.

Predictive Control Approach for Long-Term Hydropower Scheduling Using Annual Inflow Forecasting Model

Abstract This paper proposes an annual inflow forecasting model in an open-loop feedback control operational policy for long-term hydropower scheduling. A deterministic optimization model precisely represents hydropower generation by taking into consideration water head as a nonlinear function of storage, discharge and spillage. The inflow is made available by a forecasting model based on a fuzzy inference system that captures the nonlinear correlation of consecutive inflows on an annual basis, with disaggregation of the results on a monthly basis. The performance of the proposed approach is evaluated by simulation for a multi-reservoir system, based on historical inflow records and compared to the same approach on monthly basis. The results show that the proposed approach leads to an operational performance closer to that of the perfect foresight solution, providing lower spillages and higher average hydropower efficiency and generation.

Achieving Precision and Reproducibility for Writing Patterns of n‐alkanethiol Self‐assembled Monolayers with Automated Nanografting

Nanografting is a high-precision approach for scanning probe lithography, which provides unique advantages and capabilities for rapidly writing arrays of nanopatterns of thiol self-assembled monolayers (SAMs). Nanografting is accomplished by force- induced displacement of molecules of a matrix SAM, followed immediately by the self-assembly of n-alkanethiol ink molecules from solution. The feedback loop used to control the atomic force microscope tip position and displacement enables exquisite control of forces applied to the surface, ranging from pico to nanonewtons. To achieve high-resolution writing at the nanoscale, the writing speed, direction, and applied force need to be optimized. There are strategies for programing the tip translation, which will improve the uniformity, alignment, and geometries of nanopatterns written using open-loop feedback control. This article addresses the mechanics of automated nanografting and demonstrates results for various writing strategies when nanografting patterns of n-alkanethiol SAMs.

Geração de planos de produção via otimização seqüencial subótima

Neste artigo são discutidos aspectos relacionados à tomada de decisão dentro de um processo hierárquico de planejamento da produção. Neste contexto, foi desenvolvido um modelo agregado para um problema de planejamento estocástico, com restrições de chances nas variáveis de decisão, que serve como meta de produção a ser atingida nos níveis inferiores da hierarquia. Solução ótima global para este tipo de problema seqüencial é muito difícil, a menos em casos de pequena dimensão via algoritmo de programação dinâmica estocástica. Assim, como alternativa, investigou-se a utilização de uma heurística subótima denominada open-loop feedback controller (OLFC), que é muito simples de ser implementada computacionalmente. Como exemplo de aplicação, um problema mono-produto de planejamento agregado da produção foi formulado e a política subótima OLFC foi comparada à solução ótima usando o algoritmo de programação dinâmica estocástica. Além dos aspectos numéricos, algumas propriedades são analisadas, como a quase adaptabilidade do procedimento OLFC.

Adaptive Optimization and Systematic Probing of Infrastructure System Maintenance Policies under Model Uncertainty

We present an application of systematic probing for selecting optimal maintenance, repair, and reconstruction (MR&R) policies for systems of infrastructure facilities under model uncertainty. We use an open-loop feedback control approach, where the model parameters are updated sequentially after every inspection round. The use of systematic probing improves the convergence of the model parameters by ensuring that all permissible actions are applied to every condition state. The results of the parametric analyses demonstrate that the MR&R policies converge earlier when systematic probing is used. However, the savings in the expected total costs as a result of probing are minor, and are only realized when the optimal probing fractions are used. On the other hand, the additional costs incurred when the wrong probing fractions are used are significant. The major conclusion from this work is that state-of-the-art adaptive infrastructure management systems, that do not use probing, provide sufficiently close to optimal policies.

Effects of Open-Loop Feedback on Physical Activity and Television Viewing in Overweight and Obese Children: A Randomized, Controlled Trial

Television viewing and physical inactivity increase the risk of obesity in youth. Thus, identifying new interventions that increase physical activity and reduce television viewing would be helpful in the prevention and treatment of pediatric obesity. This study evaluated the effects of open-loop feedback plus reinforcement versus open-loop feedback alone on physical activity, targeted sedentary behavior, body composition, and energy intake in youth. Thirty overweight or obese 8- to 12-year-old children were randomly assigned to an intervention (n = 14) or control group (n = 16). Participants wore accelerometers every day for 8 weeks and attended biweekly meetings to download the activity monitors. For children in the open-loop feedback plus reinforcement (intervention) group, accumulating 400 counts of physical activity on pedometers earned 1 hour of television/VCR/DVD time, which was controlled by a Token TV electronic device. Open-loop feedback control subjects wore activity monitors but had free access to targeted sedentary behavior. Compared with controls, the open-loop feedback plus reinforcement group demonstrated significantly greater increases in daily physical activity counts (+65% vs +16%) and minutes per day of moderate-to-vigorous physical activity (+9.4 vs +0.3) and greater reductions in minutes per day spent in television viewing (-116.1 vs +14.3). The intervention group also showed more favorable changes in body composition, dietary fat intake, and energy intake from snacks compared with controls. Reductions in sedentary behavior were directly related to reductions in BMI, fat intake, snack intake, and snack intake while watching television. Providing feedback of physical activity in combination with reinforcing physical activity with sedentary behavior is a simple method of modifying the home environment that may play an important role in treating and preventing child obesity.

Neural Approximation of Open-Loop Feedback Rate Control in Satellite Networks

A resource allocation problem for a satellite network is considered, where variations of fading conditions are added to those of traffic load. Since the capacity of the system is finite and divided in finite discrete portions, the resource allocation problem reveals to be a discrete stochastic programming one, which is typically NP-Hard. In practice, a good approximation of the optimal solution could be obtained through the adoption of a closed-form expression of the performance measure in steady-state conditions. Once we have summarized the drawbacks of such optimization strategy, we address two novel optimization approaches. The first one derives from Gokbayrak and Cassandras and is based on the minimization over the discrete constraint set using an estimate of the gradient, obtained through a "relaxed continuous extension" of the performance measure. The computation of the gradient estimation is based on infinitesimal perturbation analysis (IPA). Neither closed forms of the performance measures, nor additional feedbacks concerning the state of the system and very mild assumptions about the stochastic environment are requested. The second one is the main contribution of the present work, and is based on an open-loop feedback control (OLFC) strategy, aimed at providing optimal reallocation strategies as functions of the state of the network. The optimization approach leads us to a functional optimization problem, and we investigate the adoption of a neural network-based technique, in order to approximate its solution. As is shown in the simulation results, we obtain near-optimal reallocation strategies with a small real time computational effort and avoid the suboptimal transient periods introduced by the IPA gradient descent algorithm.

Reachability under uncertainty and measurement noise

This paper deals with the problem of reachability under unknown but bounded disturbances and piecewise open-loop controls which may be feedback-corrected at isolated ‘points of correction’. It is presumed that there are hard bounds on the controls and the unknown but bounded items. The open-loop controls are reassigned at prespecified points of correction on the basis of additional information on the state space variable which arrives at these points. Such information typically comes through a given noisy instantaneous measurement of the state space variable which sometimes may or may not be complemented by information on the forthcoming disturbance. Thus the process is ‘piecewise feedback’ with feedback introduced at points of correction. The described situation is intermediate relative to purely open-loop control and continuous measurement feedback control under uncertainty. The novelty of this paper lies in considering incomplete noisy measurements of the state space variable at points of correction rather than exact complete measurements of these. The paper also describes some numerical algorithms relevant for computer modelling. It is emphasized that effective computational results may be obtained if one relies on ellipsoidal techniques as given by Kurzhanski et al.

GUARANTEED PERFORMANCE CONTROL FOR DISCRETE-TIME LQG PROBLEMS

Guaranteed performance control is considered in this paper for discrete-time LQG problems by minimizing the probability that the performance index is over a preselected threshold. It is proven that this guaranteed performance control problem can be converted into a mean-variance control problem which can be solved by using an embedding scheme. An optimal open-loop feedback control law is derived for the guaranteed performance control of discrete-time LQG problems.

Efficiency of sediment transport by flood and its control in the Lower Yellow River

This paper presents the characteristics of sediment transport by flood in the Lower Yellow River with the reach from Huayuankou to Gaocun, which is regarded as a typical braided pattern. The Artificial Neural Network Model on Water Use for Sediment Transport (WUST) by flood was established based on the measured data from 1980 to 1998. Consequently, simulations of controlling process of sediment transport by flood were made in terms of the control theory under different scenarios. According to the situation of sediment transport by flood in the Lower Yellow River, Open-Loop control system and feedback control system were adopted in system design. In the Open-Loop control system, numerical simulations were made to reveal the relationship between average discharge of flood and the WUST with varying sediment concentrations. The results demonstrate that sediment concentration has significant influence on the controlling process of flood flow to WUST. It is practical and efficient to control WUST if sediment concentration is less than 20 kg/m3. In the feedback control system, controlling processes of sediment concentration and flood discharge for sediment transport were simulated respectively under given conditions, and it was found that sediment transport process could be controlled completely by sediment concentration and discharge at the inlet of the reach from Huayuankou to Gaocun. Using the same method, controlling processes of sediment transport by flood in other reaches in the Lower Yellow River were also simulated. For the case of sediment concentration being 20 kg/m3, the optimized controlling discharge ranges from 2390 to 2900 m3/s in the lower reach of Huayuankou. This study is also of significance to flood control and flushing sediment in the Lower Yellow River with proper operation modes of Xiaolangdi Reservoir.

Comparison between closed-loop and partial open-loop feedback control policies in long term hydrothermal scheduling

Stochastic dynamic programming has been. extensively used in the optimization of long term hydrothermal scheduling problems due to its ability to cope with the nonlinear and stochastic characteristics of such problems, and the fact that it provides a closed-loop feedback control policy. Its computational requirements, however, tend to be heavy even for systems with a small number of hydroplants, requiring some sort of modeling manipulation in order to be able to handle real systems. An alternative to closed-loop optimization is an approach that combines a deterministic optimization model with an inflow forecasting model in a partial open-loop feedback control framework. At each stage in this control policy, a forecast of the inflows during the period of planning is made, and an operational decision for the following stage is obtained by a deterministic optimization model. The present paper compares such closed-loop and partial open-loop feedback control policies in long term hydrothermal scheduling, using a single hydroplant system as a case study to focus the comparison on the feedback control performance. The comparison is made by simulation using data from historical and synthetical inflow sequences in the consideration of three different Brazilian hydroplants located in different river basins. Results have demonstrated that the performance of the partial open-loop feedback control policy is similar to that of the closed-loop control policy, and is even superior in dry streamflow periods.

ACTIVE DUAL CONTROL FOR LINEAR-QUADRATIC GAUSSIAN SYSTEM WITH UNKNOWN PARAMETERS

This paper deals with a class of linear-quadratic Gaussian control problems where there exist parameter uncertainties in both the state and observation equations. An active dual control law is derived by using a variance minimization approach while an embedding scheme is proposed to overcome nonseparability in variance minimization and the degree of an active learning is determined by an entropy measure. A solution method is adopted to achieve the optimal open-loop feedback control for the resulting auxiliary problem by treating the true system with uncertain parameters as a composition of multiple fictitious systems with completely known parameters, while the amount of contribution from the state of each fictitious system to the overall performance index at each stage is determined by the current posterior probability.

Comparison between Closed-Loop and Partial Open-Loop Feedback Control Policies in Long-Term Hydrothermal Scheduling

Comparison between Closed-Loop and Partial Open-Loop Feedback Control Policies in Long-Term Hydrothermal Scheduling