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Control-theory design package, called Optimal Regulator Algorithms for Control of Linear Systems (ORACLS), aids in design of controllers and optimal filters for systems modeled by linear, time invariant differential and difference equations. ORACLS is particularly attractive rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete forms.
We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty implies that the considered integer control problems admit minimizers. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonstrate the theoretical findings on a computational example.
The steady state solution of the linear quadratic optimal control problem with the constraint that only partial state information is available for feedback is derived. This development results in a systematic and computationally efficient approach for reducing the complexity of the control law for high order systems. Numerical examples and performance evaluation of (1) a simple fourth order system, and (2) a free-free flexible beam, are included.
Due to the changing nature of the power grid, it is increasingly important to be able to solve a high-fidelity optimal power-flow models on large power networks. This high-fidelity problem, called AC Optimal Power Flow (ACOPF), is a nonlinear, nonconvex optimization problem. One of the few reliable ways of solving such a problem is interior point methods. These methods result in sparse linear systems where the coefficient matrix is symmetric, indefinite and nearly always ill-conditioned. As such, they are particularly challenging for sparse linear solvers and represent a considerable computational bottleneck in solving the ACOPF problem. In this paper, we introduce a repository of linear systems captured from ACOPF problems when solved by the open-source optimizer IPOPT. These matrices are meant to be used as a test suite for sparse linear solver development.
A nonlinear optimization algorithm for linear predictive speech coding was developed early that not only optimizes the linear model coefficients for the open loop predictor, but does the optimization including the effects of quantization of the transmitted residual. It also simultaneously optimizes the quantization levels used for each speech segment. In this paper, we present an improved method for initialization of this nonlinear algorithm, and demonstrate substantial improvements in performance. In addition, the new procedure produces monotonically improving speech quality with increasing numbers of bits used in the transmitted error residual. Examples of speech encoding and decoding are given for 8 speech segments and signal to noise levels as high as 47 dB are produced. As in typical linear predictive coding, the optimization is done on the open loop speech analysis model. Here we demonstrate that minimizing the error of the closed loop speech reconstruction, instead of the simpler open loop optimization, is likely to produce negligible improvement in speech quality. The examples suggest that the algorithm here is close to giving the best performance obtainable from a linear model, for the chosen order with the chosen number of bits for the codebook.
Performance of linear Fresnel collectors may largely depend on the secondary-reflector profile design when small-aperture absorbers are used. Optimization of the secondary-reflector profile is an extremely challenging task because there is no established theory to ensure superior performance of derived profiles. In this work, an innovative optimization method is proposed to optimize the secondary-reflector profile of a generic linear Fresnel configuration. The method correctly and accurately captures impacts of both geometric and optical aspects of a linear Fresnel collector to secondary-reflector design. The proposed method is an adaptive approach that does not assume a secondary shape of any particular form, but rather, starts at a single edge point and adaptively constructs the next surface point to maximize the reflected power to be reflected to absorber(s). As a test case, the proposed optimization method is applied to an industrial linear Fresnel configuration, and the results show that the derived optimal secondary reflector is able to redirect more than 90% of the power to the absorber in a wide range of incidence angles. Here, the proposed method can be naturally extended to other types of solar collectors as well, and it will be a valuable tool for solar-collector designs with a secondary reflector.
In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.
Jacobi-type conditions for singular optimization problems obtained by transformation to nonsingular form adaptable to linear quadratic optimal control theory
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
The core objectives of this project is to improve the power capture of three different wave energy conversion (WEC) devices by more than 50% using an advanced control system and validate the attained improvements using wave tank and full scale testing. In parallel, we will bring along the development of a wave prediction system that is required to enable effective control and test it at full scale. The purposes of this report are to: 1. Plan and document the 1/25th scale device testing at the wave-tank facility; 2. Document the test article, setup and methodology, sensor and instrumentation, mooring, electronics, wiring, and data flow and quality assurance; 3. Communicate the testing results between the associated members; 4. Facilitate reviews that will help to ensure all aspects (risk, safety, testing procedures, etc.); 5. Provide a systematic guide to setting up, executing and decommissioning the experiment.
The occurrence of superconductivity in proximity to various strongly correlated phases of matter has drawn extensive focus on their normal state properties, to develop an understanding of the state from which superconductivity emerges. The recent finding of superconductivity in layered nickelates raises similar interests. However, transport measurements of doped infinite-layer nickelate thin films have been hampered by materials limitations of these metastable compounds: in particular, a high density of extended defects. Here, by moving to a substrate (LaAlO 3 ) 0.3 (Sr 2 TaAlO 6 ) 0.7 that better stabilizes the growth and reduction conditions, we can synthesize the doping series of Nd 1– x Sr x NiO 2 essentially free from extended defects. In their absence, the normal state resistivity shows a low-temperature upturn in the underdoped regime, linear behaviour near optimal doping and quadratic temperature dependence for overdoping. This is phenomenologically similar to the copper oxides despite key distinctions—namely, the absence of an insulating parent compound, multiband electronic structure and a Mott–Hubbard orbital alignment rather than the charge-transfer insulator of the copper oxides. In this study, we further observe an enhancement of superconductivity, both in terms of transition temperature and range of doping. These results indicate a convergence in the electronic properties of both superconducting families as the scale of disorder in the nickelates is reduced.
The environmental and economic impacts of implementing a circular economy in plastic waste supply chains are not well understood. The proposed systems analysis framework assesses environmental, social, and economic impacts of plastic waste supply chains in a circular economy. The first objective of this article is to identify datasets, models and knowledge gaps associated with waste plastic supply chain processes, mainly in the U.S. Our literature review indicated that the best datasets exist for virgin plastic resin production, mechanical recycling, landfilling, and incineration, with materials recovery facility being intermediate, and with chemical recycling the lowest. The second objective of this article is to develop an illustrative application of the framework by conducting a preliminary systems analysis of PET bottles with closed-loop recycling. Here, the preliminary systems analysis of PET bottles utilized a linear programming optimization method. Our optimization model indicated that both chemical and mechanical recycling processes are needed to achieve a true circular economy of PET bottles with the least greenhouse gas emissions, specifically reductions of 24% when compared with the linear economy. Good quality and standardized life cycle assessment and techno-economic analysis studies are needed to better understand the environmental, economic, and social impacts of advanced sorting and chemical recycling technologies.
A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established.
The application of Linear Quadratic Gaussian (LQG) techniques to the design of the 70-m axis servos is described. Linear quadratic optimal control and Kalman filter theory are reviewed, and model development and verification are discussed. Families of optimal controller and Kalman filter gain vectors were generated by varying weight parameters. Performance specifications were used to select final gain vectors.
This work is directed toward approximating the evolution of forecast error covariances for data assimilation. The performance of different algorithms based on simplification of the standard Kalman filter (KF) is studied. These are suboptimal schemes (SOSs) when compared to the KF, which is optimal for linear problems with known statistics. The SOSs considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. To employ a methodology for exact comparison among these schemes, a linear environment is maintained, in which a beta-plane shallow-water model linearized about a constant zonal flow is chosen for the test-bed dynamics. The results show that constructing dynamically balanced forecast error covariances rather than using conventional geostrophically balanced ones is essential for successful performance of any SOS. A posteriori initialization of SOSs to compensate for model - data imbalance sometimes results in poor performance. Instead, properly constructed dynamically balanced forecast error covariances eliminate the need for initialization. When the SOSs studied here make use of dynamically balanced forecast error covariances, the difference among their performances progresses naturally from conventional OI to the KF. In fact, the results suggest that even modest enhancements of OI, such as including an approximate dynamical equation for height error variances while leaving height error correlation structure homogeneous, go a long way toward achieving the performance of the KF, provided that dynamically balanced cross-covariances are constructed and that model errors are accounted for properly. The results indicate that such enhancements are necessary if unconventional data are to have a positive impact.
A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given.
Optimal control in linear feedback attitude control systems for spinning space station
Purpose: A method was developed utilizing Cherenkov imaging for rapid and thorough determination of the two gantry angles that produce the most uniform treatment plane during dual-field total skin electron beam therapy (TSET). Methods: Cherenkov imaging was implemented to gather 2D measurements of relative surface dose from 6 MeV electron beams on a white polyethylene sheet. An intensified charge-coupled device camera time-gated to the Linac was used for Cherenkov emission imaging at sixty-two different gantry angles (1° increments, from 239.5° to 300.5°). Following a modified Stanford TSET technique, which uses two fields per patient position for full body coverage, composite images were created as the sum of two beam images on the sheet; each angle pair was evaluated for minimum variation across the patient region of interest. Cherenkov versus dose correlation was verified with ionization chamber measurements. The process was repeated at source to surface distance (SSD) = 441, 370.5, and 300 cm to determine optimal angle spread for varying room geometries. In addition, three patients receiving TSET using a modified Stanford six-dual field technique with 6 MeV electron beams at SSD = 441 cm were imaged during treatment. Results: As in previous studies, Cherenkov intensity was shown to directly correlate with dose for homogenous flat phantoms (R{sup 2} = 0.93), making Cherenkov imaging an appropriate candidate to assess and optimize TSET setup geometry. This method provided dense 2D images allowing 1891 possible treatment geometries to be comprehensively analyzed from one data set of 62 single images. Gantry angles historically used for TSET at their institution were 255.5° and 284.5° at SSD = 441 cm; however, the angles optimized for maximum homogeneity were found to be 252.5° and 287.5° (+6° increase in angle spread). Ionization chamber measurements confirmed improvement in dose homogeneity across the treatment field from a range of 24.4% at the initial angles, to only 9.8% with the angles optimized. A linear relationship between angle spread and SSD was observed, ranging from 35° at 441 cm, to 39° at 300 cm, with no significant variation in percent-depth dose at midline (R{sup 2} = 0.998). For patient studies, factors influencing in vivo correlation between Cherenkov intensity and measured surface dose are still being investigated. Conclusions: Cherenkov intensity correlates to relative dose measured at depth of maximum dose in a uniform, flat phantom. Imaging of phantoms can thus be used to analyze and optimize TSET treatment geometry more extensively and rapidly than thermoluminescent dosimeters or ionization chambers. This work suggests that there could be an expanded role for Cherenkov imaging as a tool to efficiently improve treatment protocols and as a potential verification tool for routine monitoring of unique patient treatments.