49 research outputs found

    ИспользованиС r-Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠ° Π² ΠΌΠ΅Ρ‚ΠΎΠ΄Π΅ ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½ΠΎΠΉ Ρ„ΡƒΠ½ΠΊΡ†ΠΈΠΈ Π›Π°Π³Ρ€Π°Π½ΠΆΠ° для Π·Π°Π΄Π°Ρ‡ с критичСскими мноТитСлями

    No full text
    ΠŸΡ€ΠΈΠ²Π΅Π΄Π΅Π½Ρ‹ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ числСнных экспСримСнтов, связанных с критичСскими мноТитСлями Π›Π°Π³Ρ€Π°Π½ΠΆΠ° Π² нСрСгулярных Π·Π°Π΄Π°Ρ‡Π°Ρ… ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ. Π Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ ΠΏΠΎΠΊΠ°Π·Ρ‹Π²Π°ΡŽΡ‚, Ρ‡Ρ‚ΠΎ r-Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌ Н.Π—.Π¨ΠΎΡ€Π° обСспСчиваСт Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΡƒΡŽ Ρ‚ΠΎΡ‡Π½ΠΎΡΡ‚ΡŒ Ρ€Π΅ΡˆΠ΅Π½ΠΈΡ Π·Π°Π΄Π°Ρ‡ бСзусловной ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ ΠΏΡ€ΠΈ использовании ΠΌΠ΅Ρ‚ΠΎΠ΄Π° ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½ΠΎΠΉ Ρ„ΡƒΠ½ΠΊΡ†ΠΈΠΈ Π›Π°Π³Ρ€Π°Π½ΠΆΠ°.ΠŸΡ€ΠΈΠ²Π΅Π΄Π΅Π½Ρ‹ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ числСнных экспСримСнтов, связанных с критичСскими мноТитСлями Π›Π°Π³Ρ€Π°Π½ΠΆΠ° Π² нСрСгулярных Π·Π°Π΄Π°Ρ‡Π°Ρ… ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ. Π Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ ΠΏΠΎΠΊΠ°Π·Ρ‹Π²Π°ΡŽΡ‚, Ρ‡Ρ‚ΠΎ r-Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌ Н.Π—.Π¨ΠΎΡ€Π° обСспСчиваСт Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΡƒΡŽ Ρ‚ΠΎΡ‡Π½ΠΎΡΡ‚ΡŒ Ρ€Π΅ΡˆΠ΅Π½ΠΈΡ Π·Π°Π΄Π°Ρ‡ бСзусловной ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ ΠΏΡ€ΠΈ использовании ΠΌΠ΅Ρ‚ΠΎΠ΄Π° ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½ΠΎΠΉ Ρ„ΡƒΠ½ΠΊΡ†ΠΈΠΈ Π›Π°Π³Ρ€Π°Π½ΠΆΠ°.НавСдСно Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΈ Ρ‡ΠΈΡΠ΅Π»ΡŒΠ½ΠΈΡ… СкспСримСнтів, ΠΏΠΎΠ²'язаних Π· ΠΊΡ€ΠΈΡ‚ΠΈΡ‡Π½ΠΈΠΌΠΈ ΠΌΠ½ΠΎΠΆΠ½ΠΈΠΊΠ°ΠΌΠΈ Π›Π°Π³Ρ€Π°Π½ΠΆΠ°. Π Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΈ ΠΏΠΎΠΊΠ°Π·ΡƒΡŽΡ‚ΡŒ, Ρ‰ΠΎ r-Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌ Н.Π—. Π¨ΠΎΡ€Π° Π·Π°Π±Π΅Π·ΠΏΠ΅Ρ‡ΡƒΡ” Π½Π΅ΠΎΠ±Ρ…Ρ–Π΄Π½Ρƒ Ρ‚ΠΎΡ‡Π½Ρ–ΡΡ‚ΡŒ Ρ€ΠΎΠ·Π²'язання Π·Π°Π΄Π°Ρ‡ Π±Π΅Π·ΡƒΠΌΠΎΠ²Π½ΠΎΡ— ΠΎΠΏΡ‚ΠΈΠΌΡ–Π·Π°Ρ†Ρ–Ρ— ΠΏΡ€ΠΈ використанні ΠΌΠ΅Ρ‚ΠΎΠ΄Ρƒ ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΎΡ— Ρ„ΡƒΠ½ΠΊΡ†Ρ–Ρ— Π›Π°Π³Ρ€Π°Π½ΠΆΠ°.The results of numerical experiments related to critical Lagrange multipliers are reported. The results demonstrate that the r-algorithm of N.Z. Shor provides necessary accuracy for solving the unconstrained optimization problems using augmented Lagrangian method

    Variational and Time-Distributed Methods for Real-time Model Predictive Control

    Full text link
    This dissertation concerns the theoretical, algorithmic, and practical aspects of solving optimal control problems (OCPs) in real-time. The topic is motivated by Model Predictive Control (MPC), a powerful control technique for constrained, nonlinear systems that computes control actions by solving a parameterized OCP at each sampling instant. To successfully implement MPC, these parameterized OCPs need to be solved in real-time. This is a significant challenge for systems with fast dynamics and/or limited onboard computing power and is often the largest barrier to the deployment of MPC controllers. The contributions of this dissertation are as follows. First, I present a system theoretic analysis of Time-distributed Optimization (TDO) in Model Predictive Control. When implemented using TDO, an MPC controller distributed optimization iterates over time by maintaining a running solution estimate for the optimal control problem and updating it at each sampling instant. The resulting controller can be viewed as a dynamic compensator which is placed in closed-loop with the plant. The resulting coupled plant-optimizer system is analyzed using input-to-state stability concepts and sufficient conditions for stability and constraint satisfaction are derived. When applied to time distributed sequential quadratic programming, the framework significantly extends the existing theoretical analysis for the real-time iteration scheme. Numerical simulations are presented that demonstrate the effectiveness of the scheme. Second, I present the Proximally Stabilized Fischer-Burmeister (FBstab) algorithm for convex quadratic programming. FBstab is a novel algorithm that synergistically combines the proximal point algorithm with a primal-dual semismooth Newton-type method. FBstab is numerically robust, easy to warmstart, handles degenerate primal-dual solutions, detects infeasibility/unboundedness and requires only that the Hessian matrix be positive semidefinite. The chapter outlines the algorithm, provides convergence and convergence rate proofs, and reports some numerical results from model predictive control benchmarks and from the Maros-Meszaros test set. Overall, FBstab shown to be is competitive with state of the art methods and to be especially promising for model predictive control and other parameterized problems. Finally, I present an experimental application of some of the approaches from the first two chapters: Emissions oriented supervisory model predictive control (SMPC) of a diesel engine. The control objective is to reduce engine-out cumulative NOx and total hydrocarbon (THC) emissions. This is accomplished using an MPC controller which minimizes deviation from optimal setpoints, subject to combustion quality constraints, by coordinating the fuel input and the EGR rate target provided to an inner-loop airpath controller. The SMPC controller is implemented using TDO and a variant of FBstab which allows us to achieve sub-millisecond controller execution times. We experimentally demonstrate 10-15% cumulative emissions reductions over the Worldwide Harmonized Light Vehicles Test Cycle (WLTC) drivecycle.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155167/1/dliaomcp_1.pd

    Interior-point methods for PDE-constrained optimization

    Get PDF
    In applied sciences PDEs model an extensive variety of phenomena. Typically the final goal of simulations is a system which is optimal in a certain sense. For instance optimal control problems identify a control to steer a system towards a desired state. Inverse problems seek PDE parameters which are most consistent with measurements. In these optimization problems PDEs appear as equality constraints. PDE-constrained optimization problems are large-scale and often nonconvex. Their numerical solution leads to large ill-conditioned linear systems. In many practical problems inequality constraints implement technical limitations or prior knowledge. In this thesis interior-point (IP) methods are considered to solve nonconvex large-scale PDE-constrained optimization problems with inequality constraints. To cope with enormous fill-in of direct linear solvers, inexact search directions are allowed in an inexact interior-point (IIP) method. This thesis builds upon the IIP method proposed in [Curtis, Schenk, WΓ€chter, SIAM Journal on Scientific Computing, 2010]. SMART tests cope with the lack of inertia information to control Hessian modification and also specify termination tests for the iterative linear solver. The original IIP method needs to solve two sparse large-scale linear systems in each optimization step. This is improved to only a single linear system solution in most optimization steps. Within this improved IIP framework, two iterative linear solvers are evaluated: A general purpose algebraic multilevel incomplete L D L^T preconditioned SQMR method is applied to PDE-constrained optimization problems for optimal server room cooling in three space dimensions and to compute an ambient temperature for optimal cooling. The results show robustness and efficiency of the IIP method when compared with the exact IP method. These advantages are even more evident for a reduced-space preconditioned (RSP) GMRES solver which takes advantage of the linear system's structure. This RSP-IIP method is studied on the basis of distributed and boundary control problems originating from superconductivity and from two-dimensional and three-dimensional parameter estimation problems in groundwater modeling. The numerical results exhibit the improved efficiency especially for multiple PDE constraints. An inverse medium problem for the Helmholtz equation with pointwise box constraints is solved by IP methods. The ill-posedness of the problem is explored numerically and different regularization strategies are compared. The impact of box constraints and the importance of Hessian modification on the optimization algorithm is demonstrated. A real world seismic imaging problem is solved successfully by the RSP-IIP method

    A Primal-Dual Augmented Lagrangian Penalty-Interior-Point Algorithm for Nonlinear Programming

    Get PDF
    This thesis treats a new numerical solution method for large-scale nonlinear optimization problems. Nonlinear programs occur in a wide range of engineering and academic applications like discretized optimal control processes and parameter identification of physical systems. The most efficient and robust solution approaches for this problem class have been shown to be sequential quadratic programming and primal-dual interior-point methods. The proposed algorithm combines a variant of the latter with a special penalty function to increase its robustness due to an automatic regularization of the nonlinear constraints caused by the penalty term. In detail, a modified barrier function and a primal-dual augmented Lagrangian approach with an exact l2-penalty is used. Both share the property that for certain Lagrangian multiplier estimates the barrier and penalty parameter do not have to converge to zero or diverge, respectively. This improves the conditioning of the internal linear equation systems near the optimal solution, handles rank-deficiency of the constraint derivatives for all non-feasible iterates and helps with identifying infeasible problem formulations. Although the resulting merit function is non-smooth, a certain step direction is a guaranteed descent. The algorithm includes an adaptive update strategy for the barrier and penalty parameters as well as the Lagrangian multiplier estimates based on a sensitivity analysis. Global convergence is proven to yield a first-order optimal solution, a certificate of infeasibility or a Fritz-John point and is maintained by combining the merit function with a filter or piecewise linear penalty function. Unlike the majority of filter methods, no separate feasibility restoration phase is required. For a fixed barrier parameter the method has a quadratic order of convergence. Furthermore, a sensitivity based iterative refinement strategy is developed to approximate the optimal solution of a parameter dependent nonlinear program under parameter changes. It exploits special sensitivity derivative approximations and converges locally with a linear convergence order to a feasible point that further satisfies the perturbed complementarity condition of the modified barrier method. Thereby, active-set changes from active to inactive can be handled. Due to a certain update of the Lagrangian multiplier estimate, the refinement is suitable in the context of warmstarting the penalty-interior-point approach. A special focus of the thesis is the development of an algorithm with excellent performance in practice. Details on an implementation of the proposed primal-dual penalty-interior-point algorithm in the nonlinear programming solver WORHP and a numerical study based on the CUTEst test collection is provided. The efficiency and robustness of the algorithm is further compared to state-of-the-art nonlinear programming solvers, in particular the interior-point solvers IPOPT and KNITRO as well as the sequential quadratic programming solvers SNOPT and WORHP

    Optimization of Rail Profiles to Improve Vehicle Running Stability in Switch Panel of High-Speed Railway Turnouts

    Get PDF
    A method for optimizing rail profiles to improve vehicle running stability in switch panel of high-speed railway turnouts is proposed in this paper. The stock rail profiles are optimized to decrease the rolling radii difference (RRD). Such characteristics are defined through given rail profiles, and the target rolling radii difference is defined as a function of lateral displacements of wheel set. The improved sequential quadratic programming (SQP) method is used to generate a sequence of improving profiles leading to the optimum one. The wheel-rail contact geometry and train-turnout dynamic interaction of the optimized profiles and those of nominal profiles are calculated for comparison. Without lateral displacement of wheel set, the maximum RRD in relation to a nominal profile will be kept within 0.5 mm–1 mm, while that in relation to an optimized profile will be kept within 0.3 mm–0.5 mm. For the facing and trailing move of vehicle passing the switch panel in the through route, the lateral wheel-rail contact force is decreased by 34.0% and 29.9%, respectively, the lateral acceleration of car body is decreased by 41.9% and 40.7%, respectively, and the optimized profile will not greatly influence the vertical wheel-rail contact force. The proposed method works efficiently and the results prove to be quite reasonable
    corecore