The LQG game with nonclassical information pattern using a direct solution method

This paper gives a brief list of commonly used direct and indirect efficient methods for the numerical solution of optimal control problems. To improve the low accuracy of the direct methods and to increase the convergence areas of the indirect methods we suggest a hybrid approach. For this a special direct collocation method is presented. In a hybrid approach this direct method can be used in combination with multiple shooting. Numerical examples illustrate the direct method and the hybrid approach.

Optimal control strategies are very useful in manipulation problems of robots. However, most optimal controls are highly sensitive to plant-parameter variations and disturbances because optimal controls try to pick up exact information from the mathematical models in order to realize the best performance. We recognize that difficulties are involved in exact modeling of plants and prevention of disturbances. Therefore, we need a optimal control method with low sensitivity. The ideas of closed-loop control system design using LQG/TR techniques (linear quadratic Gaussian control with transfer recovery) are discussed in this paper. We combine optimal controls and LQG/TR control into two-degrees-of-freedom control systems to reduce the sensitivities of optimal control strategies. In digital simulations, we obtained excellent results of a two-link manipulator in an optimal time control problem using our method. Some modeling errors and considerable disturbances are allowed in the method. Thus, we can realize good performances in practical manipulation problems using our method.

A two-degree-of-freedom quarter-car model is used as the basis for linear quadratic (LQ) and linear quadratic Gaussian (LQG) controller design for an active suspension. The LQ controller results in the best rms performance trade-offs (as defined by the performance index) between ride, handling and packaging requirements. In practice, however, all suspension states are not directly measured, and a Kalman filter can be introduced for state estimation to yield an LQG controller. This paper (i) quantifies the rms performance losses for LQG control as compared to LQ control, and (ii) compares the LQ and LQG active suspension designs from the point of view of stability robustness. The robustness of the LQ active suspensions is not necessarily good, and depends strongly on the design of a backup passive suspension in parallel with the active one. The robustness properties of the LQG active suspension controller are also investigated for several distinct measurement sets.

<?Pub Dtl=""?> This paper introduces, formulates and evaluates an approach for damping inter-area oscillations of power systems based on supplementary current control of a line-commutated HVDC link. The proposed control is based on the model predictive control (MPC) strategy. The salient feature of the MPC as compared with other optimal control strategies, e.g., the linear quadratic Gaussian (LQG) control, is that it adjusts the control signal to achieve the objectives while explicitly respecting the plant constraints. This paper also compares the performance of the MPC with that of the LQG control. The two approaches are tested on the Western System Coordinating Council (WSCC) 9-bus system and the IEEE 14-bus system. Small-signal disturbance and large-signal disturbance stability studies are performed to demonstrate and compare the performances of the LQG and MPC methodologies. The study results show the effective and superior performance of the MPC for damping poorly damped oscillatory modes of the test systems.

A parallel circuit simulator, iPRIDE, which uses a direct solution method and runs on a shared-memory multiprocessor is described. The simulator is based on a multilevel node tearing approach which produces a nested bordered-block-diagonal (BBD) form of the circuit equation matrix. The parallel solution of the nested BBD matrix is described. Its efficiency is shown to depend on how the circuit is partitioned as well as the sequence in which the concurrent tasks (scheduling) are solved. A partitioning heuristic is proposed, assuming that an arbitrary number of processors is available. Scheduling methods are studied when the number of processors is fixed. A method for determining the optimal level of partitioning, which depends on the number of processors as well as the scheduling methods, is described. The program is implemented on an ALLIANT FX/8 multiprocessor with shared memory. The performance of the program is reported. >

Synthetic seismogram calculation by the direct solution method : A. M. Enok, Individual Studies by Participants at the International Institute of Seismology and Earthquake Engineering, 31, 1995, pp 133–142

We want to solve a system of linear equations A x = b in a parallel environment. Here, the n x n-matrix A is large, sparse, unstructured, nonsymmetric, and ill-conditioned. The solution method should be robust, easy to parallelize, and applicable as a black box solver. Direct solution methods like the Gaussian Elimination are not very effective in a parallel environment. This is caused by the sequential nature of the computation and solution of a triangular factorization A = L R with lower and upper triangular matrices L and R. Therefore, we prefer an iterative solution method like GMRES, BiCGSTAB, or QMR (see [1]). In an iterative scheme we compute

In the past decades, harmonic balance (HB) has been widely used for computing steady-state solutions of nonlinear radio-frequency (RF) and microwave circuits. However, using HB for simulating strongly nonlinear post-layout RF circuits still remains a very challenging task. Although direct solution methods can be adopted to handle moderate to strong nonlinearities in HB analysis, such methods do not scale efficiently with large-scale problems due to excessively long simulation time and prohibitively large memory consumption. In this paper, we present a novel graph sparsification approach for automatically generating preconditioners that can be efficiently applied for simulating strongly nonlinear post-layout RF circuits. Our approach allows to sparsify time-domain circuit modified nodal analysis matrices that can be subsequently leveraged for sparsifying the entire HB Jacobian matrix. We show that the resultant sparsified Jacobian matrix can be used as a robust yet efficient preconditioner in HB analysis. Our experimental results show that when compared with the prior state-of-the-art direct solution method, the proposed solver can more efficiently handle moderate to strong nonlinearities during the HB analysis of RF circuits, achieving up to $20{\boldsymbol \times }$ speedups and $6{\boldsymbol \times }$ memory reductions.

Since the approach takes into account the uncontrolled residual modes, it will not only optimize them, based on an actual performance index affected by the residual modes, but will also suppress the spillover instability. The approach is applied to the design of a controller for a simple supported beam. The example demonstrates that the resulting controller is stable even when the linear quadratic Gaussian (LQG) controller is unstable. Insensitivity of the resulting system to parameter variations is also demonstrated in comparison with the LQG controller

Optimal LQG Controller for Variable Speed Wind Turbine Based on Genetic Algorithms

This chapter starts with an overview of the basic mechanics of GAs and highlights their major differences when compared to traditional and enumerative search and optimisation techniques. The main components of the GA are then described in some detail and various alternative approaches to the major procedures are considered. After a brief discussion of other evolutionary algorithms, parallel models of the GA are then considered and it is shown how it may be possible to improve the performance of the algorithm even when it is implemented on a sequential computer. Next, considerations commonly arising in engineering systems and the manner in which they may be treated through the application of GAs are discussed. Finally, an example of the use of a GA in aircraft engine controller configuration design is presented to demonstrate how GAs may be applied to problems for which there are currently no other direct methods of solution.

0 K(t, s)x(s)ds, t ∈ I ≡ [0, 1], p1, p2 ∈ R+, tj ∈ (0, 1), mj ∈ N (j = 1, q); K and y are known continuous functions with certain properties of pointwise “smoothness“, and x is the desired function. These equations are connected with several problems of the theory of elasticity, scattering of particles, neutron transfer (see, e. g., [1] and references therein; [2]). As a rule, the intrinsic classes of solutions of the ETK are special spaces of distributions. The equations under consideration allow explicit solution in rare special cases. Therefore both the theory and the applications require approximative solution methods with the corresponding theoretical support. Several relevant results are obtained in papers [3], [4]. In [3] we propose and prove special direct solution methods for ETK (1) in the space of distributionsD{p1, p2;m, τ}. Paper [4] is dedicated to the construction of the complete solvability theory for the equations under consideration in a certain space of distributions V {p1, p2;m, τ}. In this paper, following the works [3]–[6], we propose and substantiate in the sense of [7] (Chap. 1) one special direct method for the approximate solution of ETK (1) in the space V {p1, p2;m, τ}. We prove that the constructed method is optimal by the order of exactness on a certain class Φ generated by the classHr ω among all projection solution methods for ETK (1). 1. The space of trial functions. Let C ≡ C(I) be the space of continuous on I functions with the customary max-norm and m ∈ N . According to [8], we denote by C t0 ≡ C{m; t0} the class of functions g ∈ C such that at a point t0 ∈ (0, 1) they have the Taylor derivative g{m}(t0) of the orderm. Let t1, t2, . . . , tq be arbitrarily fixed pairwise distinct points of the interval (0, 1). We associate each point tj with a certain numbermj ∈ N (j = 1, q). Let us introduce the vector space

Most of researches for large-scale parallel structural analysis using finite element method have focused on iterative solution methods since direct solution methods generally have many difficulties and disadvantages for large-scale problems. However, due to the numerical robustness of direct methods that guarantees the solution to be obtained within estimated time, direct methods are much more desirable for general application of large-scale structural analysis, as well as due to ease of use which makes most of structural engineers prefer direct methods. In this research, we propose a parallel direct solver for large-scale finite element analysis that can overcome most of difficulties and disadvantages of direct methods by using domain-wise approach for direct methods. By using the proposed solver with our own structural analysis code, we can show good scalability as a direct method and can solve the largest problem ever solved by direct solvers.

A Path Integral (PI) formulation of linear elastostatics is first presented. For this, Navier equations are modified by adding a fictitious 'time' derivative of displacements so that equilibrium corresponds to the steady state of the resulting diffusion-like equations. The evolution of displacement is then represented as the propagation, through the fictitious time co-ordinate, of an initial displacement field corresponding to the unloaded state. The resulting procedure somehow mimics the well-known Feynman path integral of quantum mechanics, which is equivalent to the differential formulation embodied in Schrödinger equation. However, the path integral for elastostatics is formulated in terms of infinitesimal propagators of local support. In its simplest form, the formulation can be used as a relaxation method of solution, by updating displacements until convergence. This may be advantageous for problems involving a very large number of unknowns. On the other hand, by equating the updated displacement field to the actual one a direct method of solution is obtained, which leads to non-symmetric (but sparse and banded) discrete equations. Unlike variational principles this formulation does not require integration over the whole domain, effectively eliminating the need of a background mesh for integration. Also, it only requires continuity of the displacement field on the propagator's support. As a consequence, the formulation lends itself to very flexible meshless implementations. To demonstrate this we describe a simple numerical method in which displacements around each node are approximated by quadratic bivariate polynomials, which is the simplest approximation technique. The feasibility of the method is assessed through a number of numerical examples and comparisons with analytical solutions and other meshless methods. Copyright © 2000 John Wiley & Sons, Ltd.

Direct control method for improving stability and reliability of nonlinear stochastic dynamical systems