Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 24 for “"Riccati Equations"”.
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ON RICCATI EQUATIONS IN NONCONVEX OPTIMIZATION
… arises due to the presence of a nonlinear Riccati equation, in the objective or constraints. We find that these Riccati equations play a large role in guaranteeing global optimality, and it certifying constraints. This suggests that when faced with nonconvexity due to the presence of …
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Reduced Order Methods for Large Scale Riccati Equations
… regulator (LQR) problem for partial differential equations (PDEs) leads to many computational challenges. The primary challenge comes from the fact that discretization methods for PDEs typically lead to very large systems of differential or differential algebraic equations. These systems are used …
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On the numerical solution of continuous coupled algebraic Riccati equations
… bound for the continuous coupled algebraic Riccati equation, which arises from the optimal control of a Markovian jump linear system. In particular, we address the issue of rank deficiency with the control matrices. In the case of rank deficiency the existing matrix upper bounds are …
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Analysis and Numerical Methods for Algebraic Riccati Equations Associated with Regular M-Matrices
The thesis is a further study about algebraic Riccati equations for which the four coe cient matrices form a regular M-matrix K. We prove a property about minimal nonnegative solutions of such an algebraic Riccati equation and its dual equation. And we show that Newton's method, SDA, ADDA are …
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Algorithms and Software for Solving Coupled Discrete-Time Riccati Equations via the L-a-S Language (computer-Aided Design, Control, Game Theory)
… with solving a set of coupled discrete-time Riccati equations. Briefly, the organization of this study is as follows. First, the problem is motivated by discussing two game situations which give rise to coupled discrete-time Riccati equations. Next, the computational aspects of solving these …
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Bounds for the solution of algebraic matrix equations arising in mathematical control theory
… of solution bounds of algebraic Lyapunov and Riccati equations are highly important in control problems, and have been an attractive re search topic over the past three decades. The solution bounds give solution estimates, and can also be applied to solve such problems involving these …
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A Distributed Parameter Approach to Optimal Filtering and Estimation with Mobile Sensor Networks
… PDE problems defined by the convection-diffusion equations. The mathematical problem is formulated as a distributed parameter optimal control problem with integral Riccati equations as constraints. In order to prove existence of the optimal sensor network and to construct a framework in which to …
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H-Infinity Norm Calculation via a State Space Formulation
… unique stabilizing solutions to two Algebraic Riccati Equations are positive semi definite as well as satisfying a spectral radius coupling condition. In this work, we describe an algorithm by Lin et al(1999), used to calculate the H-infty norm for the state feedback and output feedback control …
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Optimal Linear Feedback Control for Incompressible Fluid Flow
… for large systems of differential algebraic equations arising from discretization of saddle point problems. Necessary conditions are derived by applying the Maximum Principle and have the form of constrained Riccati equations. We consider two approaches for solving the feedback control …
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Splitting schemes for nonlinear parabolic problems
… problems with delay, as well as differential Riccati equations. Within the second theme of structure preservation, an in-depth study of operator-valued differential Riccati equations has been carried out. In such equations it is desirable for a numerical method to produce positive …
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Homotopy algorithms for H²/H<sup>∞</sup> control analysis and synthesis
… on Hyland and Bernstein's optimal projection equations. Both the input normal form and Ly form are very efficient compared to the over parametrization formulation and the optimal projection equations approach, since they utilize the minimal number of possible degrees of freedom. However, they …
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Numerical solutions of matrix equations arising in model reduction of large-scale linear -time -invariant systems
… presents and analyzes new algorithms for matrix equations arising from model reduction of linear-time-invariant (LTI) systems. Such systems arise in a variety of areas, especially in circuit simulation. When an integrated circuit has millions of devices, performing a full-system simulation can be …
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Near-optimal feedback guidance for an accurate lunar landing
… employs a new extension of the State-Dependent Riccati Equation (SDRE) technique for constrained nonlinear dynamical systems in finite time. In general, the solution procedure yields a closed-loop control law for a dynamical system with point terminal constraints. Being a closed-loop solution, …
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Stabilized Finite Element Methods for Feedback Control of Convection Diffusion Equations
… (LQR) control problems for convection diffusion equations. The motivation for this effort comes from the observation that when linearization is applied to fluid flow control problems the resulting equations have the form of a convection diffusion equation. This effort is focused on the specific …
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A partial order approach to decentralized control
… by solving a small number of uncoupled standard Riccati equations. Our approach gives important insight into the structure of optimal controllers, such as controller degree bounds that depend on the structure of the poset. A novel element in our state-space characterization of the controller is a …
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Closed-form Solutions to Robust and Optimal Control Problems of Second-Order Systems
… approaches to solving continuous-time algebraic Riccati equations (CAREs), computing coprime factorizations, and synthesizing robust controllers often lose physical insight and become computationally expensive for large-size systems. To overcome these challenges, we develop closed-form solutions …
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Parameter robust reduced-order control of flexible structures
… the solution of a system of four coupled equations - two modified Riccati equations and two modified Lyapunov equations. In addition, the optimal projection equations are applied to both robustness methods to reduce the controller order with minimal loss in performance. Comparisons are …
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Studies in system representation and control
… We present a solution that involves solving two Riccati equations and a stable projection.
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Model and Data Reduction for Control, Identification and Compressed Sensing
… a new method to solve large-scale algebraic Riccati equations, which arise in optimal control, filtering and model reduction. We present a projection based algorithm utilizing proper orthogonal decomposition, which is demonstrated to produce highly accurate solutions at low rank. The method …
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Methods of Computing Functional Gains for LQR Control of Partial Differential Equations
… defined by parabolic partial differential equations. In particular, we study various methods for computing functional gains to boundary control problems for the heat equation. These methods require us to solve various equations including the algebraic Riccati equation, the Riccati partial …
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