Journal ArticleDOI
A computational solution for the matrix riccati equation using laplace transforms
TLDR
The solution for the finite-time matrix Riccati equation is presented and it is shown that the solution is obtained in terms of the partition of the transition matrix.Abstract:
The solution for the finite-time matrix Riccati equation is presented in this paper. The solution to the Riccati equation is obtained in terms of the partition of the transition matrix. Matrix differential equations for the partition of the transition matrix are derived and solved using Laplace transforms and the computation is done by the digital computer. A numerical example for the proposed method is given.read more
Citations
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Book ChapterDOI
Matrix Riccati Equations
TL;DR: In this paper, the authors present matrix Riccati equations applicable to systems of quadratic ordinary differential equations and show that there is an exact solution available for matrix RICCati equations.
Journal ArticleDOI
Optimal control of linear time-varying systems via Fourier series
TL;DR: In this paper, the optimal control of linear time-varying systems with quadratic cost functional is obtained by Fourier series approximation, and the operational matrix of backward integration together with the product operational matrix are utilized to reduce the optimization problem to a set of simultaneous linear algebraic equations.
Journal ArticleDOI
Optimal control of linear distributed-parameter systems via polynomial series
TL;DR: In this article, the optimal control of a distributed-parameter system is simplified into the solution of a linear two-point boundary value problem, and, as a result, the optimal controller is obtained via a Taylor series.
Journal ArticleDOI
Solution of linear two-point boundary value problems and optimal control of time-varying systems by shifted Chebyshev approximations
Mohsen Razzaghi,Mehdi Razzaghi +1 more
TL;DR: In this paper, a method for finding the solution of a linear two-point boundary value problem with time-varying coefficients is discussed, where the transformation matrix relating the back vector to the current time vector together with the operational matrix are utilized to solve the two point boundary value problems.
Journal ArticleDOI
Solution of linear two-point boundary value problems via Fourier series and application to optimal control of linear systems
TL;DR: In this paper, a transformation matrix relating the back vector to the current time vector for the Fourier series is derived and utilized to solve the linear two-point boundary value problem, which can be applied to obtain the optimal control of linear systems subject to quadratic cost criteria.
References
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Book
Schaum's outline of theory and problems of state space and linear systems
TL;DR: Schaum's outline of theory and problems of state space and linear systems as mentioned in this paper, Schaum's outline, and the problems of solving state space problems in linear systems, is a good starting point for this paper.
Journal ArticleDOI
A computational solution for a Matrix Riccati differential equation
TL;DR: In this article, the solution to the Riccati equation is given in terms of the partition of the transition matrix and matrix differential equations for the partition are derived and are solved using computational methods.
Journal ArticleDOI
Solution of the matrix Riccati equation in optimal control
TL;DR: In this article, the solution to the Riccati equation is given in terms of the partition of the transition matrix and matrix differential equations are derived and solved using methods developed in the fields of free vibration theory and aircraft flutter analysis.
Journal ArticleDOI
An analytic solution for an algebraic matrix Riccati equation
TL;DR: In this paper, a procedure is given whereby an analytic solution may sometimes be found for a matrix algebraic equation, such as occurs in deterministic and stochastic optimization problems.