Search NASA⌕ Search

SEARCH · Search NASA

Results for “Riccati”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

State-Dependent Riccati Equation Regulation of Systems with State and Control Nonlinearities

The state-dependent Riccati equations (SDRE) is the basis of a technique for suboptimal feedback control of a nonlinear quadratic regulator (NQR) problem. It is an extension of the Riccati equation used for feedback control of linear problems, with the addition of nonlinearities in the state dynamics of the system resulting in a state-dependent gain matrix as the solution of the equation. In this paper several variations on the SDRE-based method will be considered for the feedback control problem with control nonlinearities. The control nonlinearities may result in complications in the numerical implementation of the control, which the different versions of the SDRE method must try to overcome. The control methods will be applied to three test problems and their resulting performance analyzed.

Beeler, Scott C.↗
NASA NTRS1970

A Riccati solution for Burgers' equation

Navier-Stokes equation approximation for nonhomogeneous case obtained by relating Burgers equation to Riccati equation through similarity transformation

Rodin, E. Y.↗
NASA NTRS1970

Constant directions of the Riccati equation

A constant direction of the Riccati equation associated with a class of singular discrete-time optimization problems is defined. The set of constant directions is completely characterized using a control viewpoint. Constant directions are used to reduce the computational complexity of the optimal system. Application to optimal filtering in colored noise is given.

Rappaport, D.↗
NASA NTRS1974

Algebraic Riccati equations in zero-sum differential games

The procedure for finding the closed-loop Nash equilibrium solution of two-player zero-sum linear time-invariant differential games with quadratic performance criteria and classical information pattern may be reduced in most cases to the solution of an algebraic Riccati equation. Based on the results obtained by Willems, necessary and sufficient conditions for existence of solutions to these equations are derived, and explicit conditions for a scalar example are given.

Johnson, T. L.↗
NASA NTRS1977

Integration-free interval doubling for Riccati equation solutions

Starting with certain identities obtained by Reid (1972) and Redheffer (1962) for general matrix Riccati equations (RE's), we give various algorithms for the case of constant coefficients. The algorithms are based on two ideas - first, relate the RE solution with general initial conditions to anchored RE solutions; and second, when the coefficients are constant, the anchored solutions have a basic shift-invariance property. These ideas are used to construct an integration-free, superlinearly convergent iterative solution to the algebraic RE. Preliminary numerical experiments show that our algorithms, arranged in square-root form, provide a method that is numerically stable and appears to be competitive with other methods of solving the algebraic RE.

Sidhu, G. S.↗
NASA NTRS1982

A general algorithm for solving the algebraic Riccati equation

The generalized eigenvalue problem provides a suitable framework for reliable solutions of many system theoretic, control, and estimation problems. A general algorithm for solving the matrix algebraic Riccati equation (ARE) which utilizes a pencil structure is described here. This algorithm avoids unnecessary inversion of cost or transition matrices, making it a numerically sound way to solve for the gains and/or ARE with singular quadratic costs, for cases satisfying detectability and stabilizability conditions. Examples are solution with discrete dead-beat control, noiseless measurements in Kalman filters and time-delays in discrete-time systems, which cause difficulties in the Hamiltonian standard eigenvalue problem formulation. The ARE algorithm implementatiton and numerical examples are shown.

Walker, R. A.↗
NASA NTRS1987

Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.

Ito, Kazufumi↗
NASA NTRS1988

An improved V-Lambda solution of the matrix Riccati equation

The authors present an improved algorithm for computing the V-Lambda solution of the matrix Riccati equation. The improvement is in the reduction of the computational load, results from the orthogonality of the eigenvector matrix that has to be solved for. The orthogonality constraint reduces the number of independent parameters which define the matrix from n-squared to n (n - 1)/2. The authors show how to specify the parameters, how to solve for them and how to form from them the needed eigenvector matrix. In the search for suitable parameters, the analogy between the present problem and the problem of attitude determination is exploited, resulting in the choice of Rodrigues parameters.

Bar-Itzhack, Itzhack Y.↗
NASA NTRS1991

Coupled Riccati equations for complex plane constraint

A new Linear Quadratic Gaussian design method is presented which provides prescribed imaginary axis pole placement for optimal control and estimation systems. This procedure contributes another degree of design freedom to flexible spacecraft control. Current design methods which interject modal damping into the system tend to have little affect on modal frequencies, i.e., they predictably shift open plant poles horizontally in the complex plane to form the closed loop controller or estimator pole constellation, but make little provision for vertical (imaginary axis) pole shifts. Imaginary axis shifts which reduce the closed loop model frequencies (the bandwidths) are desirable since they reduce the sensitivity of the system to noise disturbances. The new method drives the closed loop modal frequencies to predictable (specified) levels, frequencies as low as zero rad/sec (real axis pole placement) can be achieved. The design procedure works through rotational and translational destabilizations of the plant, and a coupling of two independently solved algebraic Riccati equations through a structured state weighting matrix. Two new concepts, gain transference and Q equivalency, are introduced and their use shown.

Strong, Kristin M.↗
NASA NTRS1990

Iterative computation of the optimal H(infinity) norm by using two-Riccati-equation method

The two-Riccati-equation method solution to a standard H(infinity) control problem can be used to characterize all possible stabilizing optimal or suboptimal H(infinity) controllers if the optimal or suboptimal H(infinity) norm is available in the literature. An iterative algorithm for computing the optimal H(infinity) norm is proposed. The algorithm employs fixed-point, double secant and bisection to guarantee a super linear convergence.

Chang, B. C.↗
NASA NTRS1993

Sensitivity analysis of Lyapunov and Riccati equations with application to controls-structures integrated design

Controls-structure integrated design is a complicated multidisciplinary design optimization problem which involves the state equations pertaining to open-loop eigenvalues and control laws. In order to alleviate the intensity of the computation, this study uses the adjoint variable method to derive sensitivity equations for the eigenvalue, Liapunov, and Riccati equations. These individual sensitivity equations are then combined together to form the multidisciplinary sensitivity equations for the control structure integrated design problems. A set of linear sensitivity equations, proportional in number to the number of performance functions involved in the optimization process, are solved. This proposed approach may provide a great saving in computer resources. The validity of the newly developed sensitivity equations is verified by numerical examples.

Hou, Gene↗
NASA NTRS2015

Systems and Methods for Parameter Dependent Riccati Equation Approaches to Adaptive Control

Systems and methods for adaptive control are disclosed. The systems and methods can control uncertain dynamic systems. The control system can comprise a controller that employs a parameter dependent Riccati equation. The controller can produce a response that causes the state of the system to remain bounded. The control system can control both minimum phase and non-minimum phase systems. The control system can augment an existing, non-adaptive control design without modifying the gains employed in that design. The control system can also avoid the use of high gains in both the observer design and the adaptive control law.

Kim, Kilsoo↗