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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Direct computation of optimal control of forced linear system

It is known that the optimal control of a forced linear system may be reduced to that of tracking the system without forces. The solution of the tracking problem is available via the costate variables method. This procedure is computationally expensive for large order systems. It requires solution of matrix Riccati equation and two final value problems. An alternate approach is outlined for the direct computation of the optimal control. Instead of Riccati equation, a matrix Volterra integral must be solved. For this purpose two computational schemes are described, and an illustrative example is given. The results compare favorably with the classical solution. This alternative approach may be especially useful for the control of large space structure where large order models are required.

Utku, S.↗
NASA NTRS1983

Approximation of feedback controls for parabolic systems

An approximation framework is presented for computation (in finite dimensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is indicated how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.

Banks, H. T.↗
NASA NTRS1983

Orbit structure of Hamiltonian systems arising from Lie transformation group actions

This paper associates the Riccati group and its group action on linear-quadratic optimal control problems to the action of a Lie transformation group on a set of Hamiltonian matrices. In this Lie theoretic setting results are presented concerning the associated orbit structure and the structure of the group itself. These results are of importance in understanding the solution structure of matrix Riccati differential equations, and thus also of importance in linear-quadratic optimal control.

Garzia, M. R.↗
NASA NTRS1985

Chandrasekhar equations for infinite dimensional systems

The existence of Chandrasekhar equations for linear time-invariant systems defined on Hilbert spaces is investigated. An important consequence is that the solution to the evolutional Riccati equation is strongly differentiable in time, and that a strong solution of the Riccati differential equation can be defined. A discussion of the linear-quadratic optimal-control problem for hereditary differential systems is also included.

Ito, K.↗
NASA NTRS1986

Time scale analysis of a closed-loop discrete optimal control system

A two-time scale discrete control system is considered. The closed-loop optimal linear quadratic (LQ) regulator for the system requires the solution of a full-order algebraic matrix Riccati equation. Alternatively, the original system is decomposed into reduced-order slow and fast subsystems. The closed-loop optimal control of the subsystems requires the solution of two algebraic matrix Riccati equations of order lower than that required for the full-order system. A composite, closed-loop suboptimal control is created from the sum of the slow and fast feedback optimal controls. Numerical results obtained for an aircraft model show a very close agreement between the exact (optimal) solutions and computationally simpler composite (suboptimal) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the closed-loop optimal control of digital flight systems.

Naidu, D. S.↗
NASA NTRS1987

Factorization and the synthesis of optimal feedback kernels for differential-delay systems

A combination of ideas from the theories of operator Riccati equations and Volterra factorizations leads to the derivation of a novel, relatively simple set of hyperbolic equations which characterize the optimal feedback kernel for the finite-time regulator problem for autonomous differential-delay systems. Analysis of these equations elucidates the underlying structure of the feedback kernel and leads to the development of fast and accurate numerical methods for its computation. Unlike traditional formulations based on the operator Riccati equation, the gain is characterized by means of classical solutions of the derived set of equations. This leads to the development of approximation schemes which are analogous to what has been accomplished for systems of ordinary differential equations with given initial conditions.

Milman, Mark M.↗
NASA NTRS1989

State-space solutions to standard H2 and H(infinity) control problems

Simple state-space formulas are derived for all controllers solving the standard H(infinity) problem of finding, for a given number gamma greater than 0, all controllers such that the H(infinity) norm of the closed-loop transfer function is (strictly) less than gamma. It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma squared. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive stable free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e., H2) theory. A standard H2 solution is developed in parallel.

Doyle, John C.↗
NASA NTRS1990

Robust control of systems with real parameter uncertainty and unmodelled dynamics

Two significant contributions have been made during this research period in the research 'Robust Control of Systems with Real Parameter Uncertainty and Unmodelled Dynamics' under NASA Research Grant NAG-1-1102. They are: (1) a fast algorithm for computing the optimal H(sub infinity) norm for the four-block, the two block, or the one-block optimal H(sub infinity) optimization problem; and (2) a construction of an optimal H infinity controller without numerical difficulty. In using GD (Glover and Doyle) or DGKF (Doyle, Glover, Khargonekar, and Francis) approach to solve the standard H infinity norm which required bisection search. In this research period, we developed a very fast iterative algorithm for this computation. Our algorithm was developed based on hyperbolic interpolations which is much faster than any existing algorithm. The lower bound of the parameter, gamma, in the H infinity Riccati equation for solution existence is shown to be the square root of the supremum over all frequencies of the maximum eigenvalue of a given transfer matrix which can be computed easily. The lower band of gamma such that the H infinity Riccati equation has positive semidefinite solution can be also obtained by hyperbolic interpolation search. Another significant result in this research period is the elimination of the numerical difficulties arising in the construction of an optimal H infinity controller by directly applying the Glover and Doyle's state-space formulas. With the fast iterative algorithm for the computation of the optimal H infinity norm and the reliable construction of an optimal H infinity controller, we are ready to apply these tools in the design of robust controllers for the systems with unmodelled uncertainties. These tools will be also very useful when we consider systems with structured uncertainties.

Chang, Bor-Chin↗
NASA NTRS1991

Optimal control study for the Space Station Solar Dynamic power module

The authors present the design of an optimal control system for the Space Station Freedom's Solar Dynamic Fine Pointing and Tracking (SDFPT) module. A very large state model of six rigid body modes and 272 flexible modes is used in conjunction with classical LQG optimal control to produce a full-order controller which satisfies the requirements. The results obtained are compared with those of a classically designed PID (proportional plus integral plus derivative) controller that was implemented for a six-rigid-body-mode forty-flexible-mode model. A major difficulty with designing LQG controllers for large models is solving the Riccati equation that arises from the optimal formulation. A Riccati solver based on a Pade approximation to the matrix sign function is used. A symmetric version of this algorithm is derived for the special class of Hamiltonion matrices, thereby yielding, for large problems, a nearly twofold speed increase over a previous algorithm.

Papadopoulos, P. M.↗
NASA NTRS1992

A parameterization of minimal plants

The authors present the input-normal Riccati parameterization which allows a minimal plant (A, B, C, D) to be represented completely by its B, C, and D matrices. In addition to the basic parameterization, they present useful gradient expressions for a cost functional J(A, B, C, D) when the plant is restricted to the input-normal Riccati form. The parameterization is valid for both stable and unstable, and continuous-time and discrete-time systems.

Davis, L.↗
NASA NTRS2000

An Indirect Mixed-Sensitivity Approach to Microgravity Vibration Isolation: The Exploitation of Kinematic Coupling In Frequency-weighting Design-Filter Selections

Many space-science experiments need an active isolation system to provide them with the requisite microgravity environment. The isolation systems planned for use with the International Space Station have been appropriately modeled using relative position relative velocity, and acceleration states. In theory, frequency-weighting design filters can be applied to these state-space models, in order to develop optimal H2 or mixed-norm controllers with desired stability and performance characteristics. In practice, however, the kinematic coupling among the various states can lead, through the associated frequency-weighting-filters, to conflicting demands on the Riccati design "machinery." The results can be numerically ill-conditioned regulator and estimator Riccati equations and/or reduced intuition in the design process. In addition, kinematic coupling can result in a redundancy in the demands imposed by the frequency weights. Failure properly to account for this type of coupling can lead to an unnecessary increase in controller dimensionality and, in turn, controller complexity. This paper suggests a rational approach to the assignment of frequency-weighting design filters, in the presence of the kinematic coupling among states that exists in the microgravity vibration isolation problem.

Hampton, R. David↗
NASA NTRS2000

An Indirect Mixed-Sensitivity Approach to Microgravity Vibration Isolation: The Exploitation of Kinematic Coupling In Frequency-Weighting Design-Filter Selections

Many space science experiments need an active isolation system to provide them with the requisite microgravity environment. The isolation systems planned for use with the International Space Station have been appropriately modeled using relative position, relative velocity, and acceleration states. In theory, frequency design filters can be applied to these state-space models, in order to develop optimal H, or mixed-norm controllers with desired stability- and performance characteristics. In practice. however, the kinematic coupling among the various states can lead, through the associated frequency-weighting-filters, to conflicting demands on the Riccati design "machinery." The results can be numerically ill-conditioned regulator and estimator Riccati equations and/or reduced intuition in the design process. In addition, kinematic coupling can result in a redundancy in the demands imposed by the frequency weights. Failure properly to account for this type of coupling can lead to an unnecessary increase in controller dimensionality and, in turn, controller complexity. This paper suggests a rational approach to the assignment of frequency weighting design filters, in the presence of the kinematic coupling among states that exists in the microgravity vibration isolation problem.

Hampton, R. David↗
NASA NTRS1966

Matrix quadratic solutions.

Matrix quadratic equation solution derivation applied in finding steady state solutions of Riccati differential equations with constant coefficients

OPTIMAL CONTROL↗