A linearquadratic optimal controlproblem with coexisting initial and persistent disturbances is studied. Upper and lower values and relevant algebraic Riccati equations (ARE for short) are introduced. Various relati...
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A linearquadratic optimal controlproblem with coexisting initial and persistent disturbances is studied. Upper and lower values and relevant algebraic Riccati equations (ARE for short) are introduced. Various relations among these values are presented. The solvability of the resulting AREs is shown to be closely related to the solvability of the original optimal controlproblem. A formula is obtained for the solution of one of the AREs, which is of nonstandard form. Several unexpected features of the original problem are revealed from the standpoint of differential games. Some known results on the so-called H(infinity) optimal controlproblem are recovered.
This Note has presented the analytic derivation of the optimal closed-loop guidance law for a finite-bandwidth homing missile intercepting a maneuvering target and has provided a simple analytic means of solving the m...
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This Note has presented the analytic derivation of the optimal closed-loop guidance law for a finite-bandwidth homing missile intercepting a maneuvering target and has provided a simple analytic means of solving the matrix Riccati differential equation. The resulting optimal guidance law agrees with the result obtained by Cottrel and Asher. The major contribution of this Note lies in the analytic solution of the matrix Riccati differential equation.
For a host of dynamic systems, periodic motion is more efficient than steady-state operation. This work focuses on atmospheric fuel-efficient periodic flight. To understand some of the generic properties of periodic o...
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For a host of dynamic systems, periodic motion is more efficient than steady-state operation. This work focuses on atmospheric fuel-efficient periodic flight. To understand some of the generic properties of periodic optimal flight, the theoretical aspects are presented, which form the basis for the numerical computation of periodic optimal paths. Furthermore, the simplest problem for which periodic optimal control can be induced is formulated and various solutions based on asymptotic analysis are given. Intuitive physical mechanisms that contribute to producing periodic optimal flight are discussed on the basis of various levels of approximation of the aircraft dynamic models and upon perturbation analysis about the steady-state cruise path. The performance improvement and the dramatic periodic optimal flight path of a hypersonic vehicle are computed. To mechanize this flight path, a neighboring optimum perturbation guidance law is developed and its performance is presented.
Application of filters for the frequency weighting of Markov parameters (pulse response functions) is described in relation to system/observer identification. The time domain identification approach recovers a model t...
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Application of filters for the frequency weighting of Markov parameters (pulse response functions) is described in relation to system/observer identification. The time domain identification approach recovers a model that has a pulse response weighted according to frequency. The identified model is composed of the original system and filters. The augmented system occurs in a form that can be used directly for frequency-weighted linearquadraticcontroller design. Data from either single or multiple experiments can be used to recover the Markov parameters. Measured acceleration signals from a truss structure are used for system identification and the model obtained is for frequency-weighted controller design. The procedure makes the identification and controller design complementary problems.
Gaps in the derivation of early fixed-interval smoothers are filled in. Particular attention is paid to the use of the yariational approach introduced by Bryson and Frazier. The notion of complementary models introduc...
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A simple iterative algorithm has been presented for selecting terminal penalty weighting matrices for linear-quadraticcontrolproblems. The algorithm selects a weighting matrix which yields acceptable system performa...
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A simple iterative algorithm has been presented for selecting terminal penalty weighting matrices for linear-quadraticcontrolproblems. The algorithm selects a weighting matrix which yields acceptable system performance, while avoiding the large changes in magnitude in final values of the feedback gains. The algorithm is made computationally efficient by using closed-form solutions for the time-varying Riccati equation and the closed-loop system response. The method is heuristic, but offers a systematic approach to terminal weight selection.
The laws describing modern guidance systems are based on the methods of optimal control. This note compares an angular guidance law optimized by the adjoint technique and a metric law comprising an optimal estimator c...
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The laws describing modern guidance systems are based on the methods of optimal control. This note compares an angular guidance law optimized by the adjoint technique and a metric law comprising an optimal estimator connected to a terminal controller forcing the estimated miss distance to zero. The terms of comparison are miss distance and realizability. An analytical solution is given for one specific but significant case.
linear quadratic control problems are considered where frequency-dependent weighting on the control is assumed. When high frequencies are weighted more heavily than low frequencies, two qualitative conclusions can be ...
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A generalized singular linearquadraticcontrol technique is developed to design an optimal trajectory tracking system. The output feedback control law is designed using this technique. The feedback gain matrix is syn...
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