On the control of a linear functional- differential equation with quadratic cost
Riccati-like linear functional differential equation with quadratic cost, analyzing feedback control solution existence and uniqueness
Barnea, D. I.↗
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A quadratic performance index for a VTOL aircraft prefilter model reference attitude control system
Quadratic performance index for VTOL aircraft model reference attitude control system
Corliss, L. D.↗
Computing quadratic programming problems: Linear inequality and equality constraints
Algorithm for solving general quadratic programming problem with linear constraints
Hanson, R. J.↗
On quadratic optimization in distributed parameter systems
Distributed parameter systems described by parabolic differential equations in Hilbert space, discussing existence of optimal control based on quadratic cost criteria
Greenberg, S. G.↗
Equilibrium feedback control in linear games with quadratic costs
Equilibrium strategies for linear games with quadratic costs in Hilbert space, deriving nonlinear equation in allowed operator feedback spaces
Lukes, D. L.↗
Application of quadratic optimization to supersonic inlet control
The application of linear stochastic optimal control theory to the design of the control system for the air intake (inlet) of a supersonic air-breathing propulsion system is discussed. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant control systems are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain the best linear controller that minimizes the nonquadratic performance index. The two systems are compared on the basis of unstart prevention, control effort requirements, and sensitivity to parameter variations.
Lehtinen, B.↗
The role and use of the stochastic linear-quadratic-Gaussian problem in control system design.
The role of the linear-quadratic stochastic control problem in engineering design is reviewed in tutorial fashion. The design approach is motivated by considering the control of a nonlinear uncertain plant about a desired input-output response. It is demonstrated how a design philosophy based on (1) deterministic perturbation control, (2) stochastic state estimation, and (3) linearized stochastic control leads to an overall closed-loop control system. The emphasis of the paper is on the philosophy of the design process, the modeling issue, and the formulation of the problem; the results are given for the sake of completeness, but no proofs are included. The systematic off-line nature of the design process is stressed throughout.
Athans, M.↗
Quadratic performance index generation for optimal regular design.
Application of optimal control theory to practical problems has been limited by the difficulty of prescribing a performance index which accurately reflects design requirements. The task of deriving equivalent performance indices is considered in the present paper for a plant that is a completely controllable, scalar linear system with state feedback. A quadratic index is developed which leads to an optimal design performance satisfying some of the classical performance criteria.
Bullock, T. E.↗
Application of quadratic optimization to supersonic inlet control.
This paper describes the application of linear stochastic optimal control theory to the design of the control system for the air intake, the inlet, of a supersonic air-breathing propulsion system. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant controllers are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain a linear controller that minimizes the nonquadratic index. The two controllers are compared on the basis of unstart prevention, control effort requirements, and frequency response. It is concluded that while controls designed to minimize unstarts are desirable in that the index minimized is physically meaningful, computation time required is longer than for the minimum mean square shock position approach. The simpler minimum mean square shock position solution produced expected unstart frequency values which were not significantly larger than those of the nonquadratic solution.
Lehtinen, B.↗
Solution of quadratic matrix equations for free vibration analysis of structures.
An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.
Gupta, K. K.↗
Random vibrations of quadratic damping systems
An oscillating system with quadratic damping subjected to white noise excitation is replaced by a nonlinear, statistically equivalent system for which the associated Fokker-Planck equation can be exactly solved. The mean square responses are calculated and the optimum damping coefficient is determined with respect to the minimum mean square acceleration criteria. An application of these results to the optimization of automobile suspension damping is given.
Sireteanu, T.↗
Optimization of structures to satisfy a flutter velocity constraint by use of quadratic equation fitting
Using the first and the second derivative of flutter velocity with respect to the parameters, the velocity hypersurface is made quadratic. This greatly simplifies the numerical procedure developed for determining the values of the design parameters such that a specified flutter velocity constraint is satisfied and the total structural mass is near a relative minimum. A search procedure is presented utilizing two gradient search methods and a gradient projection method. The procedure is applied to the design of a box beam, using finite-element representation. The results indicate that the procedure developed yields substantial design improvement satisfying the specified constraint and does converge to near a local optimum.
Motiwalla, S. K.↗
Applications of a quadratic extended interior penalty function for structural optimization
A quadratic extended interior penalty function formulation especially well suited for second-order unconstrained optimization procedures is presented. Analytical derivatives of constraints and an approximate analysis technique are used. Minimum-mass design results are presented which indicate that the combination of these procedures can help make mathematical programming a useful optimization tool for large-order structural design problems with a large number of design variables and multiple constraints. Examples include statically loaded high- and low-aspect-ratio wings simultaneously subjected to stress, displacement, minimum gage and, in some cases, maximum strain constraints.
Haftka, R. T.↗
On the quadratic sampled-data regulator with unstable random disturbances
This paper is concerned with the design of a digital controller, optimizing a quadratic cost function, for a linear system subjected to plant disturbance. The disturbance is viewed as a Gaussian random process generated by a linear system which may be unstable. It is shown that the optimal control consists of the sum of two terms: the optimal control when no disturbance is present and a term depending on the estimates of the disturbance. Necessary and sufficient conditions for the convergence of the gain matrices is given.
Halyo, N.↗
A linear-quadratic-Gaussian control problem with innovations-feedthrough solution
The structure of the separation-theorem solution to the standard linear-quadratic-Gaussian (LQG) control problem does not involve direct output feedback as a consequence of the form of the performance index. It is shown that the performance index may be generalized in a natural fashion so that the optimal control law involves output feedback or, equivalently, innovations feedthrough (IF). Applications where this formulation may be advantageous are indicated through an examination of properties of the IF control law.
Platzman, L. K.↗
Closed-loop structural stability for linear-quadratic optimal systems
This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.
Wong, P. K.↗
The quarter-point quadratic isoparametric element as a singular element for crack problems
The quadratic isoparametric elements which embody the inverse square root singularity are used for calculating the stress intensity factors at tips of cracks. The strain singularity at a point or an edge is obtained in a simple manner by placing the mid-side nodes at quarter points in the vicinity of the crack tip or an edge. These elements are implemented in NASTRAN as dummy elements. The method eliminates the use of special crack tip elements and in addition, these elements satisfy the constant strain and rigid body modes required for convergence.
Hussain, M. A.↗
Closed-loop structural stability for linear-quadratic optimal system
This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that will not destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.
Wong, P. K.↗