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Deterministic optimal control, discussing Bellman dynamic programming method, Pontryagin maximum principle, orbital transfer, interplanetary guidance, etc
In the ordinary theory of optimal control (LQR and Kalman filter), the variances of the actuators and the sensors are assumed to be known (not related to the capacities of the devices). This assumption is not true in practice. Generally, a device with greater capacity to exert actuating forces and a sensor capable of sensing greater sensing range will generate noise of greater power spectral density. When the ordinary theory of optimal control is used to estimate the errors of the outputs in such cases it will lead to faulty results, because the capacities of such devices are unknown before the system is designed. The performance of the system designed by the ordinary theory will not be optimal as the variances of the sensors and the actuators are neither known nor constant. The interaction between the control system and structure could be serious because the ordinary method will lead to greater feedback (Kalman gain) matrices. Methods which can optimize the performance of systems when noises of the actuators and the sensors are related to their capacities are developed. These methods will result in smaller feedback (Kalman gain) matrix.
Deterministic optimal control, discussing Bellman dynamic programming method, Pontryagin maximum principle, orbital transfer, interplanetary guidance, etc
The maneuver considered in the present investigation involves the coplanar transfer of a spacecraft from a high earth orbit (HEO) to a low earth orbit (LEO). HEO can be a geosynchronous earth orbit (GEO). The basic concept utilized involves the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. The considered type of flight is also called synergetic space flight. With respect to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The Bolza problem of optimal control is stated, and the first-order optimality conditions for this problem are given. The one-arc approach, the two-arc approach, and the three-subarc approach are discussed. Attention is given to the Chebyshev problem of optimal control, details concerning aeroassisted orbital transfer (AOT), AOT optimization problems, and numerical experiments.
The purpose of this research effort was to begin the study of the application of hp-version finite elements to the numerical solution of optimal control problems. Under NAG-939, the hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element. One possible drawback is the increased computational effort within each element required in implementing hp-version finite elements. We are trying to determine whether this computational effort is sufficiently offset by the reduction in the number of time elements used and improved Newton-Raphson convergence so as to be useful in solving optimal control problems in real time. Because certain of the element interior unknowns can be eliminated at the element level by solving a small set of nonlinear algebraic equations in which the nodal values are taken as given, the scheme may turn out to be especially powerful in a parallel computing environment. A different processor could be assigned to each element. The number of processors, strictly speaking, is not required to be any larger than the number of sub-regions which are free of discontinuities of any kind.
Sensitivity design characteristics for feedback optimal controls
Book on applications of optimal control theory to computer controller design
Optimal control systems with pure time delay, discussing design parameters
Dual type method solving discrete optimal control problems with linear plants, convex cost and constraint taking into account dynamic structure
Linear time dependent stochastic optimal control with nonquadratic performance indices using function space approach
The problem of optimal control with a minimum time criterion as applied to a single boom system for achieving two axis control is discussed. The special case where the initial conditions are such that the system can be driven to the equilibrium state with only a single switching maneuver in the bang-bang optimal sequence is analyzed. The system responses are presented. Application of the linear regulator problem for the optimal control of the telescoping system is extended to consider the effects of measurement and plant noises. The noise uncertainties are included with an application of the estimator - Kalman filter problem. Different schemes for measuring the components of the angular velocity are considered. Analytical results are obtained for special cases, and numerical results are presented for the general case.
An iterative optical processor has been developed for applications in the optimal control of advanced sensor systems. The processor is designed for the realization of the Richardson algorithm on bipolar data, using as input a linear array of LEDs. The usefulness of the processor has been demonstrated by the solution of the linear quadratic regulator problem for the optimal control signals of the F100 turbofan engine. In this case study, the algebraic Riccati equation matrix was solved by the use of a modified Kleinman algorithm along with the Richardson algorithm applied to a system of linear algebraic equations. Preliminary experimental results demonstrate the gradual convergence of the processor.
A new approach is proposed for solving dual structural-control optimization problems for high-order flexible space structures where reduced-order structural models are employed. For a given initial structural dessign, a quadratic control cost is minimized subject to a constant-mass constraint. The sensitivity of the optimal control cost with respect to the stuctural design variables is then determined and used to obtain successive structural redesigns using a contrained gradient optimization algorithm. This process is repeated until the constrained control cost sensitivity becomes negligible. A numerical example is presented which demonstrates that this new approach effectively addresses the problem of dual optimization for potentially very high-order structures.
Optimal control solution for linear stationary regulator with quadratic performance index and fixed terminal time in terms of time invariant nonlinear control law
Computational algorithms and techniques for solving variable time optimal control problems
The design of a new position loop controller for the 34-meter High Efficiency Deep Space antennas using linear quadratic (LQ) optimal control techniques is discussed. The LQ optimal control theory is reviewed, and model development and verification are discussed. Families of optimal gain vectors are generated by varying weight parameters. Performance specifications were used to select a final gain vector. Estimator dynamics were selected and the corresponding gain vectors were computed. Final estimator selection was based on position, commanded rate, and estimator error responses.
Optimal control applications for electrothermal multijet systems for attitude control and station keeping of 24-hour synchronous satellite
An analytical solution is provided of a simple control problem. A rigid symmetric spinning satellite is considered and the optimal control torque vector is obtained. It is pointed out that optimal control can be obtained even with unequal torque magnitudes.