On the separation theorem of stochastic control.
Optimal control and filtering problem for stochastic linear dynamic system reduced to independent equations
Wonham, W. M.↗
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On the degree of optimality of suboptimal controls.
Optimality degree of suboptimal controls
Aggarwal, J. K.↗
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.↗
Numerical methods for the solution of the degenerate nonlinear elliptic equations arising in optimal stochastic control theory.
Optimal control problems for Markov chains solved by iterative method, using nonlinear finite difference equations to approximate degenerate elliptic functions
Kleinman, A. J.↗
Hybrid computer methods for direct functional optimization
Control and trajectory optimization involves the minimization of a performance index (PI) of integral form where some optimal control law exists in a dynamic system. In this paper, a hybrid minicomputer with an adaptive random-search algorithm implements an iterative search for the optimal control. The search assumes that some initial control is randomly perturbed and a fast analog computer generates respective PI from the analog response of the dynamic system. An improved PI informs the digital computer to utilize the perturbed control as a basis for the next iteration; otherwise a new perturbation replaces the old perturbation in the next iteration. The search terminates when no further improvements occur.
Andrews, M.↗
A Closed-Loop Optimal Neural-Network Controller to Optimize Rotorcraft Aeromechanical Behaviour: Output from Two Sample Cases - Volume 2
A closed-loop optimal neural-network controller technique was developed to optimize rotorcraft aeromechanical behaviour. This technique utilities a neural-network scheme to provide a general non-linear model of the rotorcraft. A modem constrained optimisation method is used to determine and update the constants in the neural-network plant model as well as to determine the optimal control vector. Current data is read, weighted, and added to a sliding data window. When the specified maximum number of data sets allowed in the data window is exceeded, the oldest data set is and the remaining data sets are re-weighted. This procedure provides at least four additional degrees-of-freedom in addition to the size and geometry of the neural-network itself with which to optimize the overall operation of the controller. These additional degrees-of-freedom are: 1. the maximum length of the sliding data window, 2. the frequency of neural-network updates, 3. the weighting of the individual data sets within the sliding window, and 4. the maximum number of optimisation iterations used for the neural-network updates.
Leyland, Jane Anne↗
Neighboring optimal feedback control of multi- input nonlinear dynamical systems using discontinuous control
Neighboring optimal feedback control of multi-input nonlinear dynamic systems
Fluegge-Lotz, I.↗
Physics-Informed Neural Networks for PDE-Constrained Optimization and Control
The goal of optimal control is to determine a sequence of inputs for maximizing or minimizing a given performance criterion subject to the dynamics and constraints of the system under observation. This work introduces Control Physics-Informed Neural Networks (PINNs), which simultaneously learn both the system states and the optimal control signal in a single-stage framework that leverages the system’s underlying physical laws. While prior approaches often follow a two-stage process-modeling, the system first and then devising its control—the presented novel framework embeds the necessary optimality conditions directly into the network architecture and loss function. We demonstrate the effectiveness of the novel methodology by solving various open-loop optimal control problems governed by analytical, one-dimensional, and two-dimensional partial differential equations (PDEs).
97 MATHEMATICS AND COMPUTING↗
A mathematical basis for the design optimization of adaptive trusses in precision control
Optimal actuator placement schemes are presently studied for cases of adaptive truss precision control and prestressing control, with a view to the maximization of actuator efficiencies. In statically indeterminate truss structures, the optimal placement criteria and techniques differ, depending on whether the primary determinate structure is known. A suboptimal actuator-placement solution to the global optimization problem which combines displacement control and prestressing control is suggested, by combining the separate displacement control and prestressing control optimization results. Attention is given to the results obtained for the illustrative case of a two-bay, three-dimensional precision truss structure.
Das, S. K.↗
Differential geometric methods in system theory.
Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.
Brockett, R. W.↗
Lie theory and control systems defined on spheres
It is shown that in constructing a theory for the most elementary class of control problems defined on spheres, some results from the Lie theory play a natural role. To understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is the most natural departure from the usual linear system/vector space problems which have dominated control systems literature. For this reason results are compared with those previously available for the finite dimensional vector space case.
Brockett, R. W.↗
Control of an orbiting flexible square platform in the presence of solar radiation
An analysis is made of the dynamics of a thin, homogeneous, flexible square plate exposed to solar radiation disturbance. It is shown that only the first three flexible modes of the plate generate a first order net moment about the center of mass and that the solar radiation pressure does not influence the flexible modes of the plate for small-amplitude vibrations. In the absence of control, for a symmetrical homogeneous square platform, the solar radiation induces a steady angular drift about one of the body principal axes. For extremely flexible platforms, nominally oriented in the local horizontal plane, appreciable rigid modal amplitudes can be induced due to solar radiation, even in the presence of both active and passive control. Optimal control law and feedback gain values are obtained using linear quadratic Gaussian methods.
Bainum, P. M.↗
Maneuvering and vibration control of flexible spacecraft
This paper is concerned with the problem of slewing a large structure in space and suppressing any vibration at the same time. The structure is assumed to undergo large rigid-body motions and small elastic deformations. A perturbation method permits a maneuver strategy independent of the vibration control. Optimal control and pole placement techniques, formulated to include first-order actuator dynamics, are used to suppress the vibration during maneuver. The theory is illustrated by simultaneous maneuvering and vibration control of the Spacecraft Control Laboratory Experiment (SCOLE) model in a space environment.
Meirovitch, L.↗
Space stress and genome shock in developing plant cells
In the present paper I review symptoms of stress at the level of the nucleus in cells of plants grown in space under nonoptimized conditions. It remains to be disclosed to what extent gravity "unloading" in the space environment directly contributes to the low mitotic index and the chromosomal anomalies and damage that is frequently, but not invariably, demonstrable in space-grown plants. Evaluation of the available facts indicates that indirect effects play a major role and that there is a significant biological component to the susceptibility to stress damage equation as well. Much remains to be learned on how to provide strictly controlled, optimal environments for plant growth in space. Only after optimized controls become possible will one be able to attribute any observed space effects to lowered gravity or to other significant but more indirect effects of the space environment.
Review, Tutorial↗
Quadratic optimal cooperative control synthesis with flight control application
An optimal control-law synthesis approach is presented that involves simultaneous solution for two cooperating controllers operating in parallel. One controller's structure includes stochastic state estimation and linear feedback of the state estimates, while the other controller involves direct linear feedback of selected system output measurements. This structure is shown to be optimal under the constraint of linear feedback of system outputs in one controller. Furthermore, it is appropriate for flight control synthesis where the full-state optimal stochastic controller can be adjusted to be representative of an optimal control model of the human pilot in a stochastic regulation task. The method is experimentally verified in the case of the selection of pitch-damper gain for optimum pitch tracking, where optimum implies the best subjective pilot rating in the task. Finally, results from application of the method to synthesize a controller for a multivariable fighter aircraft are presented, and implications of the results of this method regarding the optimal plant dynamics for tracking are discussed.
Schmidt, D. K.↗
Optimal singular control with applications to trajectory optimization
A comprehensive discussion of the problem of singular control is presented. Singular control enters an optimal trajectory when the so called switching function vanishes identically over a finite time interval. Using the concept of domain of maneuverability, the problem of optical switching is analyzed. Criteria for the optimal direction of switching are presented. The switching, or junction, between nonsingular and singular subarcs is examined in detail. Several theorems concerning the necessary, and also sufficient conditions for smooth junction are presented. The concepts of quasi-linear control and linearized control are introduced. They are designed for the purpose of obtaining approximate solution for the difficult Euler-Lagrange type of optimal control in the case where the control is nonlinear.
Vinh, N. X.↗