Optimal control of the linear regulator with constant disturbances.
Optimal control problem for linear regulators with constant external disturbance
Johnson, C. D.↗
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On suboptimal controls.
Suboptimal control with high performance index as alternative in restricted class of optimal control problems
Verma, J. P.↗
Singular extremaloids in optimal control theory and the calculus of variations
Definitions of extremaloids in relation to optimal control problems and Lagrange problems based on Pontryagin principles
Straeter, T. A.↗
An algorithm for minimum energy control
Algorithm for fixed time minimum energy discrete optimal control problems of linear plants with convex constraints imposed on terminal state
Deparis, M.↗
On the removal of ill conditioning effects in the computation of optimal controls
Dual type method solving discrete optimal control problems with linear plants, convex cost and constraint taking into account dynamic structure
Polak, E.↗
On second order necessary conditions of optimality
Second order necessary conditions of optimality with straightforward application to nonlinear programming of optimal control problems
Messerli, E. J.↗
Sensitivity design of output feedback controllers
Output feedback control systems design, considering closed loop system sensitivity to plant parameters based on linear optimal control problem
Cassidy, J. F., Jr.↗
Necessary conditions for joining optimal singular and nonsingular subarcs
Necessary conditions for optimality of junctions between singular and nonsingular subarcs for singular optimal control problems
Mc Daniel, J. P.↗
Optimal control using imbedding of the terminal conditions
Use of imbedding theory to construct autonomous optimal control problems with free termination time
Montgomery, R. C.↗
Optimal control theory for non-scalar-valued performance criteria
The theory of optimal control for nonscalar-valued performance criteria is discussed. In the space, where the performance criterion attains its value, the relations better than, worse than, not better than, and not worse than are defined by a partial order relation. The notion of optimality splits up into superiority and non-inferiority, because worse than is not the complement of better than, in general. A superior solution is better than every other solution. A noninferior solution is not worse than any other solution. Noninferior solutions have been investigated particularly for vector-valued performance criteria. Superior solutions for non-scalar-valued performance criteria attaining their values in abstract partially ordered spaces are emphasized. The main result is the infimum principle which constitutes necessary conditions for a control to be a superior solution to an optimal control problem.
Gerring, H. P.↗
Bounded state variables and the calculus of variations
An optimal control problem with bounded state variables is transformed into a Lagrange problem by means of differentiable mappings which take some Euclidean space onto the control and state regions. Whereas all such mappings lead to a Lagrange problem, it is shown that only those which are defined as acceptable pairs of transformations are suitable in the sense that solutions to the transformed Lagrange problem will lead to solutions to the original bounded state problem and vice versa. In particular, an acceptable pair of transformations is exhibited for the case when the control and state regions are right parallelepipeds. Finally, a description of the necessary conditions for the bounded state problem which were obtained by this method is given.
Hanafy, L. M.↗
Bounded state space
This investigation is divided functionally into three different areas: (1) study of bounded state space, (2) nonlinear smoothing theory, and (3) system identification. (1) Study of bounded state space: necessary and sufficient conditions for an optimal control are obtained for a bounded state space optimal control problem. The difficulty of determining the so-called jump conditions is eliminated; however, the problem of determining the points where the response either enters or leaves the boundary still remains unsolved. (2) Nonlinear smoothing theory: nonlinear fixed-interval, fixed-point and fixed-lag smoothing of a random signal generated by a stochastic differential equation are investigated. Results on the asymptotic stability of a linear constant-parameter fixed-interval smoothing filter are obtained. (3) System identification: a particular stochastic modelling problem is solved. An Ito stochastic integral equation is used to mathematically model a black box having multiple inputs and multiple outputs. A new method for identifying system parameters is presented.
Eyman, E. D.↗
Minimum-energy control of a class of electrically driven vehicles.
A minimum-energy controller is designed and built for a class of electrically driven vehicles according to the theoretical concepts determined by the application of modern control theory. Theoretical results are obtained by making several justifiable assumptions in the dynamical equations of the system and solving the resulting stochastic optimal control problem by Bellman's dynamic programming technique. Several practical and economical considerations are taken into account for the mechanization of the minimum-energy control law.
Sahinkaya, Y. E.↗
The optimal control of merging aircraft - Implementation of the hybrid air traffic controller.
The control of merging aircraft is formulated as a finite-time, quadratic optimal control problem of a linear system with state and control constraints. The purpose of this paper is to demonstrate that the Hybrid Air Traffic Controller (HAC), which has been previously developed as a solution to this problem, may be easily implemented. Use is made of both the properties of the algebraic solution to the matrix Riccati equation and the structure of the linear model. This approach results in a real-time synthesis procedure for the HAC which does not rely on iterative numerical integration techniques.
Schatz, J. G.↗
An adaptive precision gradient method for optimal control.
This paper presents a gradient algorithm for unconstrained optimal control problems. The algorithm is stated in terms of numerical integration formulas, the precision of which is controlled adaptively by a test that ensures convergence. Empirical results show that this algorithm is considerably faster than its fixed precision counterpart.-
Klessig, R.↗
Optimal local control of flexible structures
The steady state solution of the linear quadratic optimal control problem with the constraint that only partial state information is available for feedback is derived. This development results in a systematic and computationally efficient approach for reducing the complexity of the control law for high order systems. Numerical examples and performance evaluation of (1) a simple fourth order system, and (2) a free-free flexible beam, are included.
Schaechter, D. B.↗
Stochastic control and the second law of thermodynamics
The second law of thermodynamics is studied from the point of view of stochastic control theory. We find that the feedback control laws which are of interest are those which depend only on average values, and not on sample path behavior. We are lead to a criterion which, when satisfied, permits one to assign a temperature to a stochastic system in such a way as to have Carnot cycles be the optimal trajectories of optimal control problems. Entropy is also defined and we are able to prove an equipartition of energy theorem using this definition of temperature. Our formulation allows one to treat irreversibility in a quite natural and completely precise way.
Brockett, R. W.↗
On maneuvering large flexible spacecraft using an annular momentum control device
A scheme for the control and maneuvering of a large flexible spacecraft by means of two flexible AMCD's using noncontacting magnetic suspension is presented. The system consists of a flexible vehicle, two flexible rings and a magnetic suspension and driving assembly. The necessary skewing of the rings for maneuvering of the vehicle is accomplished by moving the pairs of magnets along tracks distributed around the circumference of the vehicle. The equations of motion for each subsystem are derived by the Lagrangian approach. Attitude motions are described in terms of quasi-coordinates. For small vehicle angular rates and rings attitude motions, an ordering scheme can be used to separate the equations of motion according to the magnitude of the terms. The ordered equations of motion lead to a linear time-variant optimal control problem for the maneuvering of the spacecraft.
Oz, H.↗