Optimal Control Procedure Research Articles

The industrial implications of an optimal reflationary mix for the British economy

This paper derives an optimal reflationary mix for the next decade and comments on the industrial implications of this policy. The discussion is based on simulations of the multisectoral dynamic model of the UK economy developed by members of the Cambridge Growth Project. The results suggest that the concentration on macroeconomic policy alone may be misguided and that instruments which attack the roots of Britain's industrial problems should receive more attention. The paper also demonstrates that the optimal control procedure is a reliable tool for steering an economy towards a desired target trajectory and that this is feasible for very large econometric models.

Optimal control-system design for solar-tracking concentrators

An optimal control procedure is presented for minimising the sun tracking error of solar concentrators. The sun tracking system is a point-focusing collector which is subject to wind disturbance. The optimal control law considered herein is a proportional plus integral control, and the following two feedback schemes are used for the controller implementation: 1. state estimation via an observer; and 2. suboptimal control The observer is constructed to estimate the unmeasurable tracking error variables and designed optimally to minimise the deviation of estimated errors from actual error values. The suboptimal control, on the other hand, uses only the output variables available from sensor. Investigation of the comparative performances of the two schemes indicates that sub-optimal control is only marginally inferior and could therefore provide a satisfactory and cost-effective solution under the conditions assumed.

Stochastic control for linear discrete-time distributed-lag models

In an important class of linear stochastic control problems distributed-lag state or control variables appear in the dynamics or in the observations. Optimal control and estimation procedures are derived for such problems in discrete time. The results reduce computations from order N 3 in the usual methods to order N 2 they show the special structure of the time-lag controller and estimator more clearly ; and they correspond closely to the known results for the continuous-time case.

On economically based quality control decisions

A new approach to the problem of quality control is investigated. It is based on the theories and models developed for optimal maintenance policies for equipment subject to stochastic failure. Four alternative sampling/inspection procedures are examined. They are easy to implement, do not require the process operator to compute his own operating decisions, and are capable of finding optimal intervals between successive samplings/inspections. Both fixed and variable costs are included in the models. Relatively efficient algorithms have been developed for finding the optimal quality control procedures; this is due, partially, to the simple form of the objective function.

Computer-aided anaesthesia administration

Certain repetitive tasks of the anaesthesiologist are studied and modelled for automatic processing. These analyses make it possible for optimal control procedures to be programmed and administered by less trained anaesthesia professionals. A dynamic programming model is developed and validated with real data collected from several hospitals in the Cleveland, Ohio, area. By conjunctively monitoring certain transients in the anaesthesia administration process, the scarce supply of anaesthesiology manpower can be more efficiently deployed.

Optimal combination of control and observation: PMM vol. 35, no. 4, 1971, pp. 609–618

Optimal control under incomplete information i.e., under incomplete and inexact measurements of the state of the controlled plant, is of essential interest for practical control problems. In the case when the observer can modify, along with the control, also the measurement program, there arises various problems of the optimal choice of the control and of the observation process, one of which we consider in this paper. We show that under assumptions made on the characteristics of the control systems. Bellman's method and the maximum principle method can be applied for solving the problem under investigation, allowing us to find in a number of cases an explicit form of the optimal control and observation procedure. We remark that for deterministic systems the problem of the optimal combination of control and observation has been examined in monographs [1,2] in a formulation other than the one adopted here.

Matrix Quadratic Solutions

Matrix quadratic equation solution derivation applied in finding steady state solutions of Riccati differential equations with constant coefficients

An Iterative Procedure for Optimal Control of a System by Sampled Input

ABSTRACT Optimal control of a given system by an amplitude constrained sampled input is achieved by using an iterative procedure. The optimality is based on the minimization of a function ⊘ of the state x(tf), tf being the end of the time over which control is applied. The iterative procedure is based on taking the F-derivative )Todd 1962) of ⊘ when a small change in state and input control is assumed. A steepest descent procedure based on p-norm in control space is used to produce a small δ⊘ for a small change in control. This change δ for minimization of ⊘ is made negative to decrease ⊘ and the procedure is now iteratively continued till no significant improvement in ⊘ is possible without violating a constraint. This then specifies the input control over given (to tf). If tf is varied the minimum time problem can also be solved. Computational technique as well as examples are given.

Analysis of a Procedure for Controlling Discrete Stochastic Processes

In this paper an analysis is made of a specific procedure for controlling one independent variable described by a discrete stochastic process. Operational or actual tolerances are specified for the variable, that is, a range of acceptable variation is given. The control procedure involves the making of corrective actions to maintain the process within the actual tolerance. To accomplish this, effective tolerance limits (which are smaller than the actual tolerance limits) are set. Corrective actions are then made whenever the process exceeds the effective tolerance limits. A method for setting the effective tolerance limits to minimize the expected equilibrium cost of control per trial of operation is given. The method uses the assumption that corrective actions can be considered as recurrent events. From the theory of recurrent events, expressions for the probabilities of making corrective actions can be developed for inclusion in the equation which relates the cost measure to tolerance setting. By differentiating the cost measure with respect to the effective tolerance setting, a minimum solution can be obtained. The equations for minimization are developed first for general stochastic processes. The recurrent-event method is then extended to processes not necessarily returned to initial conditions by corrective actions. Specific equations are developed which optimize the control of discrete homogeneous Markov Gaussian processes. An example is given in which the optimal control procedure is analyzed as a function of the parameters of such a process.