On the behaviour of optimal linear sampled-data regulators†
TL;DR: In this paper, the optimal sampled-data control for linear processes with quadratic criteria is determined through application of the discrete minimum principle, and the effect of sampling on the closed-loop system's performance is investigated and the asymptotic behaviour of the optimal cost for large sampling periods is determined.
Abstract: Optimal sampled-data controls for linear processes with quadratic criteria are determined through application of the discrete minimum principle. The effect of sampling on the closed-loop system's performance is investigated and the asymptotic behaviour of the optimal cost for large sampling periods is determined. The resulting design method is applicable to continuous, sampled-data and discrete regulators.
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TL;DR: In this article, the authors summarize some results obtained for the adaptive control of the F-8C aircraft using the so-called MMAC method, including the selection of the performance criteria for both the lateral and the longitudinal dynamics, the design of the Kalman filters for different flight conditions, the identification aspects of the design using hypothesis testing ideas, and the performance of the closed-loop adaptive system.
Abstract: The purpose of this paper is to summarize some results obtained for the adaptive control of the F-8C aircraft using the so-called MMAC method. The discussion includes the selection of the performance criteria for both the lateral and the longitudinal dynamics, the design of the Kalman filters for different flight conditions, the "identification" aspects of the design using hypothesis testing ideas, and the performance of the closed-loop adaptive system.
345 citations
TL;DR: In this paper the optimal discrete-time linear-quadratic regulator problem is carefully presented and the basic results are reviewed.
Abstract: In this paper the optimal discrete-time linear-quadratic regulator problem is carefully presented and the basic results are reviewed. Dynamic programming is used to determine the optimization equations. Special attention is given to problems unique to the discrete-time case; this includes, for example, the possibility of a singular system matrix and a singular control-effort weighting matrix. Some problems associated with sampled-data systems are also summarized, e.g., sensitivity to sampling time, and loss of controllability due to sampling. Computational methods for the solution of the optimization equations are outlined and a simple example is included to illustrate the various computational approaches.
290 citations
TL;DR: The H/sub 2/-optimal control of continuous-time linear time-invariant systems by sampled-data controllers is discussed and the H/ Sub 2/ sampled- data problem is shown to be equivalent to a certain discrete-time H/ sub 2/ problem.
Abstract: The H/sub 2/-optimal control of continuous-time linear time-invariant systems by sampled-data controllers is discussed. Two different solutions, state space and operator theoretic, are given. In both cases, the H/sub 2/ sampled-data problem is shown to be equivalent to a certain discrete-time H/sub 2/ problem. Other topics discussed include input-output stability of sampled-data systems, performance recovery in digital implementation of analog controllers, and sampled-data control of systems with the possibility of multiple-time delays. >
168 citations
Cites background or methods from "On the behaviour of optimal linear ..."
...Section V extends the result in [ 17 ] and [6] to give a solution to the .#,-optimal sampleddata problem when the plant G is finitedimensional and heme admits a state-space representation....
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...The first work in this direction is that of Levis et al. in [ 17 ]....
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...In this case, the technique of [ 17 ] and [6] carries over to our X2 problem with sampled-data dynamic feedback....
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TL;DR: It is shown that the -'~2 optimal control problem for a sampled-data system is equivalent to a standard ,9~' 2 optimal control problems for a related discrete-time system.
142 citations
TL;DR: A survey of traditional design approaches and techniques for multirate digital control is presented in this paper, along with a brief survey of potential future areas of research and application of multi-rate control.
Abstract: Multiple sample rate digital control systems are of prominent interest in current control research, development, and applications. Modern aerospace vehicles and systems are described by high-order dynamic models which typically include phenomena covering a wide range of characteristic frequencies and instrumentation measurements available at multiple rates. A multirate control structure allows the designer to accommodate multiple information rates and implement required control computations within the finite computational capabilities of an on-board computer. In this paper the historical development, representative design approaches, and example applications of multirate digital control are outlined. A brief survey of traditional design approaches and techniques currently in development is presented. Potential future areas of research and application of multirate control are suggested and discussed.
115 citations
References
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87 citations
TL;DR: The optimal linear time-invariant sampled-data feedback control system is determined, and the general results are presented and are used to study the effect of changing the sampling time T upon the control-system performance.
Abstract: This paper deals with the control of the positions and velocities of high-speed vehicles in a single guideway. It is assumed that each and every vehicle measures its position and velocity every T seconds. The appropriate accelerations or decelerations to be applied to each vehicle are constrained to be constant during the sampling interval. Through the use of a control cost functional, which penalizes the system for any deviations from the desired headway and velocity, the required control accelerations and decelerations are obtained by deriving the system equations in discrete-time and, through the use of available results in the theory of discrete optimal control, the optimal linear time-invariant sampled-data feedback control system is determined. The general results are presented and are used to study the effect of changing the sampling time T upon the control-system performance. Since, in general, the cost of the communication system (in terms of required channel capacity, band-width, etc.) decreases...
25 citations