Showing papers on "Separation principle published in 1978"
TL;DR: A double inverted pendulum is successfully stabilized at the upright position by using a computer control using a linear functional observer and requires less computation time and controls the system in more stable way.
80 citations
TL;DR: In this paper, the problem of designing output deadbeat controllers having the property that the control input to the system converges to zero as time goes to infinity, for discrete-time multivariable linear systems is treated.
Abstract: This short paper Treats the problem of designing output deadbeat controllers having the property that the control input to the system converges to zero as time goes to infinity, for discrete-time multivariable linear systems. Two configurations of controllers are considered: one is of state feedback; the other is a dynamic controller using an observer. The existence of such controllers is examined, and the methods are presented for designing such controllers when they exist. The controller using a state feedback obtained in this paper is optimal in the sense that the controller settles the output in zero for any initial state in the minimum number of steps. On the other hand, the dynamic controller is not optimal in that sense, but it minimizes t , where t is defined as an integer such that the controller drives the output to zero in no more than t steps for any set of initial conditions of the system and the observer.
36 citations
TL;DR: The recently developed mathematical framework of Hilbert resolution space valued random processes is used to formulate and solve an abstract quadratic optimization problem and rediscovers and generalizes most of the classical estimation and control theory problem statements and results.
Abstract: The recently developed mathematical framework of Hilbert resolution space valued random processes is used to formulate and solve an abstract quadratic optimization problem. By particularizing the description of the operators appearing in the statement and solution formula of the problem, one rediscovers and generalizes most of the classical estimation and control theory problem statements and results. These include, among others, the Wiener smoothing prediction filter, the Kalman regulator, the Kalman-Bucy filter, the stochastic control separation principle and the more recent Youla-Jabr-Bongiorno optimal servo problem solution.
33 citations
01 Jan 1978
28 citations
TL;DR: It is shown that the one-step delay sharing system is a special case satisfying this condition and a counterexample is given to the conjecture that the separation will hold for the more-than-one- step delay sharing systems.
24 citations
TL;DR: In this article, an adaptive control technique to improve the flying qualities of an aircraft in turbulence was investigated and the approach taken was to obtain maximum likelihood estimates of the unknown coefficients of the aircraft system and then, using these estimates along with the separation principle, to define the stochastic optimal control.
Abstract: An adaptive control technique to improve the flying qualities of an aircraft in turbulence was investigated. The approach taken was to obtain maximum likelihood estimates of the unknown coefficients of the aircraft system and then, using these estimates along with the separation principle, to define the stochastic optimal control. The maximum likelihood estimation technique that accounts for the effects of turbulence provided good estimates of the unknown coefficients and of the turbulence. The assessment of the stochastic optimal control based on the maximum likelihood estimates showed that the desired effects were attained for the regulator problem of minimizing pitch angle and the tracking problem of requiring normal acceleration to follow the pilot input.
20 citations
TL;DR: In this paper, an observer which uses only one output of the system to estimate the states is developed and used to implement an optimal state feedback control strategy on the micro-alternator system.
Abstract: Experimental results obtained from the application of modern control techniques to a microalternator system are presented. An observer which uses only one output of the system to estimate the states is developed and used to implement an optimal state feedback control strategy on the microalternator system. Extensive tests of the proposed control scheme are effected over a wide range of conditions which include close-up three phase faults and operation beyond the dynamic stability limit of the system without supplementary control. These: experimental results, supported by extensive digital computer simultation indicate the effectiveness of the control scheme in improving the systee performance in practice.
13 citations
TL;DR: In this paper, a procedure for designing an optimal observer for a linear continuous time invariant system is described, where the parameters of the observer are chosen so as to assign its eigenvalues to desired locations and at the same time a measure of the deviation of the estimate of the observed state from its actual value is minimized.
Abstract: A procedure for designing an optimal observer for a linear continuous time invariant system is described in this paper. The parameters of the observer are chosen so as to assign its eigenvalues to desired locations and at the same time a measure of the deviation of the estimate of the observed state from its actual value is minimized, A numerical example is included to show that the estimate of the state obtained by the optimal observer is much closer to the actual state than the estimate obtained from another observer with the same eigenvalues as the optimal observer.
11 citations
10 citations
TL;DR: In this article, the optimal control problem of time-delay systems with partial state measurements is studied through the application of a Walsh function expansion, and the main purpose of the paper is to provide a computational technique for determining the expansion coefficient matrices for both the system state and the observer output.
Abstract: The optimal control problem of time-delay systems with partial state measurements is studied through the application of a, Walsh function expansion. The main purpose of the paper is to provide a computational technique for determining the expansion coefficient matrices for both the system state and the observer output. It is shown that the known initial conditions of the state and the observer can be used iteratively to compute the state and the observer at any subsequent time and thus implement the optimal controller. Also, by subdividing the time interval of interest, the procedure is simplified such that it does not involve any matrix inversion.
7 citations
TL;DR: In this article, the relationship between the three different optimality conditions for controlled jump Markov processes is analyzed in the case of a partially observed controlled-jump Markov process, where the optimality condition is defined in terms of the probability that the Markov Markov Process is complete.
Abstract: The relationship between the three different optimality conditions for controlled jump processes mentioned in the title is exhibited in the case of a partially observed controlled jump Markov process.
TL;DR: In this paper, the problem of designing an observer insensitive to the variation of system parameters is considered, and the existence of the K-insensitive observer is examined, where possible, the class of the observers is obtained.
TL;DR: In this article, a class of finite-state, finite-memory stochastic control problems is considered and a minimum principle is derived, and signaling strategies are defined and related to the necessary conditions of the minimum principle.
Abstract: A class of finite-state, finite-memory stochastic control problems is considered. A minimum principle is derived. Signaling strategies are defined and related to the necessary conditions of the minimum principle. Min-H algorithms for the problem are described.
TL;DR: In this article, an observer-estimator is derived by using the Luenberger observer relation for the reconstruction of the system state from the uncorrupted system outputs as a constraint on the Kalman filter differential equation for the state estimate.
Abstract: This paper considers the problem of designing an observer-estimator for the state of a continuous-time, finite-dimensional, linear, stochastic system having input disturbance noise and some outputs which are not corrupted by measurement noise. The observer-estimator is derived by using the Luenberger observer relation for the reconstruction of the system state from the uncorrupted system outputs as a constraint on the Kalman filter differential equation for the state estimate which involves the noise-corrupted system outputs. In this fashion both types of system output are utilized by the observer-estimator. The optimal value of the observer-estimator parameter matrices are found by resorting to variational techniques.
01 Jan 1978
01 Jul 1978
TL;DR: In this article, Luenberger's minimal-order observer is used as an alternate to the Kalman filter for obtaining state estimates in linear discrete-time stochastic systems, where optimality is in the mean square sense.
Abstract: : This report investigates the idea of utilizing Luenberger's minimal-order observer as an alternate to the Kalman filter for obtaining state estimates in linear discrete time stochastic systems. More specifically, this dissertation presents a solution to the problem of construction as optimal minimal order observer for linear discrete time stochastic systems where optimality is in the mean square sense. The approach taken in this report leads to a completely unified theory for the design of optimal minimal-order observers and is applicable to both time-varying and time-invariant linear systems. To illustrate the theory and application of the observer designs developed in the dissertation, the problem of designing a radar tracking system is considered. Examples are included which illustrate clearly the practicality and usefulness of the proposed optimal observer design technique. Finally, a host of topics for future research is presented in the hope of stimulating further research in the domain of observer theory.
TL;DR: In this article, it is shown that the maximum principle in optimal control and the min-max principle in differential games are consequences of a certain global principle, which is stated in this paper.
Abstract: It is shown that the maximum principle in optimal control and the min-max principle in differential games are consequences of a certain global principle which is stated here.
TL;DR: The choice of a particular canonical representation for the system is shown to lead to a simple design procedure and the resulting observer is shown also to possess the minimum-time state-estimation property.
Abstract: The problem of constructing an observer for a discrete linear system so as to minimize a quadratic function of the state estimation error is considered. The choice of a particular canonical representation for the system is shown to lead to a simple design procedure. The resulting observer is shown also to possess the minimum-time state-estimation property.
01 Jan 1978
TL;DR: The procedure which realizes the minimum-time system identification and state observation is presented and numerical examples are given to illustrate the effectiveness of the procedure.
Abstract: This paper discusses a minimum-time adaptive observer and state regulator for linear discrete systems. A necessary and sufficient condition for the identifiability of the system is obtained in terms of the system structure and its input signal. The procedure which realizes the minimum-time system identification and state observation is presented. Numerical examples are given to illustrate the effectiveness of the procedure. An application of the adaptive observer is given for a minimum-time regulator problem for linear unknown plant.
01 Jan 1978
TL;DR: This paper considers the problem of finding optimal locations for sensors and controllers for stochastic regulator problems for evolution equations using a semigroup approach and the separation principle.
Abstract: In this paper we consider the problem of finding optimal locations for sensors and controllers for stochastic regulator problems for evolution equations using a semigroup approach and the separation principle. The existence of an optimal location is shown under very general assumptions. Then the theory is illustrated by specializing to a heat equation and some computational results are presented.
14 May 1978
TL;DR: Here the authors have briefly sketched what, in their opinion, appears to be a program for the development of computer codes useful in optimal control theory, taking into account the importance of feedback decisions in control.
Abstract: Here we have briefly sketched what, in our opinion, appears to be a program for the development of computer codes useful in optimal control theory. Taking into account the importance of feedback decisions in control, it has been shown that the methods available for solving classical variational problems and their associated BVP may not be suitable for optimal control considerations. It can only be hoped that some of the problems indicated here will soon be addressed by the computer community and that efficient, widely available codes for optimal control will soon become available.