Showing papers on "Separation principle published in 1976"

Introduction to Control Theory

Abstract: Introduction PART I: ORDINARY CONTROL THEORY 1. Ordinary linear systems 2. Feedback control and integral action 3. Stability of feedback systems 4. Root locus diagrams 5. Transfer functions for controllers 6. Nonlinear systems PART II: OPTIMAL CONTROL THEORY 7. Linear state equations and their properties 8. Optimal LQP control 9. Optimal, linear, feedback controllers 10. Optimal control theory PART III: STOCHASTIC CONTROL THEORY 11. Probability and random processes 12. Estimating uncertain states 13. Optimal stochastic control 14. Information and feedback control

Minimal order state observers for bilinear systems

Abstract: This paper considers a minimal order state observer for a bilinear system. The given observer is an extension of one for a linear system and can be designed without considering inputs because the estimation error is made to be independent of inputs. The necessary condition for the existence of a minimal order observer and a standard form of a bilinear system satisfying this condition are presented. A standard form of a minimal order state observer is also obtained and the design procedure of this observer is shown. As an example, the observer of a d.c. motor is designed.

Decentralized stochastic control with delayed sharing information pattern

Abstract: The control of discrete time nonlinear stochastic systems under an n -step-delay sharing pattern is considered. Nonclassical separation properties are derived. It is shown that only the "common data" to the controllers are to be used for estimation purposes. Furthermore, for LQG systems with a delayed sharing information pattern, the best linear controller is shown to obey a separation principle.

On the exact model matching controller design

Abstract: The problem of designing a static state feedback controller which matches a given multivariable system to a desired ideal system (model) is treated. The system under control is assumed in state space form while the model is assumed in transfer matrix form. An algorithm is developed which separates the conditions which must be satisfied by the system under control and the model to be matched from the equations which must be solved to find the gains of the feedback controller. Two examples are included.

A class of systems with the same observer

Abstract: Compatibility of the observer designed for a linear time-invariant system is discussed and a class of systems to which a given observer is compatible is explicitly stated. This class gives allowable variations of system parameters such that the designed observer is still compatible to the system when the system changes its characteristics. An application to the regulator problem is described briefly.

The Separation Principle in Stochastic Control via Girsanov Solutions

Abstract: This paper deals with the separation of estimation and control for linear systems with additive Gaussian white noise and nonquadratic cost function. All measurable functions of the observations are admissible as controls, the corresponding solutions being defined by the Girsanov measure transformation. The separation principle is established, under certain conditions, if the dimension of the observation process is equal to that of the state; if there are fewer observations, then additional ones of arbitrarily low signal-to-noise ratio can be adjoined such that there is a separated policy based on the augmented observations which is superior to any policy using the original observations.

A separation theorem for the stochastic sampled-data LQG problem†

Abstract: This paper considers the control of a continuous linear plant disturbed by white plant noise when the control is constrained to be a piecewise constant function of time; ie a stochastic sampled-data system The cost function is the integral of quadratic error terms in the state and control, thus penalizing errors at every instant of time while the plant noise disturbs the system continuously The problem is solved by reducing the constrained continuous problem to an unconstrained discrete one It is shown that the separation principle for estimation and control still holds for this problem when the plant disturbance and measurement noise are Gaussian

Feedback control systems with low-frequency stochastic disturbances

Abstract: Optimal controllers are investigated for linear feedback systems with low-frequency stochastic disturbances, measurement noise and power constraint on the control signal. By adoption of simplified models closed-form expressions are obtained for the optimal controller. These expressions facilitate the study of the controller structure and of the stability margin of the optimal system. It is found that if measurement noise is neglected, the resulting optimal system has a very poor stability margin. If the power constraint on the control signal is neglected, the resulting system is usually again impractical because it. requires excessive control power. On the other hand, if both measurement noise and power constraint are taken into account in the design, the system has a good stability margin, at least in low-order cases. Furthermore, the optimal controller approximates a conventional type such as proportional plus integral. It is concluded that in most cases it is essential to take into account (a) low-freq...

Estimation of characteristics and stochastic control of an aircraft flying in atmospheric turbulence

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 accounted 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.

A feedback near-optimum control for nonlinear systems

Abstract: A near-optimum feedback controller based on the sensitivity of state and control functions with respect to a coupling parameter is introduced for nonlinear systems. The method makes use of Pontryagin's maximum principle and the Riccati formulation of the linear regulator problem. A numerical example with previously known results is solved using the method.

Discrete-Time Optical Stochastic Observers

Abstract: Publisher Summary This chapter reviews the status of observer theory and presents the results obtained in stochastic observer theory as applied to discrete-time linear systems. The Kalman filter solves the problem of state estimation in the mean-square sense for linear discrete-time stochastic systems, numerical and computational problems associated with the real-time implementation of Kalman filters have led researchers to seek out computationally simpler solutions to the minimum mean-square state-estimation problem. The chapter reviews some of the alternate approaches to the discrete-time state-estimation problem based on the extension of Luenberger's observer theory to stochastic systems. The chapter discusses the notion of an observer for discrete stochastic systems. It presents a method of constructing a reduced-order observer estimator. The case of some perfect measurements is considered. The interpretations of Brammer's optimal observer, namely, a Kalman-type algorithm and a Luenberger-type algorithm have been presented. Computational advantages of the reduced-order observer algorithm have been presented.

Eigenvalue control in distributed-parameter systems with parameter variations

Abstract: The state-feedback eigenvalue control problem is studied for a class of distributed-parameter systems subject to parameter variations about given nominal values. The feedback controller derived contains two parts, namely, the nominal controller which is based upon the nominal open-loop system parameter values, and the correcting controller which is designed such as to compensate for the parameter variations. Actually, the resulting eigenvalue controller may be regarded as a controller which reduces the sensitivity of the closed-loop eigenvalues to variations of the open-loop parameters. Two examples are worked out to support the theoretical results.

A new adaptive observer

Abstract: : An adaptive observer is defined as one which estimates the state variables and parameters of an unknown stable linear time-invarient plant from its input-output data. At the present time, there are two distinct approaches to the design of adaptive observers for a plant whose input output behavior can be represented by an n-th order differential equation. In the first approach, the observer is of the same order as the plant and is referred to as a minimal (order) observer. Using the second approach, a non-minimal observer of order (2n-1) is obtained. Minimal observers are considerably more difficult to synthesize than non-minimal observers and require the generation of additional signals for the stabilization of the adaptive loop. However, they have the advantage of yielding simultaneously both parameter and state estimates of the plant. Non-minimal observers are considerably simpler in structure both the n state variables of the plant have to be estimated from the available (2n-1) state variables of the observer. In this brief paper, a new observer is proposed which appears to combine the advantages of the two types of observers described above, With this observer, the parameter estimates of the plant are directly obtained with a structure which is no more complex than that of a non-minimal observer which is widely used at the present time. The parameter estimates are simultaneously used to determine directly the state estimates of the plant. Under certain conditions, the new observer has a faster rate of convergence than the observers known at present, which makes it particularly attractive for use in the control problem.