Showing papers on "Separation principle published in 1982"

An observer design for linear systems with unknown inputs

Abstract: A method is presented for designing an observer for the state of a linear time-invariant system with unknown inputs. The structure algorithm developed by Silverman is applied to obtain the observer which estimates the maximum estimable subspace of the state. It is shown that the observer equation can be derived from the maximum uncontrollable subspace of the original system with the aid of a left inverse for a transposed linear system. This leads us to the necessary and sufficient condition for the existence of a state observer. An application to the insensitivity observer synthesis is also included.

Robust Kalman filter design for active flutter suppression systems

Abstract: Additional insight is provided into the use of the Doyle-Stein (1979, 1981) technique in aeroelastic control problems by examining the application of the method to a flutter control problem. The system to be controlled consists of a full-size wind tunnel model of a wing, plus an aileron, an actuator, and an accelerometer used to sense the motion of the wing. A full-state feedback controller was designed using linear optimal control theory, and a Kalman filter was used in the feedback loop for state estimation. The filter design procedure is explained along with that to improve closed-loop properties of the system. The locus of the poles of the filter is examined as a scalar design parameter is varied. The Doyle-Stein design procedure is shown to substantially improve the stability properties of an active flutter controller designed using the linear quadratic Gaussian control theory.

Minimal order robust observer-based compensators

Abstract: An optimal minimal order observer implementation of the optimal regulator is considered. A method is devised for selecting the observer dynamics so that the robustness properties of the resulting control system can be made arbitrarily close to those of the optimal linear quadratic regulator.

State-observer with low sensitivity and its application to Maglev vehicle suspension control

Abstract: A linear time-invariant multi-input/multi-output dynamical system with uncertain parameters is considered. In general the separate design of the regulator and of the observer is not possible because the separation principle does not hold for parameter variations. However, in certain cases the observer matrices may be chosen in a special manner that an observer with low sensitivity can be designed. Then the separation principle is also valid for parameter variations. The existence and the design of such insensitive observers are discussed. The theoretical results are illustrated by an application to the suspension control of a Maglev vehicle.

Generalised Wiener and Kalman filters for uncertain systems

Abstract: A linear stationary optimal filtering problem is considered in which the plant dynamics and noise covariances are incompletely known. Unknown plant parameters in the plant model, such as gains and time constants are treated as random variables with specified means and variances. The assumption is made that the parameter variations are small, however, if the model is linear in the unknown parameters, the assumption is unnecessary. Generalised Wiener and Kalman-Bucy filters are derived on the basis of transfer-function matrix or state-space representations of the plant, respectively. These estimators are similar in structure to the case where the plant dynamics are completely determined and significantly extend the uses of such estimators to an important class of uncertain systems. An application of the generalised filter to the LQG optimal control of plants with unknown disturbances is also described and a separation principle is shown to apply.

Output feedback optimal controller for linear single-input system

Abstract: The design of an optimal controller for a linear single-input system with incomplete state measurements is described. The optimal controller is so designed that only some or all the system output variables are required for the feedback. Application examples to a power system are included.

Stochastic control with noisy observations

Abstract: The last few years have seen considerable progress in nonlinear filtering theory; the proceedings [23] of the 1980 Les Arcs summer school can be consulted for an up-to-date account. It is natural to ask what the impact of these developments might be on control theory for stochastic systems with noisy observations, since, as indicated by the "separation principle", filtering plays an essential part in the optimal control of such systems. In my talk at the Cocoyoc meeting I discussed the general problem of control with incomplete observations and outlined some recent approaches based on nonlinear filtering theory. Most of this material is covered in a survey [14] written for a special issue of Stochastics. In this paper I aim to provide a very brief summary of recent work together with an updated list of references.

Supervision of dynamic systems: Monitoring, decision-making and control

Abstract: Effects of task variables on the performance of the human supervisor by means of modelling techniques are discussed. The task variables considered are: The dynamics of the system, the task to be performed, the environmental disturbances and the observation noise. A relationship between task variables and parameters of a supervisory model is assumed. The model consists of three parts: (1) The observer part is thought to be a full order optimal observer, (2) the decision-making part is stated as a set of decision rules, and (3) the controller part is given by a control law. The observer part generates, on the basis of the system output and the control actions, an estimate of the state of the system and its associated variance. The outputs of the observer part are then used by the decision-making part to determine the instants in time of the observation actions on the one hand and the controls actions on the other. The controller part makes use of the estimated state to derive the amplitude(s) of the control action(s).

Reduced Order Observer Design for a linear Map of the State

Abstract: This paper considers the problem of designing an observer to reconstruct a set of linear functionals in the states of a given linear finite-dimensional system. The goal of the present method is the design of least dimension observers having un- restricted spectrum.

A discrete maximum principle concerning the optimal cost of deterministic control problems

Abstract: INTRODUCTION : Previously [i], we have dealt with the numerical solutions of some optimal deterministic control problems, using as a basic tool of analysis the characterization (introduced in [2~, [~ } of the optLmal cost function as the maximum element of a suitable set of subsolutlons of the associated Hamilton-Jacobl equation. In thls paper, to compute that maximum element, we present a new algorithm who makes possible to solve non-trlvlal problems in computers of small central memories. In part I we study the stationary case. In I.l is introduced a control problem to be optimized that considers the use in each strategy of stopping times, continuous and impulsive controls. So V(x) = inf J(x,r, u(.),z(.)). We present a fitted set W of subsolu~,u(.) ,z (.) tlons and it is shown that V(x) is the unique solution of the equivalent problem (P): Find the maximum element of the set W. In 1.2 we consider the discretlzed problem (Ph) , its solution, the algorithm to compute it and its properties. Using a particular scheme to dlscretlze the partial derivatives of the functions considered, we are enabled to define an algorithm that, Iteratlve and succeslvely, Increases the values of these functions in the vertices of the triangulation employed, until the approximate solution ~h is found. In 1.3 it is proved that the solutlons ~h of the problems (Ph) converge to the solution V(x) of (P). In Part II we consider the non stationary case. In particular, we give a solution to the problem of optimal control of an electricity production system, applying the methodology described in this paper. Systems with a significant number of thermal generators may be optimized in this form.

A new scheme for discrete implicit observer and controller

Abstract: Many different schemes of the adaptive observer and controller have been developed for both continuous and discrete system. In this paper we present a new scheme of the adaptive observer for the discrete linear system. The adaptation algorithm is derived based on the exponentially weighted least square method. The adaptive model following control system is also constructed according to the proposed observer scheme. The proposed observer and controller are simple structure and have fast convergence characteristic in adaptation algorithm. The effectiveness of the algorithm and structure are illustrated by the computer simulation of a third order system.

An optimal adaptive control system and its application

Abstract: This paper proposes the design method of an optimal adaptive controller to control the general plant with disturbances and parameter uncertainties. The controller is composed of a signal synthesis model following adaptive controller and a predetermined reference model with an optimal control input. The effectiveness of the proposed method is verified by a simulation result of the attitude control of a satellite.

Observers for Linear Discrete-Time Systems

Abstract: So far we have implicitly assumed that the state variables can all be observed in each period of time to establish control rules for linear discrete-time systems. However, in a real dynamic economy some of the variables will not be accessible in time. Section 3.2 of the present chapter is concerned with obtaining appropriate proxies (termed “observers”) for the unobserved variables to be incorporated into optimal control laws and with the stability check of the resultant overall system. (Section 3.1 is devoted to preliminary propositions indispensable for constructing observers.) In Section 3.3 we show that the optimal control incorporating any observer incurs a cost rise, and hence in Section 3.4 we derive an observer that has the minimum cost performance. Finally, in Section 3.5, we examine the relationship between observer and controller and establish a separation principle for designing them with minimal overall associated cost.