Joint Estimation and Control of Jump Linear Systems With Multiplicative Noises

1987 ◽  
Vol 109 (1) ◽  
pp. 24-28 ◽  
Author(s):  
M. Mariton
Keyword(s):  
Optimal Solution ◽  
Joint Estimation ◽  
Control Synthesis ◽  
Model Parameters ◽  
Linear Quadratic ◽  
Multiplicative Noises ◽  
Matrix Differential Equations ◽  
Estimation And Control ◽  
Matrix Differential ◽  
And Control

Jump Linear Quadratic Gaussian systems are considered in the presence of state-and control-dependent noises. Assuming that the jumps of the model parameters are perfectly observed, it is possible to formulate and solve an optimal input synthesis problem. It is found that the optimal solution does not present the certainty equivalence property, so that the estimation and control synthesis must be treated simultaneously. Optimal equations for the filter and regulator gains are obtained in terms of a set of coupled nonlinear matrix differential equations.

Using a Response Time–Based Expected A Posteriori Estimator to Control for Differential Speededness in Computerized Adaptive Test

2021 ◽  
pp. 014662162110146
Author(s):  
Justin L. Kern ◽  
Edison Choe
Keyword(s):  
Response Times ◽  
Real Data ◽  
Joint Estimation ◽  
Item Selection ◽  
A Posteriori ◽  
Computerized Adaptive Test ◽  
Maximum Information ◽  
Adaptive Test ◽  
Estimation And Control ◽  
And Control

This study investigates using response times (RTs) with item responses in a computerized adaptive test (CAT) setting to enhance item selection and ability estimation and control for differential speededness. Using van der Linden’s hierarchical framework, an extended procedure for joint estimation of ability and speed parameters for use in CAT is developed following van der Linden; this is called the joint expected a posteriori estimator (J-EAP). It is shown that the J-EAP estimate of ability and speededness outperforms the standard maximum likelihood estimator (MLE) of ability and speededness in terms of correlation, root mean square error, and bias. It is further shown that under the maximum information per time unit item selection method (MICT)—a method which uses estimates for ability and speededness directly—using the J-EAP further reduces average examinee time spent and variability in test times between examinees above the resulting gains of this selection algorithm with the MLE while maintaining estimation efficiency. Simulated test results are further corroborated with test parameters derived from a real data example.

Modeling and Control of a Complex Interacting Process

2011 ◽  
Vol 403-408 ◽  
pp. 3758-3762
Author(s):  
Subhajit Patra ◽  
Prabirkumar Saha
Keyword(s):  
Storage System ◽  
Linear Quadratic Regulator ◽  
Model Parameters ◽  
Linear Quadratic ◽  
Modeling And Control ◽  
Dynamic Matrix ◽  
Liquid Storage ◽  
Efficient Control ◽  
And Control

In this paper, two efficient control algorithms are discussed viz., Linear Quadratic Regulator (LQR) and Dynamic Matrix Controller (DMC) and their applicability has been demonstrated through case study with a complex interacting process viz., a laboratory based four tank liquid storage system. The process has Two Input Two Output (TITO) structure and is available for experimental study. A mathematical model of the process has been developed using first principles. Model parameters have been estimated through the experimentation results. The performance of the controllers (LQR and DMC) has been compared to that of industrially more accepted PID controller.

scholarly journals Explicit solutions for a system of coupled Lyapunov differential matrix equations

1987 ◽  
Vol 30 (3) ◽  
pp. 427-434 ◽  
Author(s):  
L. Jodar ◽  
M. Mariton
Keyword(s):  
Cauchy Problem ◽  
Explicit Expression ◽  
Linear Quadratic ◽  
The Cauchy Problem ◽  
Matrix Differential Equations ◽  
Lyapunov Matrix ◽  
Error Accumulation ◽  
Matrix Differential ◽  
Image Position ◽  
Differential Matrix

This paper is concerned with the problem of obtaining explicit expressions of solutions of a system of coupled Lyapunov matrix differential equations of the typewhere Fi, Ai(t), Bi(t), Ci(t) and Dij(t) are m×m complex matrices (members of ℂm×m), for 1≦i, j≦N, and t in the interval [a,b]. When the coefficient matrices of (1.1) are timeinvariant, Dij are scalar multiples of the identity matrix of the type Dij=dijI, where dij are real positive numbers, for 1≦i, j≦N Ci, is the transposed matrix of Bi and Fi = 0, for 1≦i≦N, the Cauchy problem (1.1) arises in control theory of continuous-time jump linear quadratic systems [9–11]. Algorithms for solving the above particular case can be found in [12]]. These methods yield approximations to the solution. Without knowing the explicit expression of the solutions and in order to avoid the error accumulation it is interesting to know an explicit expression for the exact solution. In Section 2, we obtain an explicit expression of the solution of the Cauchy problem (1.1) and of two-point boundary value problems related to the system arising in (1.1). Stability conditions for the solutions of the system of (1.1) are given. Because of developed techniques this paper can be regarded as a continuation of the sequence [3, 4, 5, 6].

Application of the Nonlinear Tschauner-Hempel Equations to Satellite Relative Position Estimation and Control

2017 ◽  
Vol 71 (1) ◽  
pp. 44-64 ◽  
Author(s):  
Ranjan Vepa
Keyword(s):  
Relative Motion ◽  
Position Estimation ◽  
True Anomaly ◽  
Linear Quadratic ◽  
Control Laws ◽  
Motion Equations ◽  
Motion Models ◽  
Estimation And Control ◽  
Oblateness Effect ◽  
And Control

In this paper we develop the nonlinear motion equations in terms of the true anomaly varying Tschauner–Hempel equations relative to a notional orbiting particle in a Keplerian orbit, relatively close to an orbiting primary satellite to estimate the position of a spacecraft. A second orbiting body in Earth orbit relatively close to the first is similarly modelled. The dynamic relative motion models of the satellite and the second orbiting body, both of which are modelled in terms of independent relative motion equations, include several perturbing effects, such as the asymmetry of the Earth gravitational field resulting in the Earth's oblateness effect and the third body accelerations due to the Moon and the Sun. Linear control laws are synthesised for the primary satellite using the transition matrix so it can rendezvous with the second orbiting body. The control laws are then implemented using the state estimates obtained earlier to validate the feedback controller. Thus, we demonstrate the application of a Linear Quadratic Nonlinear Gaussian (LQNG) design methodology to the satellite rendezvous control design problem and validate it.

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