Control linear quadratic Gaussian

Linear Quadratic Gaussian control system design... 

The new paradigm of robust optimal control is well on the way to rendering the linear quadratic Gaussian control obsolete (or at least less important) because it can deal explicitly with model error. 

A control system that contains a LQ Regulator/Tracking controller together with a Kalman filter state estimator as shown in Figure 9.8 is called a Linear Quadratic Gaussian (LQG) control system. 

Atlians, M. (1971) The Role and Use of the Stochastic Linear-Quadratic-Gaussian Problem in Control System Design, IEEE Trans, on Automatic Control AC-16, 6, pp. 529-551. 

Lehtomaki, N.A., Sandell, Jr., N.R. and Athans, M. (1981) Robustness Results in Linear-Quadratic Gaussian Based Multivariable Control Designs, IEEE Trans, on Automat. Contr., AC-26(1), pp. 75-92. 

The proposed strategies for stabilization of gas-lifted oil wells are offline methods which are unable to track online dynamic changes of the system. However, system parameters such as flow rate of injected gas and also noise characteristic are not constant with respect to time. An adaptive Linear Quadratic Gaussian (LQG) approach is presented in this paper in which the state estimation is performed using an Adaptive Unscented Kalman Filter (AUKF) to deal with unknown time-varying noise statistics. State-feedback gain is adaptively calculated based on Linear Quadratic Regulator (LQR). Finally, the proposed control scheme is evaluated on a simulation case study. 

LQG-Benchmark The achievable performance of a linear system characterized by quadratic costs and Gaussian noise can be estimated by solving the linear quadratic Gaussian (LQG) problem. The solution can be plotted as a trade-off curve that displays the minimal achievable variance of the controlled variable versus the variance of the manipulated variable [115] which is used as a CPM benchmark. Operation close to optimal performance is indicated by an operating point near this trade-off curve. For multivariable control systems, H2 norms are plotted. The LQG objective function and the corresponding H2 norms are [115]... 

Chapter 12 considers the combination of optimal control with state and parameter estimation. The separation principle is developed, which states that the design of a control problem with measurement and model uncertainty can be treated by first performing a Kalman filter estimate of the states and then developing the optimal control law based upon the estimated states. For linear regulator problems, the problem is known as the linear quadratic Gaussian (LQG) problem. The inclusion of model parameter identification results in adaptive control algorithms. 

It has been noted [95] that 2 in Eq. 34 plays two rather distinct roles 2 in the quadratic expression is a solvation energy which defines (with AC°) the vertical gap at equilibrium, whereas the other 2 s control the width of the Gaussian distribution characteristic of the linear coupling model. 

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