Non-linear generalized minimum variance feedback, feedforward and tracking control

Target tracking in wireless sensor networks is an important area of research with applications in both the military and civilian domains. One of the most fundamental and widely used approaches to target tracking is the Kalman filter. In presence of unknown noise statistics there are difficulties in the Kalman filter yielding good results. In Kalman filter operation for state variable models with near constant noise and system parameters, it is well known that after the initial transient the gain tends to a steady state value. Hence working directly with Kalman gains it is possible to obtain good tracking results dispensing with the use of the usual covariances. The present work applies an innovations based cost function minimization approach to the target tracking problem in wireless sensor networks, in order to obtain the constant Kalman gain for both the stand-alone and data-fusion modes. Our numerical studies show that the constant gain Kalman filter gives good comparative performance in both the stand-alone and data-fusion modes for the target tracking problem. This is a significant finding in that the constant gain Kalman filter circumvents or in other words trades the gains with the filter statistics which are more difficult to obtain. To the best of our knowledge, these are the only studies of a constant gain Kalman filter in wireless sensor network scenarios, that also incorporate data fusion.

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A constant gain Kalman filter approach to target tracking in wireless sensor networks

A non-linear generalized minimum variance control law is proposed for the control of non-linear continuous-time multivariable systems with common delays on input and output channels. The quadratic cost index involves both error and control signal costing terms. The solution for the control law is obtained using a non-linear operator representation of the plant and a linear state-equation model for the disturbance and reference models. The reference and disturbance models are represented by linear subsystems. However, the plant model can be in a very general non-linear operator form, which could involve state-space, transfer operators or non-linear function look up tables. The structure of the system and criterion is chosen so that a simple controller structure and solution is obtained. The controller obtained is simple to implement, particularly in one form, which might be considered to be a state-space version of a non-linear Smith predictor. The results are related to those for discrete-time systems but...

GMV control of non-linear continuous-time systems including common delays and state-space models

A non-linear generalised minimum variance (NGMV) control law is derived for systems represented by an input-output state dependent non-linear (NL) subsystem that may be open-loop unstable. The solution is obtained using a model for the multivariable discrete-time process that includes a state-dependent (NL and possibly unstable) model that links the output and any `unstructured' NL input subsystem. The input subsystem can involve an operator of a very general NL form, but this has to be assumed to be stable. This is the first NGMV control solution that is suitable for systems containing an unstable NL sub-system which is contained in the state-dependent model. The process is also assumed to include explicit common delays in input or output channels. The generalised minimum variance cost index to be minimised involves both dynamically weighted error and control signal costing terms. It may also include weighted values of the system states for greater generality. The controller derived is simple to implement considering the complexity of the system represented. If the plant is stable the controller structure can be manipulated into an internal model control form. This form of the controller is like an NL version of the Smith Predictor which is valuable for providing confidence in the solution.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2011.0706

Non-linear generalised minimum variance control using unstable state-dependent multivariable models

A non-linear predictive generalised minimum variance control algorithm is introduced for the control of nonlinear discrete-time state-dependent multivariable systems. The process model includes two different types of subsystems to provide a variety of means of modelling the system and inferential control of certain outputs is available. A state dependent output model is driven from an unstructured non-linear input subsystem which can include explicit transport delays. A multi-step predictive control cost function is to be minimised involving weighted error, and either absolute or incremental control signal costing terms. Different patterns of a reduced number of future controls can be used to limit the computational demands.

/pdf/non-linear-predictive-generalised-minimum-variance-state-ucno03y8f0.pdf

M. J. Grimble

Papers

Nonlinear Filters and Operators and the Constant-Gain Extended Kalman Filter