#### Linear Quadratic Gaussian Predictive Control Benchmarking

The Linear Quadratic Gaussian Predictive Control (LQGPC) cost function is the dynamic form of the Generalised Predictive Control (GPC) criterion, i.e. using it would result in a true variance cost.

It is desirable as a benchmark in that the LQG-type cost function:

- Is more robust than the MV or GMV-type cost functions (used in the case of SISO loop benchmarking).
- Provides the lowest practically achievable performance bound.

The LQGPC is also useful in benchmarking dynamic performance of controllers in the process industries, as well as supervisory control systems. The LQGPC benchmark can be used in situations where the main area of interest is the transient stage of a process as opposed to the steady-state performance.

For continuous processes, the performance of a controller in steady state is very important. Variance is hence the most important key performance indicator, and can be related to process revenue. For the assessment of transient performance, although the signal variances are still important, other key performance indicators have direct effect on process revenue. These indicators include:

- Rise Time
- Percentage overshoot
- Settling time
- Steady state output error

The LQGPC cost function provides an optimal benchmark for dynamic performance assessment, using measures like integral square error (ISE), integral square control action and some weighted combination of variances over a period that may includes a step change to the system inputs.

Using predictive control benchmarks is also advantageous in that it can be applied to assess the performance of supervisory controllers.