I think for every change in the system, optimization should be calculated; so the gain should be renewed. By the way it still will use the old matrices gain to calculated new gain.

For online optimization of control parameters, population-based algorithms such as PSO, GA are not suitable beacuse to get an optimum solution you need to run these algorithms for many generations with reasonable population size which is not possible to complete in a single sampling time for most online applications.

You may use algorithms such CMA-ES, which despite being a population-based heuristic follows a more local-search exploration strategy. Everytime you problem specfications change you may restart the algorithm on the previously found optimum.

Antonio, do you think it takes a considerable time while searching another optimum answer with respect of new changes, because at least it needs to calculate a kind of cost function in each iteration?

I agree with all three answers added so far. Your problem is that controller parameters change with the operating conditions. You need to design an adaptive controller with fixed structure and variable parameter values. The parameters are adjusted as per the operating condition.

Heuristics optimization techniques such as PSO, GA, and BF are not suitable to tune the parameters online for two reasons. First is the slowness of convergence: the condition itself may change before the algorithm finds suitable parameters. Second is the stochastic nature of search: sometimes you need to run the algorithm more than once for the same case before you can get an acceptable set of parameters. However, the problem has gotten a solution.

What you can do is to select a set of operating conditions which fairly span over the whole operating range. You run the algorithms offline to find the suitable set of controller parameters at each and every point. Then, you train an artificial intelligence (AI) module on the results you obtained offline. The inputs would be the variables which determine your operating condition, and the outputs are the required controller parameters. An accurate representative training data set is the core of your work; once you develop it, the rest is easy. The development, training, and testing of the AI module are also performed offline. Then, it can carry out  the task of controller parameter tuning online. You may use artificial neural networks, adaptive fuzzy systems, or any other AI paradigm of your choosing.

I applied this idea to many systems; it just works. Please refer to:

E.H.E. Bayoumi, M.A. Awadallah, and H.M. Soliman, "Deadbeat performance of vector-controlled induction motor drives using particle swarm optimization and adaptive neuro-fuzzy inference systems," Electromotion, Vol. 18, No. 4, pp. 231-242, 2011.

M.A. Awadallah and H.M. Soliman, "A neuro-fuzzy adaptive power system stabilizer using genetic algorithms," Electric Power Components and Systems, Vol. 37, No. 2, pp. 158-173, 2009.

M.A. Awadallah, E.H.E. Bayoumi, and H.M. Soliman, "Adaptive deadbeat controllers for brushless DC drives using PSO and ANFIS techniques," Journal of Electrical Engineering (JEEEC), Vol. 60, No. 1, pp. 3-11, 2009.

M.A. Awadallah and H.M. Soliman, "An adaptive power system stabilizer based on fuzzy and swarm intelligence," International Journal of Modeling, Identification, and Control, Vol. 5, No. 1, pp. 55-65, 2008.

Good Luck,

Mohamed

It is not necessary for gains that become optimal for the different tasks. 

It may be applied for solving online economic load dispatch, voltage control, adoptive relay settings calculation etc.