Optimal Control of Class of Non-linear Plants Using Artificial Immune Systems: Application of the Clonal Selection Algorithm

The function of natural immune system is to protect the living organisms against invaders/pathogens. Artificial Immune System (AIS) is a computational intelligence paradigm inspired by the natural immune system. Diverse engineering problems have been solved in the recent past using AIS. Clonal selection is one of the few algorithms that belong to the family of AIS techniques. Clonal selection algorithm is the computational implementation of the clonal selection principle. The process of affinity maturation of the immune system is explicitly incorporated in this algorithm. This paper presents the application of AIS for the optimal control of a class of non-linear plants which are affine in control. The clonal selection algorithm is adapted for optimal control. A new mutation operator that operates on real values and one that aids in fast convergence is developed in this paper. AIS is used to obtain constant coefficient Kalman gain matrices. The validation and evaluation of the results thus obtained are carried out by comparing with standard and the widely used State Dependent Algebraic Riccati Equation (SDARE) method for the non-linear plants. In case of non-linear systems with hard state constraints, the SDARE formulation requires the use of mathematically involved expressions to incorporate these state constraints. However, the modified clonal selection algorithm developed in this paper has been used with hardly any changes to incorporate the hard state constraints and obtain the Kalman gain matrix.