Hybrid H2∕H∞ sub-optimal stochastic risk-sensitive control for polynomial systems of first degree

Abstract This paper presents the novelty RS (Risk-Sensitive) H 2 optimal control problem with criterion J 2 , showing the energy of the control spent into the process, H ∞ RS control approach with level of attenuation λ 1 is obtained, with cost criterion J ∞ . Robustness is added when hybridized H 2 ∕ H ∞ RS sub-optimal control problem is solved, as optimization approach, taking J 2 as cost function criterion, with H ∞ inequality constraint. The sub-optimal solution is obtained imposing that the H ∞ constraint holds with the equality sign. Values of the criterion J 2 versus exponential quadratic cost criterion J , (RS traditional criterion), illustrate advantages of exponential quadratic cost criterion J for different values of diffusion parameter ϵ into the state equation in the final time through an application to the model of the immune system. The experiments show the values of level of attenuation λ 1 in H ∞ RS control problem and hybrid H 2 ∕ H ∞ RS sub-optimal control problem which holds with equality sign. The results of the different experiments that were carried out show that the proposed methodology is feasible and meets the conditions required in H 2 , and H ∞ approaches.