A robust algorithm for a class of optimal control problems subject to regional stability constraints and disturbances

A robust globally convergent algorithm for solving the optimization control problem (OCP) in both state feedback controller and observation control system is investigated. Finding the OCP adjoint parameter for computing the optimal observer gain and feedback gain vectors are desired. First, the optimal control problem considering stability of degree constrains and disturbance that affects the dynamics of system is converted into a two-point boundary value problem (TPBVP). Then, we apply the He’s polynomials based on homotopy perturbation method (HPM) as an efficient method to find both optimal gains. The algorithm will be modified do decrease the number of iterations required to attain a desired control problem cost function. As a result lower computational complexity is required when compared with other state of the art methods. Applying the HPM makes the solution procedure become easier, simpler and more straightforward. In the proposed method the control problem can be solved with lower amplitudes of the input signal (control effort), comparing with analytical method. Lower control efforts may also help to avoid saturation effects, and to restrain the system to work within linear operating areas of the state space. On the other hand, there is a tradeoff between control effort and the degree of optimality obtained. For demonstrating the simplicity and efficiency of the proposed optimal control method, the algorithm is compared with a control architecture using the Kalman filter estimator and a controller gain designed by the Lyapunov’s second method.