A new method for suboptimal control of a class of nonlinear systems

This research focuses on developing a new nonlinear control synthesis technique (&thetas;-D approximation). This approach obtains suboptimal solutions to nonlinear optimal control problems by finding an approximate solution to the Hamilton-Jacobi-Bellman (HJB) equation. The approximation is made through a constructed perturbation to the cost function. By manipulating the perturbation terms both semi-global asymptotic stability and suboptimality properties can be achieved. In addition, this new formulation overcomes the large-control-for-large-initial-states problem that occurs in some other Taylor series expansion based methods. The detailed development of this method and proof of stability and error estimates in cost are given. Effectiveness of this new technique is demonstrated through some benchmark problems. Practical applications of this approach are shown through missile autopilot designs by employing a &thetas;-D H ₂ formulation and a &thetas;-D outer/inner loop controller structure. Excellent tracking performance is observed in a wide flight envelope with the &thetas;-D design in both cases. In this research, the &thetas;-D method is extensively compared with the State Dependent Riccati Equation (SDRE) technique due to similarities in bringing the nonlinear dynamics into a linear-like structure. One of the major contributions of this research is the avoidance of on-line computation of the algebraic Riccati equations.