Optimal tracking control of nonlinear dynamic systems with control bounds

Using the Hamilton-Jacobi theory, we solve the constrained optimization problem for nonlinear multivariable continuous-time systems. It is illustrated that through the use of positive-definite performance integrands, the designer can analytically synthesize the constrained control laws within the admissible control set. We extend the class of dynamic systems for which the constrained optimization problem can be solved. The paper demonstrates the ability of the constrained optimization concept to design the bounded controller for multivariable advanced aircraft. The fighter longitudinal and lateral dynamics are mapped by a set of nine highly nonlinear differential equations with six bounded control inputs. The complete aircraft model, as derived using the Lagrange equations and nonlinear fluid dynamics, is applied to synthesize an optimal controller using the mechanical limits imposed on the angular deflections of the control surfaces. This very complex multivariable flight control problem for highly nonlinear aircraft have challenged the control community for many years. The results documented in the paper show that a constrained controller synthesized allows one to attain the desired flying and handling qualities and expand the operating envelope. The desired agility, controllability, maneuverability and other pilotage requirements are assessed minimizing the nonquadratic performance cost, and highly detailed nonlinear simulations were performed to demonstrate the advantages of the controller designed.