Role of performance functionals in control laws design

The research in optimal control has been concentrated on design of control laws in order to optimize the dynamic performance of systems. These optimization problems were explicitly formulated and solved using the Hamilton-Jacobi theory and Lyapunov concept. To solve the control design problems, the system models in form of differential equations, performance functionals, optimality criteria, conditions on the Lyapunov pair, and other criteria were used. The importance of synthesis of performance functionals lays on the matter that the controllers are predefined, by the functionals used. It must be emphasized that for dynamic systems, modeled using differential or difference equations; the closed-loop system performance is optimal and stability margins (robustness) are assigned in the specific sense as implied by the performance functionals and optimization/design concepts. The innovative performance integrands, which allow one to measure the system performance as well as to design bounded (admissible) robust control laws, received much attention in recent years. In particular, novel nonquadratic and generalized functionals were introduced for continuous- and discrete-time systems. However, the system optimality depends to a large extent on the specifications imposed and the inherent system capabilities. This paper overcomes the current limitations in the synthesis of performance functionals, and a new class of robust control laws is designed. The results documented significantly complement modern control theory