Optimization of dynamic systems using novel performance functionals

Optimization problems were explicitly formulated and solved using different concepts, e.g., the Hamilton-Jacobi theory, dynamic programming, maximum principle, Lyapunov´s concept, nonlinear optimization, etc. To solve control problems, the system dynamics is optimized using different performance functionals and optimality criteria. Necessary and sufficient conditions for optimality and stability must be guaranteed, and these conditions are used to synthesize controllers. Viable paradigms have been developed. The quadratic performance functionals, as well as quadratic return and Lyapunov functions have been widely used due to simplicity and mathematical tractability. However, nonquadratic performance functionals should be used to guarantee superior performance (accuracy, robustness, minimum-time dynamics, etc.). The paper concentrates on the design of performance functionals and synthesis of optimal controllers. Innovative procedures reported are illustrated, and the advantages of the documented concept are demonstrated.