Control of linear dynamic systems with constraints: optimization issues and applications of nonquadratic functionals

This paper addresses to the constrained optimization problem for continuous-time dynamical systems. We extend and modify the existing results in constrained optimization to multi-input open-loop unstable systems, and the generalized nonquadratic cost is introduced. The paper elaborates a new procedure that exploits the beneficial advantages of an innovative design framework. Necessary and sufficient conditions for optimality are embedded and a computationally tractable technique is developed for synthesizing the nonlinear control laws. The key theorem, two propositions and three lemmas are formulated and proved. The procedure is illustrated through an example. This example illustrates the application of the explored optimization methodology to design a bounded smooth controller for the AFTI/F-16 fighter. This control law ensures the optimality in an entire flight envelope and belongs to a specified admissible set that satisfies the bounds imposed on deflections of the control surfaces.