Nonlinear discrete-time systems: constrained optimization and application of nonquadratic costs

In this paper, the constrained optimization problem is solved for nonlinear discrete-time systems. The Hamilton-Jacobi theory is applied to design a new class of bounded controllers, and an innovative nonquadratic performance index is minimized. These innovations extend the optimization theory. In particular, the reported framework ensures straightforward analytical and numerical results, and the presented concept significantly reduces the computational conservatism of the conventional methods. It is shown that for open-loop unstable systems, the constrained optimization problem is solvable if the sufficient conditions are satisfied. This leads to the application of the admissibility framework, and the maximal positively invariant admissible set of stability is found by applying the Lyapunov stability criteria. The results are verified and illustrated by solving the motion control problem for a high-performance aircraft.