Control Synthesis for Discrete-Time Nonlinear Control Systems Under State and Input Constraints

In this article, the control synthesis of discrete-time nonlinear control systems with state and input constraints is considered. Functional inequalities are used to express these restrictions. Based on the barrier method, an online nonconvex optimization problem is solved to obtain a feasible control signal at each time step. The convergence of the solution algorithm is demonstrated. Results for a special case in which the constraints are in quadratic forms are presented. The necessary conditions for regional stabilization are derived. We also discuss the issue of modifying constraints when the original state constraints are infeasible. For validation and comparison, a numerical example is provided.