Suboptimal stabilization and tracking control for nonlinear systems with general input constraints

This paper introduces a novel control strategy based on the state-dependent Riccati equation (SDRE) framework for the optimal stabilization and trajectory tracking of nonlinear systems with input constraints. To address control input constraints, the proposed method employs an augmented system integrating an integral control structure and input-barrier states, formulated within a state-dependent coefficient (SDC) representation. A systematic procedure is developed for constructing SDC matrices to guarantee the solvability of the associated Riccati equations. Theoretical analysis provides a mathematical foundation by establishing necessary and sufficient conditions for pointwise stabilizability and detectability of the augmented system, ensuring both asymptotic closed-loop stability and strict input constraint satisfaction. The method is also extended to time-varying trajectory tracking problems under input constraints. By augmenting the system with trajectory dynamics and redefining the cost function, a suboptimal SDRE-based tracking controller is derived. Stability and constraint satisfaction are formally proven through Riccati solvability conditions. Effectiveness and robustness are demonstrated through four simulation case studies.