Unified Design Method for Suboptimal Control of Nonlinear System with Multiple Constraints

This article proposes a unified suboptimal controller design method for unknown general nonlinear systems subject to multiple constraints, including state, input, and output constraints. All inequality constraints are transformed into equality constraints using slack functions and Pade approximation. An unconstrained augmented system is then defined to describe the dynamics of original system and the equality constraints, where the optimal controller of the augmented system can be viewed as a suboptimal controller for the original system. Furthermore, considering the unmodeled dynamics of the original system, neural networks (NNs) are utilized and a data-based solution strategy of integral reinforcement learning (IRL) is presented for the augmented system. Ultimately, the simulation results are given to reflect the effectiveness of the unified design method.