Decentralized nonlinear control of process networks based on dissipativity—A Hamilton–Jacobi equation approach

• A dissipative-based decentralized nonlinear control for process networks developed.
• Candidate dissipativity functions distributed for the global performance.
• A dissipativity shaping method using Hamilton–Jacobi equation developed.
• A link to Hamilton–Jacobi approximation using the expansion approach revealed.

This paper presents an approach of decentralized nonlinear control for process networks based on the theory of dissipative systems. First, the dissipativity analysis is performed to determine the candidate dissipative functions for each subsystem such that desired global network performance criteria are achieved. Then, a nonlinear control law is designed for each subsystem to locally shape the candidate dissipative function. We show that the dissipativity shaping of each subsystem is equivalent to the robust nonlinear H∞H∞ control problem for an equivalent system. The solution to such problem can be obtained by solving a linear partial differential Hamilton–Jacobi equation, for which many approximate solution methods have been developed. In particular, our results are related to the expansion approach. The performance of the proposed algorithm is demonstrated via a benchmark example of a reactor–separator network.