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It is a long lasting open problem to synthesize a general PI control for nonlinear systems with its gains analytically determined, yet ensuring stability and transient performance. The problem is further complicated if modeling uncertainties and external disturbances as well as actuation failures are involved in the systems. In this note, a generalized PI control with adaptively adjusting gains is presented, which gracefully avoids the adhoc and time-consuming “trial and error” process for determining the gains as involved in traditional PI control; collectively accommodates modeling uncertainties, undetectable disturbances and undetectable actuation failures that might occur in the systems; and dynamically maintains pre-specified transient and steady-state performance.
Song et al. (Thu,) studied this question.