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We are introducing a model-free control and a control with a restricted modelfor finite-dimensional complex systems. This control design may be viewed as acontribution to "intelligent" PID controllers, the tuning of which becomesquite straightforward, even with highly nonlinear and/or time-varying systems.Our main tool is a newly developed numerical differentiation. Differentialalgebra provides the theoretical framework. Our approach is validated byseveral numerical experiments.

Model-free control and intelligent PID controllers: towards a possible trivialization of nonlinear control?