By Professor Panagiotis D. Christofides, Professor Nael H. El-Farra (auth.)

This monograph offers perception and primary knowing into the suggestions keep watch over of nonlinear and hybrid method structures. It offers state of the art equipment for the synthesis of nonlinear suggestions controllers for nonlinear and hybrid structures with uncertainty, constraints and time-delays with quite a few functions, in particular to chemical methods. It covers either nation suggestions and output suggestions (including nation estimator layout) controller designs. regulate of Nonlinear and Hybrid method platforms contains a variety of reviews and feedback delivering perception and primary realizing into the suggestions keep watch over of nonlinear and hybrid platforms, in addition to functions that reveal the implementation and effectiveness of the offered keep an eye on equipment. The e-book comprises many certain examples that are simply converted by way of a regulate engineer to be adapted to a selected program. This publication turns out to be useful for researchers up to speed structures thought, graduate scholars pursuing their measure up to the mark platforms and keep watch over engineers.

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**Extra info for Control of Nonlinear and Hybrid Process Systems: Designs for Uncertainty, Constraints and Time-Delays**

**Example text**

This procedure is called two-time-scale decomposition [153]. 43) g(x, zs , θ, 0) = 0 where zs denotes a quasi-steady-state for the fast state vector z. 42) is in standard form. 44) with the properties that h : IRn ×IRq → IRp and its partial derivatives are locally Lipschitz. 45) is called the reduced system or slow subsystem. 46) τ= and the new coordinate y := z − h(x, θ). 48) = g(x, h(x, θ) + y, θ, 0) dτ Here, x and θ are to be thought of as constant vectors. 48) as the fast subsystem or the boundary layer system.

16. 13 is the one proposed in [163] which involves incorporating the uncertainty compensator within (rather than adding it to) the “nominal” gain of Sontag’s formula. The resulting Lg V controller in this case has a scalar gain that is structurally-similar to that of 46 3 Control of Nonlinear Systems with Uncertainty Sontag’s formula, except that the term Lf V appears with the uncertainty compensator added to it. 33) (Lg¯ V )2 where q L∗f¯V = Lf¯V + χ θbk Lwk ¯ V k=1 Using calculations similar to those in the appendix, one can show that the above control law is also globally robustly stabilizing and inverse optimal with respect to a meaningful cost.

The one that maximizes V˙ ) is given by θ = sgn[Lw V (x)]θb where θb = θ s (which is an admissible uncertainty since it is both measurable and bounded). 7) 0 ≡ l(x) + Lf V − Lg V R−1 (x)Lg V + Lw V θb 4 and the optimal (minimal) value of the cost J is V (x(0)). At this point, we need to recall the deﬁnition of a robust control Lyapunov function which will be used in the development of the main results of this chapter. 1. [97] A smooth, proper, and positive-deﬁnite function V : IRn → IR+ is called a robust control Lyapunov function for a system of the form x˙ = f (x) + g(x)u + w(x)θ when there exist a function, αv (·), of class K, and cv > 0 such that: inf sup [Lf V (x) + Lg V (x)u + Lw V (x)θ + αv (x)] < 0 u∈U θ∈W whenever V (x) > cv , where Lf V (x) = Lw V (x) = ∂V ∂x w(x).