By Lars Grüne
This booklet deals readers a radical and rigorous creation to nonlinear version predictive keep watch over (NMPC) for discrete-time and sampled-data platforms. NMPC schemes with and with no stabilizing terminal constraints are particular, and intuitive examples illustrate the functionality of other NMPC variations. NMPC is interpreted as an approximation of infinite-horizon optimum regulate in order that very important homes like closed-loop balance, inverse optimality and suboptimality may be derived in a uniform demeanour. those effects are complemented by means of discussions of feasibility and robustness. An creation to nonlinear optimum keep an eye on algorithms yields crucial insights into how the nonlinear optimization routine—the center of any nonlinear version predictive controller—works. Accompanying software program in MATLAB® and C++ (downloadable from extras.springer.com/), including an explanatory appendix within the e-book itself, allows readers to accomplish machine experiments exploring the chances and barriers of NMPC.
The moment version has been considerably rewritten, edited and up to date to mirror the numerous advances which were made because the book of its predecessor, including:
• a brand new bankruptcy on fiscal NMPC enjoyable the belief that the working price penalizes the gap to a pre-defined equilibrium;
• a brand new bankruptcy on dispensed NMPC discussing equipment which facilitate the keep an eye on of large-scale platforms via splitting up the optimization into smaller subproblems;
• a longer dialogue of balance and function utilizing approximate updates instead of complete optimization;
• alternative of the pivotal enough for balance with out stabilizing terminal stipulations with a weaker substitute and inclusion of another and lots more and plenty easier facts within the research; and
• extra adaptations and extensions in keeping with feedback from readers of the 1st edition.
Though basically geared toward educational researchers and practitioners operating up to the mark and optimization, the textual content is self-contained, that includes heritage fabric on infinite-horizon optimum keep an eye on and Lyapunov balance thought that still makes it available for graduate scholars on top of things engineering and utilized mathematics.
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Additional resources for Nonlinear Model Predictive Control: Theory and Algorithms
To obtain it, a transformation of coordinates is applied which shifts one unstable equilibrium to the origin and then the system is linearized. Using a simplified set of parameters including only the gravitational constant g and a linear friction constant k, this leads to the linear control system ⎛ 0 ⎜g x(t) ˙ =⎜ ⎝0 0 1 −k 0 0 0 0 0 0 ⎞ ⎛ ⎞ 0 0 ⎜1⎟ 0⎟ ⎟ x(t) + ⎜ ⎟ u(t). 11 In contrast to the inverted pendulum example where our task was to stabilize one of the upright equilibria, the control task for the Arm/Rotor/Platform (ARP) model illustrated in Fig.
Springer, New York (1998) 16. : Input to state stability: basic concepts and results. In: Nonlinear and Optimal Control Theory, Lecture Notes in Mathematics, vol. 1932, pp. 163–220. Springer, Berlin (2008) 17. : Rigid-body dynamics with friction and impact. SIAM Rev. 42(1), 3–39 (2000) 18. : Optimal control of partial differential equations, Graduate Studies in Mathematics, vol. 112. American Mathematical Society, Providence, RI. Theory, methods and applications, Translated from the 2005 German original by Jürgen Sprekels (2010) Chapter 3 Nonlinear Model Predictive Control In this chapter, we introduce the nonlinear model predictive control algorithm in a rigorous way.
For these reasons, we choose our cost function to be of the form : X × U → R+ 0. In any case, we require that if we are in the equilibrium x∗ and use the control value u∗ in order to stay in the equilibrium, then the cost should be 0. , (x∗ , u∗ ) = 0 and (x, u) > 0 for all x ∈ X, u ∈ U with x = x∗ . , X = Rd and U = Rm , then we may always assume x∗ = 0 and u∗ = 0 without loss of generality: if this is not the case we can replace f (x, u) by f (x + x∗ , u + u∗ ) − x∗ which corresponds to a simple linear coordinate transformation on X and U.