By Francesco Borrelli

ISBN-10: 354000257X

ISBN-13: 9783540002574

ISBN-10: 3540362258

ISBN-13: 9783540362258

Many functional keep an eye on difficulties are ruled by means of features resembling nation, enter and operational constraints, alternations among various working regimes, and the interplay of continuous-time and discrete occasion platforms. at the present no method is out there to layout controllers in a scientific demeanour for such platforms. This e-book introduces a brand new layout idea for controllers for such limited and switching dynamical structures and results in algorithms that systematically clear up regulate synthesis difficulties. the 1st half is a self-contained creation to multiparametric programming, that is the most approach used to review and compute kingdom suggestions optimum keep an eye on legislation. The book's major goal is to derive houses of the kingdom suggestions answer, in addition to to procure algorithms to compute it successfully. the point of interest is on restricted linear platforms and limited linear hybrid structures. The applicability of the speculation is validated via experimental case stories: a mechanical laboratory procedure and a traction keep an eye on method built together with the Ford Motor corporation in Michigan.

Show description

Read or Download Constrained Optimal Control of Linear and Hybrid Systems PDF

Similar system theory books

Download e-book for iPad: Cooperative Control Design: A Systematic, Passivity-Based by He Bai

Cooperative keep an eye on layout: a scientific, Passivity-Based technique discusses multi-agent coordination difficulties, together with formation regulate, angle coordination, and contract. The publication introduces passivity as a layout instrument for multi-agent platforms, presents exemplary paintings utilizing this tool,and illustrates its merits in designing strong cooperative keep watch over algorithms.

Bernt Øksendal's Stochastic Differential Equations: An Introduction with PDF

From the studies to the 1st variation: many of the literature approximately stochastic differential equations turns out to put a lot emphasis on rigor and completeness that it scares the nonexperts away. those notes are an try to strategy the topic from the nonexpert perspective. : no longer understanding whatever .

Ordinary Differential Equations: Analysis, Qualitative by Hartmut Logemann PDF

The publication includes a rigorous and self-contained remedy of initial-value difficulties for usual differential equations. It also develops the fundamentals of keep an eye on conception, that is a special characteristic in present textbook literature. the next subject matters are relatively emphasised:• lifestyles, area of expertise and continuation of solutions,• non-stop dependence on preliminary data,• flows,• qualitative behaviour of solutions,• restrict sets,• balance theory,• invariance principles,• introductory keep watch over theory,• suggestions and stabilization.

Additional info for Constrained Optimal Control of Linear and Hybrid Systems

Sample text

11. Consider two set of active constraints Aj and Aj and let CRi and CRj be the corresponding critical region, respectively. 34) is non-degenerate and that CR ¯ i and CR ¯ j denote the closure of the sets CRi and CRj , respectively. where CR Then, Ai ⊂ Aj and #Ai = #Aj − 1 or Aj ⊂ Ai and #Ai = #Aj + 1. 2. 10. This fact, together with the convexity of the set of feasible parameters K ∗ ⊆ K and the piecewise linearity of the solution z ∗ (x) is proved in the next Theorem. 12. 34) and let H 0. Then, the set of feasible parameters K ∗ ⊆ K is convex.

The function J ∗ : K ∗ → R will denote the function which expresses the dependence on x of the minimum value of the objective function over K ∗ , J ∗ (·) will be called value function. The set-valued function sc s Z ∗ : K ∗ → 2R × 2{0,1} d will describe for any fixed x ∈ K ∗ the set of ∗ optimizers z (x) related to J ∗ (x). We aim at determining the region K ∗ ⊆ K of feasible parameters x and at finding the expression of the value function J ∗ (x) and the expression an optimizer function z ∗ (x) ∈ Z ∗ (x).

38) where nT is the number of rows Ti of the matrix T . 34) is feasible for such an x0 . 34) is infeasible for all x in the interior of K. 34), in order to obtain the corresponding optimal solution z0 . 34). 10. Let H 0. Consider a combination of active constraints A0 , and assume that LICQ holds. Then, the optimal z ∗ and the associated vector of Lagrange multipliers λ∗ are uniquely defined affine functions of x over the critical region CR0 . 39a) λi (Gi z − Wi − Si x) = 0, i = 1, . . 39b) to obtain the complementary slackness condition λ∗ ( −G H −1 G λ∗ − W − Sx) = 0.

Download PDF sample

Constrained Optimal Control of Linear and Hybrid Systems by Francesco Borrelli


by Kenneth
4.4

Rated 4.09 of 5 – based on 18 votes