162 research outputs found
Control synthesis for polynomial discrete-time systems under input constraints via delayed-state Lyapunov functions
This paper presents a discrete-time control design methodology for input-saturating systems using a Lyapunov function with dependence on present and past states. The approach is used to bypass the usual difficulty with full polynomial Lyapunov functions of expressing the problem in a convex way. Also polynomial controllers are allowed to depend on both present and past states. Furthermore, by considering saturation limits on the control action, the information about the relationship between the present and past states is introduced via Positivstellensatz multipliers. Sum-of-squares techniques and available semi-definite programming (SDP) software are used in order to find the controller.The research work by J.L. Pitarch and A. Sala has been partially supported by the Spanish government under research project [grant number DPI2011-27845-C02-01 (MINECO)]; Generalitat Valenciana [grant number PROMETEOII/2013/004]. The work by T.M. Guerra and J. Lauber has been supported by the International Campus on Safety and Intermodality in Transportation, the European Community, Delegation Regionale a la Recherche et a la Technologie, Ministere de l'Enseignement superieur et de la Recherche, Region Nord Pas de Calais and the Centre National de la Recherche Scientifique.Pitarch PĂ©rez, JL.; Sala Piqueras, A.; Lauber, J.; Guerra, TM. (2016). Control synthesis for polynomial discrete-time systems under input constraints via delayed-state Lyapunov functions. International Journal of Systems Science. 47(5):1176-1184. https://doi.org/10.1080/00207721.2014.915357S1176118447
Survey of Gain-Scheduling Analysis & Design
The gain-scheduling approach is perhaps one of the most popular nonlinear control design approaches which has
been widely and successfully applied in fields ranging from aerospace to process control. Despite the wide
application of gain-scheduling controllers and a diverse academic literature relating to gain-scheduling extending
back nearly thirty years, there is a notable lack of a formal review of the literature. Moreover, whilst much of
the classical gain-scheduling theory originates from the 1960s, there has recently been a considerable increase in
interest in gain-scheduling in the literature with many new results obtained. An extended review of the gainscheduling
literature therefore seems both timely and appropriate. The scope of this paper includes the main
theoretical results and design procedures relating to continuous gain-scheduling (in the sense of decomposition
of nonlinear design into linear sub-problems) control with the aim of providing both a critical overview and a
useful entry point into the relevant literature
Closed-form estimates of the domain of attraction for nonlinear systems via fuzzy-polynomial models
In this work, the domain of attraction of the origin of
a nonlinear system is estimated in closed-form via level sets with
polynomial boundary, iteratively computed. In particular, the
domain of attraction is expanded from a previous estimate, such
as, for instance, a classical Lyapunov level set. With the use of
fuzzy-polynomial models, the domain-of-attraction analysis can
be carried out via sum of squares optimization and an iterative
algorithm. The result is a function wich bounds the domain of
attraction, free from the usual restriction of being positive and
decrescent in all the interior of its level sets
Polytopic invariant and contractive sets for closed-loop discrete fuzzy systems
In this work a procedure for obtaining polytopic lambda-contractive sets for Takagi Sugeno fuzzy systems is
presented, adapting well-known algorithms from literature on discrete-time linear difference inclusions
(LDI) to multi-dimensional summations. As a complexity parameter increases, these sets tend to the
maximal invariant set of the system when no information on the shape of the membership functions is
available. lambda-contractive sets are naturally associated to level sets of polyhedral Lyapunov functions proving a decay-rate of lambda. The paper proves that the proposed algorithm obtains better results than a class of Lyapunov methods for the same complexity degree: if such a Lyapunov function exists, the proposed
algorithm converges in a finite number of steps and proves a larger lambda-contractive set.This work has been supported by Projects DPI2011-27845-C02-01 and DPI2011-27845-C02-02, both from Spanish Government.Arino, C.; Perez, E.; Sala Piqueras, A.; Bedate, F. (2014). Polytopic invariant and contractive sets for closed-loop discrete fuzzy systems. Journal of The Franklin Institute. 351(7):3559-3576. https://doi.org/10.1016/j.jfranklin.2014.03.014S35593576351
Designing the Model Predictive Control for Interval Type-2 Fuzzy T-S Systems Involving Unknown Time-Varying Delay in Both States and Input Vector
In this paper, the model predictive control is designed for an interval
type-2 Takagi-Sugeno (T-S) system with unknown time-varying delay in state and
input vectors. The time-varying delay is a weird phenomenon that is appeared in
almost all systems. It can make many problems and instability while the system
is working. In this paper, the time-varying delay is considered in both states
and input vectors and is the sensible difference between the proposed method
here and previous algorithms, besides, it is unknown but bounded. To solve the
problem, the Razumikhin approach is applied to the proposed method since it
includes a Lyapunov function with the original nonaugmented state space of
system models compared to Krasovskii formula. On the other hand, the Razumikhin
method act better and avoids the inherent complexity of the Krasovskii
specifically when large delays and disturbances are appeared. To stabilize
output results, the model predictive control (MPC) is designed for the system
and the considered system in this paper is interval type-2 (IT2) fuzzy T-S that
has better estimation of the dynamic model of the system. Here, online
optimization problems are solved by the linear matrix inequalities (LMIs) which
reduce the burdens of the computation and online computational costs compared
to the offline and non-LMI approach. At the end, an example is illustrated for
the proposed approach
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