In this study, a novel method is proposed to track a previewable reference signal in the polytopic time‐varying system with input saturation. Firstly, an augmented model containing future information is constructed using a new formal variable. This leads to the tracking control problem of polytopic time‐varying system with input saturation is transformed into a stability problem of augmented error system. Next, the state and static output feedback preview controls are introduced, and the corresponding controller gains are produced by the proposed conditions. Two examples are presented to validate the effectiveness of the proposed preview controller.
This paper investigates the finite-time preview saturated control
problem for linear parameter-varying systems with input saturation. The
external disturbances and input saturation, previewable reference
signals, and parameter variations are considered simultaneously. First,
using the error system method, we construct an augmented error system
with previewed information. This transforms the finite-time preview
saturated control problem into a finite-time stabilization problem.
Next, static output-feedback controllers are used to guarantee the
finite-time boundedness of the closed-loop system. Sufficient conditions
guarantee the existence of the desired controllers are obtained using
linear matrix inequalities. At last, we use a numerical simulation to
show the proposed design method’s effectiveness.
This paper is intended to study the limit theorem of Markov chain function in the environment of single infinite Markovian systems. Moreover, the problem of the strong law of large numbers in the infinite environment is presented by means of constructing martingale differential sequence for the measurement under some different sufficient conditions. If the sequence of even functions gnx,n≥0 satisfies different conditions when the value ranges of x are different, we have obtained SLLN for function of Markov chain in the environment of single infinite Markovian systems. In addition, the paper studies the strong convergence of the weighted sums of function for finite state Markov Chains in single infinitely Markovian environments. Although the similar conclusions have been carried out, the difference results performed by previous scholars are that we give weaker different sufficient conditions of the strong convergence of weighted sums compared with the previous conclusions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.