3,663 research outputs found
Supplemental Material - A novel adaptive robust control for trajectory tracking of mobile robot with uncertainties
No full textSupplemental Material for A novel adaptive robust control for trajectory tracking of mobile robot with uncertainties by Wendong Xiao, Guoliang Wang, Jin Tian, Liang Yuan in Journal of Vibration Control</p
Stability
No full textThe stability problem is an essential and important problem in control theory and dynamic equations. In this chapter, the fundamental problem of stability for SMJSs with general TRMs is considered, whose TRM may be exactly, uncertain, partially unknown and designed. The conditions guaranteeing a given SMJS stochastically admissible are expressed in terms of LMIs or LMIs with equation constraints, which can be efficiently solved by using standard numerical algorithms. Especially, when TRM is given exactly, necessary and sufficient conditions with different forms are developed. Then, the robust stability of Markovian jump singularly perturbed systems with uncertain switchings and nonlinear perturbations for any perturbation parameter ? ? (0, ?¯] is solved by an LMI approach. Instead of containing ?, such conditions guaranteeing the existence and uniqueness of a solution in addition to stochastic admissibility are established by choosing an ?-dependent Lyapunov function and only depends on stability bound ?¯. It is worth mentioning that the stability results proposed in this chapter will play important roles in dealing with other problems
Observer-Based Feedback Stabilization
No full textBecause of technical or economical limitation, it is not easy to obtain all system state variables of practical systems. In this case, it is preferable to design a controller without using all of the state variables. In this chapter, the observer-based stabilization problem of SMJSs is considered, where either the controller or the observer is mode-dependent or mode-independent. In order to obtain LMI conditions, the encountered cross terms are handled by two different techniques separately. New variables satisfying some inequalities are introduced to tackle some non-linear terms, which are used to obtain LMI conditions ultimately
H? Control
No full textH? control has been one of the popular methods for stabilizing dynamic systems with externally finite energy or power disturbance, and great attention has been paid to this problem. This chapter focuses on the mode-independent H? control problem for SMJSs. When the TRM can be selected, several sets of sufficient conditions in terms of LMIs with equation constraints are presented, where control gains can be obtained directly. When MDCs have OMs disordered, sufficient conditions for such disordered controllers are given in terms of LMIs. Without designing NOM-dependent controller directly, a kind of controller only related to OOMs is developed. Especially, another method for designing an MIC is given, which requires that the state transition probability is known exactly. In the case when the state transition probability is unaccessible or unavailable, a unified approach to H? control problem is developed in the LMI setting, where the TRM can be uncertain, partially unknown and designed, and both H? MIC and MDCs are obtained simultaneously. Based on these methods, improved results in terms of considering the probabilities of MIC and MDCs taking place are presented. The available probability of system mode described by a Bernoulli variable is taken into account, which plays an important role in system design. Finally, an adaptive controller is developed to deal with a general case when the probability is inaccessible. All these conditions are expressed in terms of LMIs, and thus they can be solved easily using the existing software package
Stabilization
No full textAs one of the most important control problem, the stabilization problem is to design a controller such that the closed-loop system will be stable and has some desired performances. Due to singular Markovian jump systems containing singular derivative matrix and Markov property simultaneously, they usually complicate the synthesis, especially the underlying SMJSs have some general conditions. In this chapter, we will focus on the stabilization problem of SMJSs. Some kinds of
controllers such that the closed-loop system is regular, stable and impulse-free are designed. A robust stabilizing controller guaranteeing the closed-loop systems robustly stochastically admissible is designed in the LMI setting. When an TRM can be designed, the stabilization for SMJSs is also discussed. The other kinds of controllers realized by noise control, proportional-derivative (PD) control and partially mode-dependent (PMD) control are put forward. Such stabilizing controller designs are formulated in terms of LMIs or LMIs with equation constraints, which can be solved easily
Adaptive Control
No full textIt is well known that adaptive control is an effective approach method to deal with system with unknown parameters. This chapter studies the adaptive control problem of SMJSs with general TRMs. First, an adaption law is proposed to estimate the upper bound on the unknown parameters related to uncertain TRM. Then, a class of adaptive state feedback controllers is designed, where the parameters can be obtained by solving a set of LMIs. It is shown that not only is the estimated error bounded almost surely but also the states of the closed-loop system are asymptotically stable almost surely. Moreover, the proposed adaptive controller can be extended to another general case of TRM when the bound of the unknown elements of TRM is unavailable. Based on the established methods, adaptive state estimation problem is further considered for a class of stochastic delay systems with state-dependent Markovian switching
Introduction
No full textSingular Markovian jump systems (SMJSs) are very pertinent to describe singular systems experiencing abrupt changes. In the past decades, it has been one of the major research areas in control field because of their extensive applications in many practical systems such as economic systems, robotics, aircraft control, electrical and mechanical models, etc. This chapter gives a brief introduction to singular systems. The past and current research on both singular systems and Markovian jump systems is reviewed. A general model named as singular Markovian jump systems which contain singular systems and Markovian jump systems as special cases, is introduced. Then, state-space representation of SMJSs is described and a few examples are presented. Finally, an overview of the monograph is given
Si shu bai hua ju jie.
No full text王天恨述解 ; 李國良注音."中國文化基本教材."Wang Tianhen shu jie ; Li Guoliang zhu yin."Zhongguo wen hua ji ben jiao cai.
Filtering
No full textFiltering has been one of the important problems in the areas of control and signal processing, which is usually used to estimate unavailable variables of a given system through noisy measurement. Particularly, H? filtering has become a hot topic due to the powerful signal estimation and good robustness performance. In this chapter, the problem of H? filtering for SMJSs will be considered. When there are uncertainties in TRM, conditions for robust H? filtering are presented for SMJSs in terms of LMIs. Based on a MD Lyapunov function approach, a PMD filter is designed and the developed conditions are expressed in LMIs. In contrast to the traditionally mode-dependent or mode-independent filtering method, the stochastic property of mode available to a filter is employed in the filter design. Finally, another general robust H? filtering is considered, where the designed filter can tolerate uncertainties on its parameters, and the TRM satisfy general cases in terms of being uncertain and partially unknown. LMI-based conditions are developed, which is used to deal with a special case of mode-independent filtering
Applications of a Markov Process
No full textThis chapter studies the applications of a Markov process on deterministic singular systems whose parameters are only with one mode. The first application is on an uncertain singular system which has norm bounded uncertainties on system matrices. According to the maximum singular value of uncertainty, the uncertainty set is separated into several different subsets. Then, the original system without jumping is transformed into an MJS, whose switching probability of subsets is considered in system analysis and synthesis. New version of BRL is developed by exploiting an uncertainty-dependent Lyapunov function. Two conditions for uncertainty-dependent controllers are established. Based on the key idea, the time-varying delay of the singular system is described by a Markov process, whose distribution property is also considered. Sufficient conditions for the solvability of delay-distribution-dependent stability with both exact known or uncertain TRMs are derived, and state feedback controllers depending on such a distribution are designed via the LMI approach
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