Extended Luenberger Observer for a MIMO Nonlinear Nonholonomic System

Ergueta, Edgar; Seifried, Robert; Horowitz, Roberto; Tomizuka, Masayoshi

doi:10.3182/20080706-5-kr-1001.01565

Cited by 7 publications

(4 citation statements)

References 7 publications

(19 reference statements)

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“…The linear form of LO applies to linear, time-invariant systems [44], but can be extended for time-variant and nonlinear systems, [47]. An LO variant is the extended Luenberger observer (ELO), which is based on an extended Jacobian linearization of the error dynamics, [48].…”

Section: A Luenberger Observermentioning

confidence: 99%

A Literature Survey on Sideslip Angle Estimation Using Vehicle Dynamics Based Methods

Puscul,

Lex,

Vignati

et al. 2024

IEEE Access

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Section: A Luenberger Observermentioning

confidence: 99%

A Literature Survey on Sideslip Angle Estimation Using Vehicle Dynamics Based Methods

Puscul,

Lex,

Vignati

et al. 2024

IEEE Access

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“…Nevertheless, in the approach of [16], [15], input-driven systems have also been taken into account, and the nonlinear observer formula can be reduced to the one adopted in this work, since in the examined example the function g is independent of the state x. Following [18], consider a multi-output system with y = [h 1 (x) h 2 (x) . .…”

Section: End Whilementioning

confidence: 99%

A simulation based MPC technique for feedback linearizable systems with input constraints

Margellos

Lygeros

2010

49th IEEE Conference on Decision and Control (CDC)

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This paper proposes a novel methodology for applying MPC for nonlinear, feedback linearizable systems with input constraints. Earlier approaches coupling MPC and Feedback linearization techniques were limited by a basic factor; although the system dynamics were transformed to a linear system via feedback linearization, the initial input constraints were mapped to a set of nonlinear, and in general non convex bounds, and hence there is no guarantee that the global optimum will be found. The main advantage of the approach proposed in this paper is that by using an iterative process, at every timestep in the resulting optimization problem both dynamics and constraints are linear. The efficiency and robustness of the proposed scheme is verified via simulations in two case studies. The stability of the zero dynamics in these examples is investigated numerically, by using a two-stage approach based on reachability analysis.

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“…The proposed control schema requires full state information. The adaption of an extended Luenberger observer to estimate the paper states is presented in [22].…”

Section: Control Of a Nonlinear Nonholonomic Mechatronic Systemmentioning

confidence: 99%

Feedback Linearization and Model Inversion of Nonlinear Systems

Seifried

2013

Dynamics of Underactuated Multibody Systems

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Nearly all real world engineering systems comprise some type of nonlinearity. Therefore, the term nonlinear systems applies to a wide range of very different systems originating from seemingly unlike fields, such as engineering, biology, physics, and chemistry. Nonlinear systems can exhibit many different complex phenomena, such as multiple equilibria, bifurcation or limit cycles. This richness in phenomena makes classification very difficult. The term non indicates the interesting fact that these systems are not clearly characterized by the possession of certain common properties, rather by the lack of properties which are characterizing a linear system. A linear system is characterized by the properties of superposition and homogeneity; the lack of either one of these properties indicates a nonlinear system.Nonlinearity of systems can have many sources. Following Slotine and Li [66], nonlinearities can be distinguished in natural and artificial nonlinearities. These can be further classified into continuous and discontinuous nonlinearities. Natural nonlinearities are inevitably present in the physical hardware and motion of a system. For example, the equation of motion of the overall dynamics of a multibody system is, generally speaking, inherently nonlinear and represents a continuous nonlinear system. In addition, nonlinearity can also be introduced by nonlinear force elements, such as nonlinear springs and dampers. While continuous nonlinearities can be locally approximated by a linear system, i.e. Jacobian linearization of the equation of motion around a stationary working point or a nominal trajectory; this is not possible for systems with discontinuities. Classical sources of discontinuous nonlinearities are, e.g., normal contact between two bodies or friction between surfaces featuring stick-slip phenomena. Artificial nonlinearities can be introduced by the control law and are mostly implemented in the control software. Applying a nonlinear feedback control law to a system without natural nonlinearities results in an overall nonlinear system. For example, adaptive control laws might result in continuous artificial nonlinearities, while bang-bang control and sliding mode control introduce discontinuous artificial nonlinearities. Since in many multibody systems the natural continuous nonlinearities are dominant they are the focus of this treatise.

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Extended Luenberger Observer for a MIMO Nonlinear Nonholonomic System

Cited by 7 publications

References 7 publications

A Literature Survey on Sideslip Angle Estimation Using Vehicle Dynamics Based Methods

A Literature Survey on Sideslip Angle Estimation Using Vehicle Dynamics Based Methods

A simulation based MPC technique for feedback linearizable systems with input constraints

Feedback Linearization and Model Inversion of Nonlinear Systems

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