Dynamics and Control of Initialized Fractional-Order Systems

By Tom T. Hartley, Carl F. Lorenzo. 2002

261 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f5235fd881f885b35b229b81e4a5b64cebff12c1

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In Control and Systems Engineering

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

On Fractional Adaptive Control (2006, background): “Moreover, Hartley and Lorenzo have shown [ 7 ] a model of the form:”
Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation (2009, methodology): “Lorenzo and Hartley [28] analyzed mathematically some important properties of candidate VO operators (invariance, memory retentiveness, adherence to the exponent rule, etc.), essentially within the same spirit that motivated the work of Samko and Ross.”
Active disturbance rejection control for nonlinear fractional‐order systems (2016, background): “Lemma 2 In [32], the fractional-order system with the characteristic function (2) is BIBO stable if and only if all poles ́i of the polynomial (4) satisfy j arg.”
Sliding mode control approaches to the robust regulation of linear multivariable fractional‐order dynamics (2010, methodology): “To emphasize this, and in accordance to [13, 16], the term vector-space model will be used in the sequel to denote (12).”
On the sliding‐mode control of fractional‐order nonlinear uncertain dynamics (2016, result): “The notion of pseudo-states was considered originally in [26], and used later in numerous publications, including [20] and [27–29].”
Fractional optimal control problems: a pseudo-state-space approach (2011, methodology): “A fractional order vector space representation including initialization response is presented in Hartley and Lorenzo (2002).”
Analog Fractional Order Controller in Temperature and Motor Control Applications (2008, background): “The memory disturbance effects outlined by Hartley and Lorenzo (2002) did not affect the performance of the temperature or motor controller.”
Fractional systems state space description: some wrong ideas and proposed solutions (2014, methodology): “In Hartley and Lorenzo (2002, 2007, 2009), it was demonstrated that if initial conditions are taken into account, the pseudo trajectories of system (2) are not the same, depending on the fractional differentiation definition used: Caputo’s or Riemann–Liouville’s definition.”
A General Formulation and Solution Scheme for Fractional Optimal Control Problems (2004, background): “Hartley and Lorenzo [28] present a general fractional-order system and control theory that includes the time-varying initialization response.”