Time-Optimal Control of Systems with Fractional Dynamics

By Christophe Tricaud, YangQuan Chen. 2010

61 citations recorded by the source corpus.

We introduce a formulation for the time-optimal control problems of systems displaying fractional dynamics in the sense of the Riemann-Liouville fractional derivatives operator. To propose a solution to the general time-optimal problem, a rational approximation based on the Hankel data matrix of the impulse response is considered to emulate the behavior of the fractional differentiation operator. The original problem is then reformulated according to the new model which can be solved by traditional optimal control problem solvers. The time-optimal problem is extensively investigated for a double fractional integrator and its solution is obtained using either numerical optimization time-domain analysis.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6c8eb2d9de290dd96b2f5ac34eab2057771f972a

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Citations in the corpus

Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints (2020, background): “Let us point out that some earlier works like [10, 42, 46, 53] already deal with fractional optimal control problems with free final time.”
Pontryagin maximum principle for fractional ordinary optimal control problems (2014, methodology): “This assumption (in case of m D 1) appears also in [13], where a fractional time-optimal control problem is studied by using the Pontryagin minimum principle.”
Fractional order optimal control problems with free terminal time (2013, methodology): “u is piecewise continuous. When N = 0 we obtain a classical optimal control problem; the case M = 0 with ﬁxed T has already been studied for diﬀerent types of fractional order derivatives (see, e.g., [1, 3, 4, 8, 9, 22, 23]). In [10] a special type of the proposed problem is also studied for ﬁxed T.”
A numerical solution for fractional optimal control problems via Bernoulli polynomials (2016, methodology): “When the FDEs are used in conjunction with the performance index and a set of initial conditions, they lead to fractional optimal control problems (FOCPs) (Agrawal, 2004, 2008a,b; Agrawal and Baleanu, 2004; Lotfi et al., 2011, 2013; Tricaud and Chen, 2010a,b).”