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dc.contributor.authorLoxton, Ryan
dc.contributor.authorLin, Qun
dc.contributor.authorPadula, Fabrizio
dc.contributor.authorNtogramatzidis, Lorenzo
dc.identifier.citationLoxton, R. and Lin, Q. and Padula, F. and Ntogramatzidis, L. 2020. Minimizing control volatility for nonlinear systems with smooth piecewise-quadratic input signals. Systems and Control Letters. 145: ARTN 104797.

We consider a class of nonlinear optimal control problems in which the aim is to minimize control variation subject to an upper bound on the system cost. This idea of sacrificing some cost in exchange for less control volatility—thereby making the control signal easier and safer to implement—is explored in only a handful of papers in the literature, and then mainly for piecewise-constant (discontinuous) controls. Here we consider the case of smooth continuously differentiable controls, which are more suitable in some applications, including robotics and motion control. In general, the control signal's total variation—the objective to be minimized in the optimal control problem—cannot be expressed in closed form. Thus, we introduce a smooth piecewise-quadratic discretization scheme and derive an analytical expression, which turns out to be rational and non-smooth, for computing the total variation of the approximate piecewise-quadratic control. This leads to a non-smooth dynamic optimization problem in which the decision variables are the knot points and shape parameters for the approximate control. We then prove that this non-smooth problem can be transformed into an equivalent smooth problem, which is readily solvable using gradient-based numerical optimization techniques. The paper includes a numerical example to verify the proposed approach.

dc.subjectScience & Technology
dc.subjectAutomation & Control Systems
dc.subjectOperations Research & Management Science
dc.subjectOptimal control
dc.subjectTotal variation
dc.subjectNonlinear optimization
dc.subjectNon-smooth optimization
dc.subjectSmooth control
dc.titleMinimizing control volatility for nonlinear systems with smooth piecewise-quadratic input signals
dc.typeJournal Article
dcterms.source.titleSystems and Control Letters
curtin.departmentSchool of Elec Eng, Comp and Math Sci (EECMS)
curtin.accessStatusFulltext not available
curtin.facultyFaculty of Science and Engineering
curtin.contributor.orcidNtogramatzidis, Lorenzo [0000-0002-7721-3229]
curtin.contributor.orcidLoxton, Ryan [0000-0001-9821-2885]
curtin.contributor.orcidLin, Qun [0000-0003-0209-6424]
curtin.contributor.orcidPadula, Fabrizio [0000-0002-0013-9526]
curtin.contributor.researcheridNtogramatzidis, Lorenzo [A-9458-2013]
curtin.contributor.researcheridLoxton, Ryan [F-9383-2014]
curtin.contributor.researcheridPadula, Fabrizio [O-7513-2015]
curtin.identifier.article-numberARTN 104797
curtin.contributor.scopusauthoridNtogramatzidis, Lorenzo [6506950340]
curtin.contributor.scopusauthoridLoxton, Ryan [24438257500]
curtin.contributor.scopusauthoridLin, Qun [36925509300]
curtin.contributor.scopusauthoridPadula, Fabrizio [56521286600]

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