Sliding Modes in a Class of Complex-Valued Nonlinear Systems
Arnau Dòria‐Cerezo, Josep M. Olm, Domingo Biel, Enric Fossas
Abstract
A number of physical systems allow a complex-valued representation. This article extends the theory of sliding modes to a class of nonlinear systems described by complex-valued variables. Hence, states, parameters, control actions, and sliding manifolds belong, in general, to the complex field. In this article, it is also shown that the proposed design in the complex-valued framework provides shorter reaching times to the sliding manifold than the standard sliding-mode design at equal initial condition and control effort. Different implementation approaches are also evaluated, and numerical examples illustrate the proposal.
Topics & Concepts
Sliding mode controlNonlinear systemControl theory (sociology)Class (philosophy)Manifold (fluid mechanics)Complex systemRepresentation (politics)MathematicsVariable structure controlField (mathematics)Mode (computer interface)Computer scienceControl (management)EngineeringPure mathematicsArtificial intelligencePhysicsLawMechanical engineeringQuantum mechanicsPolitical sciencePoliticsOperating systemControl and Stability of Dynamical SystemsDynamics and Control of Mechanical SystemsAdaptive Control of Nonlinear Systems