Multi–Controller Adaptive Control (MCAC) for a Tracking Problem using an Unfalsification approach (original) (raw)
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Several classes of identifier and non-identifier based adaptive control schemes using a supervisory switching logic have been proposed in the literature. These schemes are based on different assumptions and claim to guarantee certain stability and performance properties. The purpose of this paper is to clarify what each algorithm guarantess in theory and how it performs in simulations. The identifier based schemes: Robust Multiple Model Adaptive Control (RMMAC) and Adaptive Mixing Control (AMC) and the non-identifier based schemes: Unfalsified Adaptive Switching Control (UASC) and Multimodel Unfalsified Adaptive Switching Control (MUASC). For each scheme we present the basic features of the algorithm and state the stability and performance guaranteed in theory.
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A discrete pole placement-based adaptive controller with multiestimation is synthesized for linear time-invariant plants. A higher level switching structure between the various estimation schemes is used to supervise the re-parametrization of the adaptive controller in real time. The basic usefulness of the proposed multiestimation scheme relies to the improvement of the adaptation transient behavior while robust closed loop stability is proved even in the presence of unmodeled dynamics of sufficiently small sizes. The scheme becomes specifically attractive when the various estimators are adaptive identifiers for the plant which is being modeled as possessing different possible amounts of unmodeled dynamics including nominal different orders and parametrical uncertainties. The influence of free design parameters is discussed through exhaustively worked simulations.
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This paper presents an indirect adaptive control scheme for nominally stabilizable non-necessarily inversely stable continuous-time systems with unmodelled dynamics. The control objective is the adaptive stabilization of the closed-loop system with the achievement of a bounded tracking-error between the system output and a reference signal given by a stable filter. The adaptive control scheme includes several estimation algorithms and a supervisor which selects the appropriate estimator at every certain time and keeping it operating for at least a minimum period of residence time. This selection is based on a performance criterion related to a measure of the estimation errors obtained with each estimator. In this way, the performance of the output signal is improved with regard to the performance achieved with a unique estimation algorithm. All the estimators are either of the least-squares type or gradient type. However, any well-posed estimation algorithm is potentially valid for application. These estimators include relative dead-zones for robustness purposes and parameter 'a posteriori' modifications to ensure the controllability of the estimated models of the plant, which is crucial for proving the stabilizability of the plant via adaptive pole-placement designs.