106,482 research outputs found
Adaptive Output Feedback Model Predictive Control
Model predictive control (MPC) for uncertain systems in the presence of hard
constraints on state and input is a non-trivial problem, and the challenge is
increased manyfold in the absence of state measurements. In this paper, we
propose an adaptive output feedback MPC technique, based on a novel combination
of an adaptive observer and robust MPC, for single-input single-output
discrete-time linear time-invariant systems. At each time instant, the adaptive
observer provides estimates of the states and the system parameters that are
then leveraged in the MPC optimization routine while robustly accounting for
the estimation errors. The solution to the optimization problem results in a
homothetic tube where the state estimate trajectory lies. The true state
evolves inside a larger outer tube obtained by augmenting a set, invariant to
the state estimation error, around the homothetic tube sections. The proof for
recursive feasibility for the proposed `homothetic and invariant' two-tube
approach is provided, along with simulation results on an academic system.Comment: 6 page
Adaptive control: Myths and realities
It was found that all currently existing globally stable adaptive algorithms have three basic properties in common: positive realness of the error equation, square-integrability of the parameter adjustment law and, need for sufficient excitation for asymptotic parameter convergence. Of the three, the first property is of primary importance since it satisfies a sufficient condition for stabillity of the overall system, which is a baseline design objective. The second property has been instrumental in the proof of asymptotic error convergence to zero, while the third addresses the issue of parameter convergence. Positive-real error dynamics can be generated only if the relative degree (excess of poles over zeroes) of the process to be controlled is known exactly; this, in turn, implies perfect modeling. This and other assumptions, such as absence of nonminimum phase plant zeros on which the mathematical arguments are based, do not necessarily reflect properties of real systems. As a result, it is natural to inquire what happens to the designs under less than ideal assumptions. The issues arising from violation of the exact modeling assumption which is extremely restrictive in practice and impacts the most important system property, stability, are discussed
Connections Between Adaptive Control and Optimization in Machine Learning
This paper demonstrates many immediate connections between adaptive control
and optimization methods commonly employed in machine learning. Starting from
common output error formulations, similarities in update law modifications are
examined. Concepts in stability, performance, and learning, common to both
fields are then discussed. Building on the similarities in update laws and
common concepts, new intersections and opportunities for improved algorithm
analysis are provided. In particular, a specific problem related to higher
order learning is solved through insights obtained from these intersections.Comment: 18 page
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