(644a) Dual Adaptive Model Predictive Control with Disturbances

Over the past few decades, model predictive control (MPC) has become one of the most effective tools in handling industrial control problems. MPC exploits and optimizes trajectories of a plant given a model that simulates the plant dynamics. In many industrial applications, approximate linear models are employed and control performance can deteriorate over time if the model is not updated to take into account varying operation conditions. Model-based control requires good accuracy of model parameters to achieve high performance. Therefore, control design under parametric uncertainties is a challenging topic in control system engineering. One well-known control design for uncertain systems is adaptive control. An indirect adaptive control system, which consists of a conventional model-based control law with adjustable parameters and a model adaptation loop, is an effective method to handle such problems. Online parameter adaptation commonly utilizes recursive parametric estimation methods such as the gradient algorithm and the recursive least square (RLS) algorithm. A necessary condition for parameter convergence is persistent excitation (PE), which is satisfied when the input signals have rich information. Controllers with active learning components aim to generate more informative signals to satisfy the PE condition. However, the most common goal in control engineering is set point regulation and the degree of excitation is usually not sufficient under normal operating conditions. If external signals are applied to generate PE, control performance is compromised when the signals become excessive. Dual control theory focuses on the two seemingly conflicting aspects of adaptive control: trajectory regulation and parameter estimation. Since active learning with excessive or insufficient excitation compromises performance, a dual adaptive controller aims to improve parameter estimation while maintaining control performance.
Adaptive model predictive control (AMPC) draws increasing attention from researchers but many challenges remain open. The majority of adaptive MPC algorithms treat control and learning as separate tasks. This approach, called certainty equivalence (CE) adaptive control, generates input signals that cannot be guaranteed to be rich enough for good parameter estimation. One way of approaching this issue is to design a dual controller, which actively explores the system by ensuring a certain level of excitation, either constantly or when needed.
In this work, the parameter adaptation algorithm is RLS, which uses the empirical parameter estimation uncertainties to adjust the adaptation gain for parameter updates. The dual MPC controller we propose is based on the CE-MPC formulation and incorporates the parameter adaptation mechanism in the prediction horizon. We show that the dual formulation is equivalent to optimizing the expectation of the squared error signals in the MPC objective function. The optimization problem becomes nonconvex because of the addition of parameter adaptation rules in the constraint set and we propose to verify the optimality property of the dual formulation with global optimization solvers. The algorithm is implemented and tested on a simulated SISO system to compare the performance of dual MPC and CE MPC.

References

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