Low-Complexity Optimization-Based Control: Design, Methods and Applications

Optimization-based controllers are advanced control systems whose mechanism of determining control inputs requires the solution of a mathematical optimization problem. In this thesis, several contributions related to the computational effort required for optimization-based controller execution are provided. The content of the thesis is divided into three parts:

The first part provides methods capable of performing automatic controller tuning for constrained control of nonlinear systems. Given a specified controller structure, the presented methods are able to perform an offline tuning of the controller parameters such that some user-specified performance metric is optimized while imposing stability guarantees on the obtained closed-loop system. The methods are characterized by a broad flexibility that allows their application to many control schemes that are widely popular in practice, but also to novel user-specified control schemes that are convenient from a computational or some other point of view. The controller tuning is formulated as an optimization problem that can be tackled by black-box optimization techniques such as Bayesian optimization. The methods are demonstrated by application examples involving speed control of a permanent magnet synchronous machine and position control of a mechanical gyroscopic system.

The second part provides an accelerated version of the alternating direction method of multipliers (ADMM) optimization algorithm derived by using a recently proposed accelerated Douglas-Rachford (DR) splitting. The obtained method is an accelerated ADMM version that replaces the internal proximal point convergence mechanism of the classical ADMM by the accelerated gradient method applied on a specially constructed scaled DR envelope function. The form of the accelerated ADMM is derived and conditions are provided under which the underlying accelerated DR splitting is validly addressing the Fenchel dual problem.

The third part describes a model predictive control scheme for power electronics control which involves a combination of the integral of squared predicted tracking error as the controller's cost function together with offline computed optimal steady-state voltage signals. These offline computed optimal steady-state signals are in the power electronics community referred to as Optimized Pulse Patterns (OPPs). The method is presented by considering an industrial case study involving a grid-tied converter with LC filter. After introducing an optimal control problem based on OPPs, low computational complexity approximate versions are provided. The resulting approximate controller versions are addressed by using memory storage of the dynamic behavior of the system, leading to controller forms whose execution can be performed on embedded hardware.