Real-time MPC - Stability through robust MPC design

Recent results have suggested that online Model Predictive Control (MPC) can be computed quickly enough to control fast sampled systems. High-speed applications impose a hard real-time constraint on the solution of the MPC problem, which generally prevents the computation of the optimal controller. In current approaches guarantees on feasibility and stability are sacrificed in order to achieve a real-time setting. In this paper we develop a real-time MPC scheme based on robust MPC design that recovers these guarantees while allowing for extremely fast computation. We show that a simple warm-start optimization procedure providing an enhanced feasible solution guarantees feasibility and stability for arbitrary time constraints. The proposed method can be practically implemented and efficiently solved for dynamic systems of significant problem size. Implementation details for a real-time robust MPC method are provided that achieves computation times equal to those reported for methods without guarantees. A 12-dimensional problem with 3 control inputs and a prediction horizon of 10 time steps is solved in 2msec with a performance deterioration less than 1% and thereby allows for sampling rates of 500Hz.

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

Ivan Pejcic

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.

EPFL2019

A multiresolution approximation method for fast explicit model predictive control

Colin Neil Jones

A model predictive control law is given by the solution to a parametric optimization problem that can be pre- computed offline and provides an explicit map from state to control input. In this paper, an algorithm is introduced based on wavelet multiresolution analysis that returns a low complexity explicit model predictive control law built on a hierarchy of second order interpolets. The resulting interpolation is shown to be everywhere feasible and continuous. Further, tests to confirm stability and to compute a bound on the performance loss are introduced. Since the controller approximation is built on a grid hierarchy, convergence to a stabilizing control law is guaranteed and the evaluation of the control law in real-time systems is naturally fast and runs in a bounded logarithmic time. Two examples are provided; A two-dimensional example with an evaluation speed of 31 ns and a four-dimensional example with an evaluation speed of 119 ns.

Institute of Electrical and Electronics Engineers2011

A multiscale approximation scheme for explicit model predictive control with stability, feasibility, and performance guarantees

Colin Neil Jones, John Lygeros

In this paper, an algorithm is introduced based on classical wavelet multiresolution analysis that returns a low complexity explicit model predictive control law built on a hierarchy of second order interpolating wavelets. It is proven that the resulting interpolation is everywhere feasible. Further, tests to confirm stability and to compute a bound on the performance loss are introduced. Since the controller approximation is built on a gridded hierarchy, the evaluation of the control law in real-time systems is naturally fast and runs in a bounded logarithmic time. A simple example is provided which both illustrates the approach and motivates further research in this direction.

IEEE2009

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

Ivan Pejcic

EPFL2019