Le Feng

Robust output feedback model predictive control for linear systems via moving horizon estimation

This paper provides a simple approach to the problem of robust output feedback model predictive control (MPC) for linear systems with state and input constraints, subject to bounded state disturbances and output measurement errors. The problem of estimating the state is addressed by using moving horizon estimation (MHE). For such an MHE estimator, it is shown that the state estimation error converges and stays in some set, which is taken into account in the design of the output feedback MPC controllers. In the MPC formulation where the nominal system is considered, the constraints are tightened in a monotonic sequence such that satisfaction of the input and state constraints is guaranteed. Robust stability of an invariant set for the closed-loop original system is ensured. The performance of the approach is assessed via a numerical example.

Linear Moving Horizon Estimation With Pre-Estimating Observer

In this note, a moving horizon estimation (MHE) strategy for detectable linear systems is proposed. Like the idea of “pre-stabilizing” model-predictive control, the states are estimated by a forward simulation with a pre-estimating observer in the MHE formulation. Compared with standard linear MHE approaches, it has more degrees of freedom to optimize the noise filtering. Tuning parameters are chosen to minimize the effects of measurement noise and model errors, which is implemented by finding tightest estimation error bounds. The performance of the proposed observer is demonstrated on one linear discrete-time example.

Barrier function nonlinear optimization for optimal Decompression of divers

This paper is based on a comprehensive dynamic mathematical model (Copernicus) of vascular bubble formation and growth during and after decompression from a dive. The model is founded on the statistical correlation between measurable Venous Gas Emboli (VGE) and risk of severe Decompression Sickness (DCS) where VGE has been shown to be a reliable and sensitive predictor of decompression stress. By using the Copernicus model the diving decompression problem can be formulated as a nonlinear optimal control problem, where the objective is to minimize the total ascend time subject to constraints on the maximum bubbles volume in the pulmonary artery. A recent study reveals that the optimal solution can be obtained by solving the optimization problem with some equality constraints. Inspired by which, a simpler approach using barrier function is proposed in this paper, through which we achieve a more efficient and robust numerical implementation. The paper also studies the effect of ascent profile parameterization.

Optimal Decompression Through Multi-parametric Nonlinear Programming *

Abstract Recently, a comprehensive dynamic mathematical model named Copernicus has been established to discover the mechanism of the vascular bubble formation and growth during and after decompression from a dive. The model uses Venous Gas Emboli (VGE) as a measurement and connects it to the risk of severe Decompression Sickness (DCS). Being validated by a series of diving tests, Copernicus model is believed to be suitable and efficient to predict DCS hence generate optimal decompression profiles for the divers. This paper is based on the Copernicus model and presents a nonlinear model predictive control approach, where multi-parametric nonlinear programming is used to construct an explicit solution for the ease of implementation on a typical low-cost diving computer.

Explicit moving horizon control and estimation: A batch polymerization case study

This paper focuses on the design and evaluation of an explicit moving horizon controller and an explicit moving horizon estimator for a batch polymerization process. It is of particular interest since there are currently no reported case studies or implementations of the explicit parametric controller/estimator for batch and polymerization processes. In this paper we aim at achieving tight offset-free tracking of a desired reactor temperature profile, making accurate states estimation despite of the possible perturbations, and demonstrating the practical applicability to a case with industrially relevant complexity.

Algorithms for Online Implementations of Explicit MPC Solutions

Abstract One of the key problems in Model Predictive Control (MPC) is the inherent on-line computational complexity, which restricts its application to slow dynamic systems. To address this issue, multi-parametric programming technique is introduced in MPC (explicit MPC), where the optimization effort is moved off-line. The optimal solution is given in an explicitly piecewise affine function defined over a polyhedral subdivision of the set of feasible states. Instead of solving an optimization problem, the on-line work is simplified to identify the region the current state belongs to and simply evaluate the piecewise affine function. Hence, identifying of the member of the solution partition that contains a given point (referred to as a point location problem) impacts on the time to implement the explicit controller in real-time, which is one component of the complexity of explicit MPC. In this paper, two simple algorithms for point location problems are proposed to efficiently implement of explicit MPC solutions, which aim at reducing the number of polyhedral sets that are candidates to contain the state at the next time instant.

A framework for multiple robust explicit MPC controllers for linear systems

This article presents a multi-mode explicit controller for constrained linear systems with bounded disturbances using a switching strategy based on Model Predictive Control (MPC). In the proposed approach, the system switches among several MPC controllers having different performance levels. The switching is done so as to achieve increasing levels of performance as time evolves, reaching the desired controller in finite time steps. The conditions needed for switching and robust convergence of the multi-mode MPC controllers are provided. Compared with standard robust explicit MPC implementations, the proposed approach has the flexibility of having a large domain of attraction, a good asymptotic behaviour and a small number of partitions.

On further optimizing prediction dynamics for robust model predictive control

This paper presents a new method for further optimizing the prediction dynamic of constrained robust model predictive control. More slack variables are deployed in the proposed linear matrix inequality (LMI) formulation in order to provide extra degrees of freedom for the dynamic controller. As illustrated by a canonical example, the extra degrees of freedom allow for better performance and wider applicability. In addition, such design can be performed offline leaving only a simple optimization problem for online realization.

Robust Explicit Time Optimal Controllers for Linear Systems via Decomposition Principle

Abstract One of the key problems in time optimal control (TOC) is the inherent computational complexity, which restricts its application to low dimensional systems. Considering a constrained linear system with bounded disturbances, this paper proposes a novel approach to reduce the computational complexity of TOC, where the terminal controller is nonlinear. It comprises several predetermined local linear feedback laws, resulting in a large terminal set. Starting from this relatively large terminal set, a large domain of attraction of the proposed TOC controller can be obtained by using a short horizon, and consequently leads to a low on-line computational effort. Furthermore, by formulating a suitable cost function, as time evolves, the TOC controller reaches the desired controller to obtain a good asymptotical behavior. The performance of the proposed approach is assessed via a numerical example.

Robust Output Feedback MPC for Linear Systems via Interpolation Technique

Abstract This paper provides a simple approach to the problem of robust output feedback model predictive control (MPC) for linear discrete-time systems with state and input constraints, subject to bounded state disturbances and output measurement errors. The problem of estimating the state is addressed by using a fixed linear observer. The state estimation error converges and stays in some set of the error dynamics, which is taken into account in the design of MPC controllers. In the MPC optimization where the nominal system is considered, the constraints are tightened in a monotonic sequence such that the satisfaction of input and state constraints for the original system is guaranteed. Robust stability of an invariant set for the closed-loop original system is ensured. Furthermore, in order to reduce the inherent computational complexity of the MPC controller design, interpolation techniques are introduced in the proposed approach, where the resulting controller interpolates among several MPC controllers. This procedure leads to a relatively large domain of attraction even by employing short prediction horizons. Therefore, with short horizons, a low computational complexity is expected.