Dan Sui

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.

Moving horizon observer with regularisation for detectable systems without persistence of excitation

A constrained moving horizon observer is developed for nonlinear discrete-time systems. The algorithm is proved to converge exponentially under a detectability assumption with the data being exciting at all times. However, in many practical estimation problems, such as combined state and parameter estimation, the data may not be exciting for every period of time. The algorithm therefore has regularisation mechanisms to ensure robustness and graceful degradation of performance in cases when the data are not exciting. This includes the use of a priori estimates in the moving horizon cost function, and the use of thresholded singular value decomposition to avoid ill-conditioned or ill-posed inversion of the associated nonlinear algebraic equations that define the moving horizon cost function. The latter regularisation relies on monitoring of the rank of an estimate of a Hessian-like matrix and conditions for uniform exponential convergence are given. The method is in particular useful with augmented state space models corresponding to mixed state and parameter estimation problems, or dynamics that are not asymptotically stable, as illustrated with two simulation examples.

Linear constrained moving horizon estimator with pre-estimating observer

Abstract In this paper, a constrained moving horizon estimation (MHE) strategy for linear systems is proposed. Recently, the use of a pre-estimating linear observer in the forward prediction equations in the MHE cost function has been proposed in order to reduce the effects of uncertainty. Here we introduce state constraints within this formulation and investigate stability properties in the presence of bounded disturbances and noise. The robustness and performance of the proposed observer is demonstrated with a simulation example.

Interpolated Model Predictive Controller for Linear Systems with Bounded Disturbances

Interpolation techniques are known to reduce computational complexity of model predictive control (MPC) (Bacic et al., 2003), (Rossiter et al., 2004). This paper presents the general interpolation based MPC (IMPC) for a constrained linear system with bounded disturbances. The resulting MPC control law comprises an interpolation between several single MPC control laws. Compared with single MPC control law implementations, the proposed approach has the advantage of combining the merits of having a large domain of attraction and good asymptotic behavior. The performances of the approach are presented via an 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.

Automatic Prediction of Downhole Pressure Surges in Tripping Operations

A simplified dynamic model of the tripping operation is used together with an ensemble Kalman filter to predict transient pressure surges when running the drillstring in or out of the hole. Dynamic downhole pressure measurements from a tripping operation with mud circulation are used as input to the Kalman filter. Such data can be achieved by mud pulse telemetry at the field just before the tripping operation starts. The model is automatically adapted to the particular situation (well, bit-depths, drilling mud, etc.). This is important since exact values of some downhole parameters, like viscosity of the drilling mud, might be unknown and/or changing with time. We show by comparison with filed measurements, that the automatically updated model is capable of reproducing the transient pressure surges in consecutive runs of the string without mud circulation.

Moving horizon estimation for tire-road friction during braking

Estimation of tire-road friction forces has an important role in anti-lock brake systems (ABS), as well as for vehicle stability control systems, and road condition monitoring systems. We investigate the use of a moving horizon observer for estimation of multiple friction model parameters as well as the longitudinal wheel slip state under typical ABS braking scenarios, using wheel speed measurement and information on the brake torque. It is well known that data may not be persistently exicting for every period of time in such scenarios, expecially when estimating several friction model parameters simultaneously. The algorithm therefore has regularization mechanisms to ensure graceful degradation of the state and parameter estimation performance in cases when data are not persistently exciting. Simulations with a quarter car dynamic model and the four-parameter longitudinal Magic-formula friction model illustrates the performance of the algorithm.

Multi-mode model predictive controller for constrained linear systems with bounded disturbances

This paper presents a multi-mode controller approach for a constrained linear system with bounded disturbances based on the model predictive control (MPC) framework. Compared with single MPC controller implementations, the proposed approach has the flexibility of having a large domain of attraction, good asymptotic behavior and reasonably low on-line computation. The closed-loop control law of the multi-mode controller is available in closed-form. In this case, the proposed controller has fewer partitions of the domain of attraction compared to single MPC controller having similar domain of attraction. The performances of the approach are presented via an example

Regularized Nonlinear Moving-Horizon Observer With Robustness to Delayed and Lost Data

Moving-horizon estimation provides a general method for state estimation with strong theoretical convergence properties under the critical assumption that global solutions are found to the associated nonlinear programming problem at each sampling instant. A particular benefit of the approach is the use of a moving window of data that is used to update the estimate at each sampling instant. This provides robustness to temporary data deficiencies such as lack of excitation and measurement noise, and the inherent robustness can be further enhanced by introducing regularization mechanisms. In this paper, we study moving-horizon estimation in cases when output measurements are lost or delayed, which is a common situation when digitally coded data are received over low-quality communication channels or random access networks. Modifications to a basic moving-horizon state estimation algorithm and conditions for exponential convergence of the estimation errors are given, and the method is illustrated by using a simulation example and experimental data from an offshore oil drilling operation.