While model predictive control (MPC) is the industrially preferred method for advanced control in the process industries, it has not found much use in consumer products and safety-critical embedded systems applications in industries such as automotive, aerospace, medical, and robotics. The main barriers are implementability and dependability, where important factors are implementation of advanced numerical optimization algorithms on resource-limited embedded computing platforms and the associated complexity of verification. This challenge comes from a requirement of the use of ultrareliable hardware and software architectures in safety-critical applications, low-cost hardware in consumer products, or both. This paper surveys the state-of-the-art in the emerging field of dependable embedded MPC, and discusses some key challenges related to its design, implementation, and verification. A novel result is the study of a simulator-based performance monitoring and control selection method that monitors and predicts MPC performance and switches to a highly reliable backup controller in cases when the MPC experiences performance issues.

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Toward Dependable Embedded Model Predictive Control

The friction between wheel and track is usually called adhesion force, and it is the critical factor for the movement of trains. On one hand, excessive driving force of a train may lead to insufficient utilization of the adhesion effect and cause wasted energy; on the other hand, insufficient driving force of a train brings inefficient train operation. To balance the issues of energy consumption, operational efficiency, and security, it is necessary to control a train to obtain its maximal adhesion force, particularly in the cases of fast acceleration and emergency braking. However, since engineering experiments indicate a complex nonlinear relationship between the adhesion force and the slip ratio of a train, such a control problem is difficult and challenging, particularly when the optimal slip ratio is unknown. Facing this problem, this paper proposes a novel control method based on the modification of the famous super-twisting sliding mode algorithm, and rigorous mathematical analysis is given to guarantee the ultimate boundedness of the proposed algorithm. Furthermore, by considering four different control scenarios, detailed control and estimation algorithms are both proposed. Simulation result verifies that the proposed control strategy can control the train to obtain its maximum adhesion force.

A Super-Twisting-Like Algorithm and Its Application to Train Operation Control With Optimal Utilization of Adhesion Force

The ever-present desire of humankind to explore new limits introduced us to the syndrome of decompression sickness (DCS). This broad overview of DCS is aimed at its pathophysiology and basics of therapeutic strategies. After a brief explanation of decompression theory, historical vignettes will serve to inform the practical application of our increasing understanding of DCS risks. The pathophysiology, current practices, role of bubble monitoring, risk factors, and potential long-term effects of DCS are also discussed. The goal is to explain the current state of DCS understanding in the context of a robust observational and empirical history. However, DCS remains a syndrome consisting of a constellation of symptoms following a change in ambient pressure. Though great strides have been made, significant knowledge gaps remain. If the coming years advance the field even a fraction of what its predecessors accomplished, the health and safety of those who endeavor in the environment of changing pressures most certainly will be improved.

Decompression and decompression sickness.

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 is 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 central venous pool. A recent study reveals that the optimal solution can be obtained by solving the optimization problem with 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. To reduce the complexity of the nonlinear optimization problem this paper also studies the decompression profile parameterization and its effect. Furthermore, by applying multi-parametric nonlinear programming technique, an approximate explicit solution to the nonlinear optimization problem is obtained, which makes the practical implementation on a typical low-cost diving computer possible.

Approximate Explicit Nonlinear Receding Horizon Control for Decompression of Divers

Model predictive control (MPC) is an advanced control technique thatrequires solving an optimization problem at each sampling instant. Severalemerging applications require the use of short sampling ...

Efficient Convex Quadratic Optimization Solver for Embedded MPC Applications

Decompression modeling of divers is a research field that is over 100 years old and since the beginning has been studied mainly as a clinical and biomedical problem. The topic is largely unexplored by the technological sciences using methods and theories for modeling and control. This article outlines a structure where the process of bubble formation is modeled as a nonlinear dynamic model and then used to design a state estimator and model-based predictor. Procedures are then calculated using explicit MPC. We further discussed dive-computer implementations using approximate explicit solutions. Finally, we showed practical differences for divers using computers that implement this approach. When future advances in sensor technology are made, the present structure can be further developed to include more feedback control of the estimator and optimal control formulation.

Tor A Johansen

Papers

Optimal Decompression of Divers [Applications of Control]