scholarly journals FPGA implementation of an interior point solver for linear model predictive control

Author(s):  
Juan L. Jerez ◽  
George A. Constantinides ◽  
Eric C. Kerrigan
10.29007/qt5j ◽  
2018 ◽  
Author(s):  
Guillaume Davy ◽  
Eric Feron ◽  
Pierre-Loic Garoche ◽  
Didier Henrion

Classical control of cyber-physical systems used to rely on basic linear controllers. These controllers provided a safe and robust behavior but lack the ability to perform more complex controls such as aggressive maneuvering or performing fuel-efficient controls. Another approach called optimal control is capable of computing such difficult trajectories but lacks the ability to adapt to dynamic changes in the environment. In both cases, the control was designed offline, relying on more or less complex algorithms to find the appropriate parameters. More recent kinds of approaches such as Linear Model-Predictive Control (MPC) rely on the online use of convex optimization to compute the best control at each sample time. In these settings optimization algorithms are specialized for the specific control problem and embed on the device.This paper proposes to revisit the code generation of an interior point method (IPM) algorithm, an efficient family of convex optimization, focusing on the proof of its implementation at code level. Our approach relies on the code specialization phase to produce additional annotations formalizing the intended specification of the algorithm. Deductive methods are then used to prove automatically the validity of these assertions. Since the algorithm is complex, additional lemmas are also produced, allowing the complete proof to be checked by SMT solvers only.This work is the first to address the effective formal proof of an IPM algorithm. The approach could also be generalized more systematically to code generation frameworks, producing proof certificate along the code, for numerical intensive software.


Author(s):  
Zhi Qi ◽  
Qianyue Luo ◽  
Hui Zhang

In this paper, we aim to design the trajectory tracking controller for variable curvature duty-cycled rotation flexible needles with a tube-based model predictive control approach. A non-linear model is adopted according to the kinematic characteristics of the flexible needle and a bicycle method. The modeling error is assumed to be an unknown but bounded disturbance. The non-linear model is transformed to a discrete time form for the benefit of predictive controller design. From the application perspective, the flexible needle system states and control inputs are bounded within a robust invariant set when subject to disturbance. Then, the tube-based model predictive control is designed for the system with bounded state vector and inputs. Finally, the simulation experiments are carried out with tube-based model predictive control and proportional integral derivative controller based on the particle swarm optimisation method. The simulation results show that the tube-based model predictive control method is more robust and it leads to much smaller tracking errors in different scenarios.


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