Polytopic Approximation of Explicit Model Predictive Controllers

A model predictive control law (MPC) is given by the solution to a parametric optimization problem that can be pre-computed offline, which provides an explicit map from state to input that can be rapidly evaluated online. However, the primary limitations of these optimal explicit solutions are that they are applicable to only a restricted set of systems and that the complexity can grow quickly with problem size. In this paper we compute approximate explicit control laws that trade-off complexity against approximation error for MPC controllers that give rise to convex parametric optimization problems. The algorithm is based on the classic double- description method and returns a polyhedral approx- imation to the optimal cost function. The proposed method has three main advantages from a control point of view: it is an incremental approach, meaning that an approximation of any specified complexity can be produced, it operates on implicitly-defined convex sets, meaning that the prohibitively complex optimal explicit solution is not required and finally it can be applied to any convex parametric optimization problem. A sub-optimal controller based on barycentric in- terpolation is then generated from this approximate polyhedral cost function that is feasible and stabiliz- ing. The resulting control law is continuous, although non-linear and defined over a non-simplical polytopic partition of the state space. The non-simplical nature of the partition generates significantly simpler approx- imate control laws, which is demonstrated on several examples

Automation and Control Architecture for Hybrid Pipeline Robots

The aim of this research project, towards the automation of the Hybrid Pipeline Robot (HPR), is the development of a control architecture and strategy, based on reconfiguration of the control strategy for speed-controlled pipeline operations and self-recovering action, while performing energy and time management. The HPR is a turbine powered pipeline device where the flow energy is converted to mechanical energy for traction of the crawler vehicle. Thus, the device is flow dependent, compromising the autonomy, and the range of tasks it can perform. The control strategy proposes pipeline operations supervised by a speed control, while optimizing the energy, solved as a multi-objective optimization problem. The states of robot cruising and self recovering, are controlled by solving a neuro-dynamic programming algorithm for energy and time optimization, The robust operation of the robot includes a self-recovering state either after completion of the mission, or as a result of failures leading to the loss of the robot inside the pipeline, and to guaranteeing the HPR autonomy and operations even under adverse pipeline conditions Two of the proposed models, system identification and tracking system, based on Artificial Neural Networks, have been simulated with trial data. Despite the satisfactory results, it is necessary to measure a full set of robot’s parameters for simulating the complete control strategy. To solve the problem, an instrumentation system, consisting on a set of probes and a signal conditioning board, was designed and developed, customized for the HPR’s mechanical and environmental constraints. As a result, the contribution of this research project to the Hybrid Pipeline Robot is to add the capabilities of energy management, for improving the vehicle autonomy, increasing the distances the device can travel inside the pipelines; the speed control for broadening the range of operations; and the self-recovery capability for improving the reliability of the device in pipeline operations, lowering the risk of potential loss of the robot inside the pipeline, causing the degradation of pipeline performance. All that means the pipeline robot can target new market sectors that before were prohibitive