Rubens Junqueira Magalhães Afonso

Fractional Order Modeling of Large Three-Dimensional RC Networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

Predictive Control of a helicopter model with tolerance to actuator faults

Predictive Control formulations can be designed with nominal asymptotic stability guarantees, provided that the associated optimization problem is feasible at each sampling time. However, model-plant mismatches, external perturbations or faults may cause the optimization to become infeasible. Such a problem motivates the development of techniques aimed at recovering feasibility without violating hard physical constraints imposed by the nature of the plant. This paper investigates the possible advantages of employing a policy of setpoint management to circumvent infeasibility problems in a Predictive Control framework. The investigation is mainly concerned with robustness of the controller regarding actuator faults that can be modelled as a change in the allowed excursion of the control signal. The results obtained with the proposed setpoint management technique are compared to the default solution provided by the adopted computational toolbox in case of infeasibility. An application involving a nonlinear simulation model of a laboratory helicopter with three degrees of freedom is presented.

Predictive control with trajectory planning in the presence of obstacles

In this work, a trajectory planning technique for an autonomous vehicle is proposed. A Predictive Control formulation is used both to plan a trajectory and control the vehicle in the presence of obstacles and dynamic constraints. However, some particularities of this sort of missions may make the time required for solution of the associated optimization problem prohibitive for a given sampling period. In this context, the possibility of using smaller prediction and control horizons is important to obtain a suitable control sequence within each sampling time. For this purpose, a trajectory planner which distributes waypoints along a previously established path is employed in the present paper. Each waypoint is determined so that it can be reached in a horizon which is smaller than the one necessary to reach the target set from the initial position, thus reducing the computational burden during the control phase. Moreover, during the planning phase the waypoints are chosen under the restriction that the target set should be reached within finite time so that the mission can be accomplished.

Infeasibility Handling in Constrained MPC

Predictive Control optimization problems may be rendered infeasible in the presence of constraints due to model-plant mismatches, external perturbations, noise or faults. This may cause the optimizer to issue a control sequence which is impossible to implement, leading to prediction errors, as well as loss of stability of the control loop. Such a problem motivates the development of techniques aimed at recovering feasibility without violating hard physical constraints imposed by the nature of the plant. Currently, setpoint management approaches and techniques dealing with changes in the constraints are two of the most effective solutions to recover feasibility with low computational demand. In this chapter a review of techniques that can be understood as one of the aforementioned is presented along with some illustrative simulation examples.

Sense Avoidance Constraints for Conflict Resolution between Autonomous Vehicles

Potential conflict situations between vehicles in the presence of obstacles are addressed by a decentralized approach imposing sense constraints, i.e., requiring that the vehicles circumvent an obstacle in a predetermined sense: either clockwise or counterclockwise. Model Predictive Control is used to plan trajectories using binary decision variables. In order to do that, a novel scheme to choose the feasible regions is proposed, and then obstacle avoidance constraints are encoded using tuples of binary decision variables. Sense constraints arise naturally as an extension of the proposed encoding scheme, allowing for decentralized planning, given that the vehicles agree on the required sense of circumvention. Simulation results are used to illustrate the benefits of the proposed method.

Improving fault tolerance in model predictive control through enlargement of the recursively feasible set

Feasibility of the optimization problem in a predictive controller may be compromised in the event of a fault. One alternative to recover feasibility is to relax the constraints. The terminal constraints seem like suitable candidates for relaxation, as they are often artificially introduced to ensure recursive feasibility. As an advantage, the physical constraints over the states and controls can be preserved. To solve this infeasibility issue, this work proposes the removal of terminal constraints, followed by the enlargement of the recursively feasible set through retuning the cost function. Simulation results are presented to illustrate the potential benefits of the proposed technique.

Multitask trajectory planning based on Predictive Control

In this work, a Predictive Control formulation for trajectory planning with multiple target sets is proposed, which solves the problem of performing all tasks in finite time via minimization of a weighted-time-fuel cost function, generating a feasible trajectory. An approach involving a procedure to order the list of the target sets to be visited in terms of the distance between them is used for comparison and it is shown that the proposed technique outperforms this approach in terms of time and fuel spent to accomplish the mission.

Uso de conjuntos terminais parametrizados para tratamento de problemas de não-factibilidade em controle preditivo

Terminal constraints are usually employed in predictive control formulations to provide closed-loop stability guarantees. However, such guarantees are lost if the associated optimization problem is not feasible from the beginning or if it becomes infeasible due to the onset of faults, for example. This work presents an approach involving setpoint management and relaxation of operational constraints to address infeasibility problems in predictive control. It is assumed that infeasibility may occur either at the beginning of the control task, due to an adverse initial condition, or as the result of an actuator fault that reduces the range of admissible control values. The proposed approach involves the parametrization of the maximal output admissible set (MAS) employed as terminal constraint in the control law. This parametrization avoids the need to repeat the MAS determination during the infeasibility handling procedure. For illustration purposes, a case study involving a simulation model is presented.