Formal Performance Guarantees Research Articles

Quantized Sampled-Data Attitude Control of Ground Vehicles: An Event-Based Approach

Attitude control systems for ground vehicles have been an important topic in automotive research for decades, and have been extensively studied by resorting to classical continuous-time nonlinear design. Although this approach can incorporate saturation constraints and actuator dynamics in the design, the computed control laws are often approximated and applied within digital environments in absence of formal performance guarantees. In this work, we present a quantized sampled-data approach to the vehicle attitude control problem. Starting from classical nonlinear design achieving tracking of prescribed trajectories in continuous time (emulation approach), we derive conditions for preserving the practical stability of the error dynamics by means of quantized sampled-data event-based controllers. Simulations performed in an non-ideal setting confirm the potential of the approach.

Performance and energy aware robust specification of control execution patterns under dropped samples

Embedded control systems are prevalent in a multitude of domains such as automotive, avionics, industrial control etc. For such systems, robustness against non-idealities of the compute platform created by situations such as hardware level transient faults (memory errors, sensor reading errors), network packet drops, late arrival of messages etc., is needed to be ensured at the design level. In traditional regular periodic execution of control loops, such guarantees are obtained by oversampling the plant, which requires extra rounds of sensing, control law computation, and actuation. One possible measure for reducing such over-provisioning of computing and communication resources is allowing occasional drops in the execution leading to better resource management as well as energy efficiency. This work showcases a methodology for deriving window-based bounds on possible drops in control loop executions while assuring formal performance guarantees even in the presence of platform-level non-idealities. Derivation of such relaxation bounds in terms of control loop executions help in deciding energy efficient scheduling solutions for low-power resource-constrained embedded control platforms while retaining control performance. The present work provides a structured methodology for deriving performance-aware control execution patterns given an energy-budget and uncertainty specification of the platform executing a set of embedded control loops.

Probabilistic planning with formal performance guarantees for mobile service robots

We present a framework for mobile service robot task planning and execution, based on the use of probabilistic verification techniques for the generation of optimal policies with attached formal performance guarantees. Our approach is based on a Markov decision process model of the robot in its environment, encompassing a topological map where nodes represent relevant locations in the environment, and a range of tasks that can be executed in different locations. The navigation in the topological map is modeled stochastically for a specific time of day. This is done by using spatio-temporal models that provide, for a given time of day, the probability of successfully navigating between two topological nodes, and the expected time to do so. We then present a methodology to generate cost optimal policies for tasks specified in co-safe linear temporal logic. Our key contribution is to address scenarios in which the task may not be achievable with probability one. We introduce a task progression function and present an approach to generate policies that are formally guaranteed to, in decreasing order of priority: maximize the probability of finishing the task; maximize progress towards completion, if this is not possible; and minimize the expected time or cost required. We illustrate and evaluate our approach with a scalability evaluation in a simulated scenario, and report on its implementation in a robot performing service tasks in an office environment for long periods of time.

Event-Triggered Optimal Control With Performance Guarantees Using Adaptive Dynamic Programming.

This paper studies the problem of event-triggered optimal control (ETOC) for continuous-time nonlinear systems and proposes a novel event-triggering condition that enables designing ETOC methods directly based on the solution of the Hamilton-Jacobi-Bellman (HJB) equation. We provide formal performance guarantees by proving a predetermined upper bound. Moreover, we also prove the existence of a lower bound for interexecution time. For implementation purposes, an adaptive dynamic programming (ADP) method is developed to realize the ETOC using a critic neural network (NN) to approximate the value function of the HJB equation. Subsequently, we prove that semiglobal uniform ultimate boundedness can be guaranteed for states and NN weight errors with the ADP-based ETOC. Simulation results demonstrate the effectiveness of the developed ADP-based ETOC method.

Attention and Anticipation in Fast Visual-Inertial Navigation

We study a visual-inertial navigation (VIN) problem in which a robot needs to estimate its state using an on-board camera and an inertial sensor, without any prior knowledge of the external environment. We consider the case in which the robot can allocate limited resources to VIN, due to tight computational constraints. Therefore, we answer the following question: under limited resources, what are the most relevant visual cues to maximize the performance of VIN? Our approach has four key ingredients. First, it is task-driven, in that the selection of the visual cues is guided by a metric quantifying the VIN performance. Second, it exploits the notion of anticipation, since it uses a simplified model for forward-simulation of robot dynamics, predicting the utility of a set of visual cues over a future time horizon. Third, it is efficient and easy to implement, since it leads to a greedy algorithm for the selection of the most relevant visual cues. Fourth, it provides formal performance guarantees: we leverage submodularity to prove that the greedy selection cannot be far from the optimal (combinatorial) selection. Simulations and real experiments on agile drones show that our approach ensures state-of-the-art VIN performance while maintaining a lean processing time. In the easy scenarios, our approach outperforms appearance-based feature selection in terms of localization errors. In the most challenging scenarios, it enables accurate VIN while appearance-based feature selection fails to track robot's motion during aggressive maneuvers.

Constructive Preference Elicitation Over Hybrid Combinatorial Spaces

Peference elicitation is the task of suggesting a highly preferred configuration to a decision maker. The preferences are typically learned by querying the user for choice feedback over pairs or sets of objects. In its constructive variant, new objects are synthesized "from scratch" by maximizing an estimate of the user utility over a combinatorial (possibly infinite) space of candidates. In the constructive setting, most existing elicitation techniques fail because they rely on exhaustive enumeration of the candidates. A previous solution explicitly designed for constructive tasks comes with no formal performance guarantees, and can be very expensive in (or unapplicable to) problems with non-Boolean attributes. We propose the Choice Perceptron, a Perceptron-like algorithm for learning user preferences from set-wise choice feedback over constructive domains and hybrid Boolean-numeric feature spaces. We provide a theoretical analysis on the attained regret that holds for a large class of query selection strategies, and devise a heuristic strategy that aims at optimizing the regret in practice. Finally, we demonstrate its effectiveness by empirical evaluation against existing competitors on constructive scenarios of increasing complexity.

Optimization of oil production under gas coning conditions

Typically, a well is produced with a constant oil rate with constant gas–oil ratio (GOR) during the subcritical phase, i.e. before gas breakthrough. The presence of gas coning in production wells may reduce the oil production. The decline in the oil rate will be followed by an increase in the well head pressure. From an economical and operational point of view, this condition may be undesirable for several reasons; the gas price is much lower than the oil price, the afflicted well may be abandoned early, and the gas handling capacity often is a constraint. Therefore, there is an incentive to produce such wells in their subcritical phase for an extended period of time. In this paper, the gas coning process in a gas–oil reservoir completed with a single horizontal well is analytically modeled, simulated, and analyzed applying a nonlinear control approach. The horizontal well model which describes the interaction between the well and the reservoir may be cast into a boundary control problem of the porous media equation with two boundary conditions; a homogeneous Neumann's boundary condition describing no-flow at the outer boundary of the reservoir, and a nonlinear boundary condition describing the well production rate. A well rate controller for the boundary control problem is designed using the backstepping method. The controller holds some formal performance guarantees and requires information on the gas–oil contact (GOC) at the well heel only. Furthermore, the controller has a tuning parameter which can be used to maximize a suitable performance measure, e.g. the net present value (NPV). The controller is evaluated using a detailed Eclipse simulator of a gas coning reservoir. Simulation results show significant improvement of production profit of the proposed method compared to a conventional method which usually uses a constant rate until gas breakthrough.