Planar Cooperative Extremum Seeking with Guaranteed Convergence Using A Three-Robot Formation

In this paper, a combined formation acquisition and cooperative extremum seeking control scheme is proposed for a team of three robots moving on a plane. The extremum seeking task is to find the maximizer of an unknown two-dimensional function on the plane. The function represents the signal strength field due to a source located at maximizer, and is assumed to be locally concave around maximizer and monotonically decreasing in distance to the source location. Taylor expansions of the field function at the location of a particular lead robot and the maximizer are used together with a gradient estimator based on signal strength measurements of the robots to design and analyze the proposed control scheme. The proposed scheme is proven to exponentially and simultaneously (i) acquire the specified geometric formation and (ii) drive the lead robot to a specified neighborhood disk around maximizer, whose radius depends on the specified desired formation size as well as the norm bounds of the Hessian of the field function. The performance of the proposed control scheme is evaluated using a set of simulation experiments.Comment: Presented at the 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, FL, US

Model-free Control and Automatic Staging of Variable Refrigerant Flow System with Multiple Outdoor Units

For efficient operation of a variable refrigerant flow (VRF) air conditioning system with multiple outdoor units (ODUs), we propose a model-free control strategy based on extremum seeking control along with automatic staging control logic. The proposed strategy is evaluated with a representative VRF system consisting of 12 indoor units (IDUs) and three ODUs. The IDU zone temperature is regulated by EEV opening, and the compressor pressure is regulated by compressor speed. To optimize load sharing among multiple ODUs in operation, a set of bypass valves (BPVs) are added to the suction side of the compressors to manipulate refrigerant flow distribution among different compressors as needed. A penalty-function based multivariable extremum seeking control (ESC) method is used for real-time optimization of system operation. The performance index as the ESC feedback is the total power of the compressors, the ODU fans and the IDU fans, augmented with penalties for securing minimum superheat at the suction side of compressors. The manipulated inputs include the compressor suction pressure setpoint, the openings of BPVs at the suction side of the compressors, and a uniform setpoint of fan speed for all ODUs. As for the ESC feedback, the compressor power is normalized by its capacity. A set of control strategies for staging on/off particular ODUs is developed based on the compressor speed of the operating ODUs. Under increasing load, if the operating compressor(s) speed exceeds the higher limit of operation speed range (80% of rated speed), an additional ODU turned on to meet the load demand. Under decreasing load, it is desirable to turn off the least efficient ODU in a model-free fashion. In this study, an ESC based ODU staging-off strategy is proposed, for which the compressor shaft power normalized by the rated capacity is adopted as the ESC input. In addition to the compressor pressure setpoints and ODU fan speeds, the manipulated inputs of ESC also include the openings of suction-side BPVs in order to optimize load sharing among the multiple ODUs. With online optimization of ODU load sharing based on the normalized compressor power, the ESC can drive less efficient compressor(s) to operate at lower speed/capacity. If the compressor speed of an ODU falls below the preset lower limit of operational speed range (e.g. 20% of the rated speed) for long enough time, this ODU will be turned off. A dynamic simulation model of the multi-ODU VRF system is developed with Dymola and TIL Library. Simulation studies have been performed to evaluate the proposed ESC strategy for energy efficient operation during constant load patterns and the control logic for staging on and off ODU during load increase and decrease. The total power searched by the ESC is shown to be close to that obtained by a genetic algorithm based global optimization procedure in Dymola. Also, ESC is shown to be able to turn off least efficient ODU during load decrease without model knowledge. The load-sharing BPV at the compressor suction-side demonstrates bearable pressure loss except for the scenarios of large split ratio

Formation Flight System Extremum-Seeking-Control Using Blended Performance Parameters

An extremum-seeking control system for formation flight that uses blended performance parameters in a conglomerate performance function that better approximates drag reduction than performance functions formed from individual measurements. Generally, a variety of different measurements are taken and fed to a control system, the measurements are weighted, and are then subjected to a peak-seeking control algorithm. As measurements are continually taken, the aircraft will be guided to a relative position which optimizes the drag reduction of the formation. Two embodiments are discussed. Two approaches are shown for determining relative weightings: "a priori" by which they are qualitatively determined (by minimizing the error between the conglomerate function and the drag reduction function), and by periodically updating the weightings as the formation evolves

Self-optimizing control – A survey

Self-optimizing control is a strategy for selecting controlled variables. It is distinguished by the fact that an economic objective function is adopted as a selection criterion. The aim is to systematically select the controlled variables such that by controlling them at constant setpoints, the impact of uncertain and varying disturbances on the economic optimality is minimized. If a selection leads to an acceptable economic loss compared to perfectly optimal operation then the chosen control structure is referred to as “self-optimizing”. In this comprehensive survey on methods for finding self-optimizing controlled variables we summarize the progress made during the last fifteen years. In particular, we present brute-force methods, local methods based on linearization, data and regression based methods, and methods for finding nonlinear controlled variables for polynomial systems. We also discuss important related topics such as handling changing active constraints. Finally, we point out open problems and directions for future research

Cluster-based feedback control of turbulent post-stall separated flows

We propose a novel model-free self-learning cluster-based control strategy for general nonlinear feedback flow control technique, benchmarked for high-fidelity simulations of post-stall separated flows over an airfoil. The present approach partitions the flow trajectories (force measurements) into clusters, which correspond to characteristic coarse-grained phases in a low-dimensional feature space. A feedback control law is then sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption in flight. Unsupervised clustering of the flow trajectories for in-situ learning and optimization of coarse-grained control laws are implemented in an automated manner as key enablers. Re-routing the flow trajectories, the optimized control laws shift the cluster populations to the aerodynamically favorable states. Utilizing limited number of sensor measurements for both clustering and optimization, these feedback laws were determined in only $O(10)$ iterations. The objective of the present work is not necessarily to suppress flow separation but to minimize the desired cost function to achieve enhanced aerodynamic performance. The present control approach is applied to the control of two and three-dimensional separated flows over a NACA 0012 airfoil with large-eddy simulations at an angle of attack of $9^\circ$, Reynolds number $Re = 23,000$ and free-stream Mach number $M_\infty = 0.3$. The optimized control laws effectively minimize the flight power consumption enabling the flows to reach a low-drag state. The present work aims to address the challenges associated with adaptive feedback control design for turbulent separated flows at moderate Reynolds number.Comment: 32 pages, 18 figure

An Efficient Global Optimization Method Based on Multi-Unit Extremum Seeking

RÉSUMÉ Les problèmes d'optimisation industrielle, telle que la maximisation de la production de produits chimiques et pétrochimiques, montrent généralement plusieurs points optimaux locaux. Le développement de méthode pour la sélection du point optimal global a toujours fait l’objet de nombreuses recherches. Plusieurs techniques déterministes et stochastiques ont été explorées à cette fin. Les techniques stochastiques ne garantissent pas toujours la convergence vers la solution globale, mais sont efficaces pour les dimensions supérieures. D'autre part, les méthodes déterministes se rendent à l'optimum global, mais le défi est d'employer un cloisonnement efficace de l'espace afin de réduire le nombre d'évaluations fonctionnelles. Cette thèse propose une approche originale en matière d’optimisation globale, numérique et déterministe basée sur des techniques d'optimisation locale en temps réel et en particulier, sur des techniques sans modèle appelé les systèmes de commande extrémale. Pour les problèmes sans contrainte, les systèmes de commande extrémale représente le problème d'optimisation comme un contrôle du gradient. La façon dont le gradient est estimé constitue la différence principale entre les différentes alternatives qui sont proposées dans la littérature scientifique. Pour les méthodes de perturbation, un signal d'excitation temporelle est utilisé afin de calculer le gradient. Une alternative existe dans le cadre d'optimisation multi-unité où le gradient est estimé par la différence finie de la sortie de deux unités identiques, mais dont les données d’entré se distinguent par un décalage. Le point de départ de cette recherche a été motivée par les systèmes de commandes extrémales locales. Ces commandes sont basées sur une perturbation qui peut être utilisée comme un outil pour l'optimisation globale des polynômes scalaires du quatrième ordre avec un optimum global. L'objectif de cette thèse est d'étendre ce concept et de développer une technique d'optimisation globale déterministe pour une classe générale de systèmes multi-variables, statiques, non linéaires et continus. Dans cette thèse, il est d'abord démontré que si le décalage est réduit à zéro pour une optimisation multi-unité scalaire, le système converge vers l'optimum global. Le résultat est également étendu aux problèmes scalaires avec contraintes qui sont caractérisés par des régions non-convexes. Dans ce cas, une stratégie de commande de “Switching” est utilisée pour faire face aux contraintes.----------ABSTRACT Industrial optimization problems, e.g., maximizing production in chemical and petrochemical facilities, typically exhibit multiple local optimal points and so choosing the global one has always attracted many researchers. Many deterministic and stochastic techniques have been explored towards this end. The stochastic techniques do not always guarantee convergence to the global solution, but fare well computationally for higher dimensions. On the other hand, the deterministic methods get to the global optimum, while the challenge therein is to employ an efficient partitioning of the space in order to reduce the number of functional evaluations. This thesis proposes an original approach to numerical deterministic global optimization based on real-time local optimization techniques (in particular, model-free techniques termed the extremum-seeking schemes). For unconstrained problems, extremum-seeking schemes recast the optimization problem as the control of the gradient. The way the gradient is estimated forms the main difference between different alternatives that are proposed in the literature. In perturbation methods, a temporal excitation signal is used in order to compute the gradient. As an alternative, in the multi-unit optimization framework, the gradient is estimated as the finite difference of the outputs of two identical units driven with the inputs that differ by an offset. The starting point of this research was motivated by the perturbation-based extremum seeking schemes which can be used as a tool for global optimization of scalar fourth order polynomials, with one local and one global optimum. The objective of this thesis is to extend this concept and develop a deterministic global optimization technique for a general class of multi-variable, static, nonlinear and continuous systems. In this thesis, it is first shown that in the scalar multi-unit optimization framework, if the offset is reduced to zero, the scheme converges to the global optimum. The result is also extended to scalar constrained problems, with possible non-convex feasible regions, where a switching control strategy is employed to deal with the constraints. The next step consists of extending the algorithm to more than one variable. For two-input systems, univariate global optimization was repeated on the circumference of a circle of reducing radius. With three variables, the two-variable optimization mentioned above is repeated on the surface of a sphere of reducing radius. Time-scale separation between the various layer

Autonomous Identification and Tracking of Thermoclines

All data acquired from oceanic water features is hard and crucial work. It's hard due to the difficulty to obtain the same data given the unfavourable conditions.It requires, therefore, equipment that are reliable in the measurements of the desired characteristics and robust equipment, that is to say, equipment that are capable to withstand unfavorable and variable conditions in spatial and temporal terms. Due to these same spatial and temporal changes, the traditional methods do not prove to be the most adequate, because these methods do not have sufficient capacity to sample measurements of the dynamic characteristics of oceanographic processes.Thus, to obtain such measurements the use of the autonomous robotic systems proves to be important. With these systems, it is ensured a faster, more efficient and systematic sampling and is not subject to human error. The data acquisition is then a crucial work to understand how oceanographic process happens and varies in time and space. This work proposes an implementation of an algorithm to perform the tracking of the thermocline, from the stratification model of the oceanic water.This model is a parametric model. This work will also take into account the capacity to perform measurements with a sampling capable of adapting the depth control of the underwater vehicle.The stratification of the oceanic water happens when exists different features between different layers. One of these layers is the thermocline. At this layer, the water temperature decreases rapidly with increasing depth. The characterization of the thermocline is so important to marine biology, given the high concentration of phytoplankton in this level, as for acoustic communications equipments or military services, given the special characteristics of speed sound in this level.The model of this stratification will be used to aid in the thermocline's tracking process. This model will serve as a basis for the algorithm to adapt the control in order to carry out the tracking with the greatest success, in real time. This algorithm will focus on the variations in the vertical temperature gradient.The algorithm responsible detect and track of the thermocline will be run on a profiler. The profiler is a vehicle that moves along the vertical axis. However, when subject to tides, the natural process in aquatic environments drifts along the horizontal axis. A set of sensors capable of measuring the water temperature and the depth at which the vehicle is below water shall be placed in this vehicle. These sensors will be important to calculate the vertical gradient