Eigenvalue placement by quantifier elimination : the static output feedback problem

This contribution addresses the static output feedback problem of linear time-invariant systems. This is still an area of active research, in contrast to the observer-based state feedback problem, which has been solved decades ago. We consider the formulation and solution of static output feedback design problems using quantifier elimination techniques. Stabilization, as well as more specified eigenvalue placement scenarios, are the focus of the paper

Geometric algorithms for input constrained systems with application to flight control.

In this thesis novel numerical algorithms are developed to solve some problems of analysis and control design for unstable linear dynamical systems having their input constrained by maximum amplitude and rate of the control signals. Although the results obtained are of a general nature, all the problems considered are induced by flight control applications. Moreover, all these problems are stated in terms of geometry, and because of this their solution in the thesis was effectively achieved by geometrically-oriented methods. The problems considered are mainly connected with the notions of the controllable and stability regions. The controllable region is defined as the set of states of an unstable dynamical system that can be stabilized by some realizable control action. This region is bounded due to input constraints and its size can serve as a controllability measure for the control design problem. A numerical algorithm for the computation of two-dimensional slices of the region is proposed. Moreover, the stability region design is also considered. The stability region of the closed-loop system is the set of states that can be stabilized by a particular controller. This region generally utilizes only a part of the controllable region. Therefore, the controller design objective may be formulated as maximizing this region. A controller that is optimal in this sense is proposed for the case of one and two exponentially unstable open-loop eigenvalues. In the final part of the thesis a linear control allocation problem is considered for overactuated systems and its real-time solution is suggested. Using the control allocation, the actuator selection task is separated from the regulation task in the control design. All fault detection and reconfiguration capabilities are concentrated in one special unit called the control allocator, while a general control algorithm, which produces 'virtual' input for the system, remains intact. In the case of an actuator fault, only the control allocation unit needs to be reconfigured and in many cases it can generate the same 'virtual' input using a different set of control effectors. A novel control allocation algorithm, which is proposed in the thesis, is based on multidimensional interval bisection techniques

Algebraic geometric methods for the stabilizability and reliability of multivariable and of multimode systems

The extent to which feedback can alter the dynamic characteristics (e.g., instability, oscillations) of a control system, possibly operating in one or more modes (e.g., failure versus nonfailure of one or more components) is examined

Aircraft loss-of-control prevention and recovery: a hybrid control strategy

The Complexity of modern commercial and military aircrafts has necessitated better protection and recovery systems. With the tremendous advances in computer technology, control theory and better mathematical models, a number of issues (Prevention, Recon guration, Recovery, Operation near critical points, ... etc) moderately addressed in the past have regained interest in the aeronautical industry.Flight envelope is essential in all ying aerospace vehicles. Typically, ying the vehicle means remaining within the ight envelope at all times. Operation outside the normal ight regime is usually subject to failure of components (Actuators, Engines, Deection Surfaces) , pilots's mistakes, maneuverability near critical points and environmental conditions(crosswinds...) and in general characterized as Loss-Of-Control (LOC) because the aircraft no longer responds to pilot's inputs as expected.For the purpose of this work,(LOC) in aircraft is de ned as the departure from the safe set (controlled flight) recognized as the maximum controllable (reachable) set in the initial ight envelope. The LOC can be reached either through failure, unintended maneuvers, evolution near irregular points and disturbances. A coordinated strategy is investigated and designed to ensure that the aircraft can maneuver safely in their constraint domain and can also recover from abnormal regime. The procedure involves the computation of the largest controllable (reachable) set (Safe set) contained in the initial prescribed envelope. The problem is posed as a reachability problem using Hamilton-Jacobi Partial Di erential Equation(HJ - PDE) where a cost function is set to be minimized along trajectory departing from the given set. Prevention is then obtained by computing the controller which would allow the flight vehicle to remain in the maximum controlled set in a multi-objective set up. Then the recovery procedure is illustrated with a two - point boundary value problem. Once illustrate, a set of control strategies is designed for recovery purpose ranging from nonlinear smooth regulators with Hamilton Jacobi-Bellman (HJB) formulation to the switching controllers with High Order Sliding Mode Controllers (HOSMC). A coordinated strategy known as a high level supervisor is then implemented using the multi-models concept where models operate in specified safe regions of the state space.Ph.D., Mechanical Engineering and Mechanics -- Drexel University, 201

Contrôle du vol longitudinal d'un avion civil avec satisfaction de qualités de manoeuvrabilité

RÉSUMÉ Satisfaire les qualités de manœuvrabilité demeure toujours une contrainte essentielle lors de la conception des commandes de vol. Ces critères de différentes natures sont le fruit d'une longue expérience d'essais en vol et d'analyse de données et il convient de les considérer pour espérer un bon comportement de l'appareil en vol. Dans ce cadre, l'enjeu de cette thèse est d'élaborer des méthodes de synthèse capables de satisfaire au mieux ces critères en respectant d'une part des architectures classiques imposées par le constructeur et, d'autre part, en adoptant une nouvelle architecture de contrôle. Le travail est effectué sur le vol longitudinal d'un avion d'affaire de Bombardier Inc., le Challenger 604. Une première étape consiste à rassembler les qualités de manœuvrabilité les plus souvent utilisées et de les confronter. Nous étudions plus particulièrement le critère du dropback pour lequel une analyse théorique permet d'établir une formulation pratique utilisable lors d'une synthèse. De plus, la confrontation de ces critères sur un modèle standard met en évidence des critères dominants, qui, une fois satisfaits, impliquent que d'autres critères le sont aussi. Nous pouvons dès lors considérer le problème de satisfaction de ces critères dominants dans le cadre d'une loi de contrôle dont l'architecture est imposée. Nous nous tournons alors du côté des applications gardiennes (Saydy et al., 1990). Initialement destinées à l'étude de la robustesse, elles sont intégrées dans différents algorithmes pour la synthèse de correcteur. Ce problème s'inscrit dans le cadre plus général de stabilisation par retour de sortie et de synthèse de correcteurs d'ordre réduit. Il en ressort des algorithmes permettant la stabilisation de système et le placement de pôles dans une région du plan complexe. Ceux-ci sont étendus dans le cadre du séquencement du contrôleur sur toute l'enveloppe de vol en fonction de certains paramètres. Nous faisons ensuite fi de la structure du correcteur en conservant seulement les mêmes sorties. L'idée est à présent d'utiliser une synthèse H pour obtenir un correcteur satisfaisant les qualités de manœuvrabilité grâce à l'appariement avec un modèle de référence et robuste à des variations de masse et de centrage de l'avion. Grâce aux travaux sur la commande modale robuste (Magni, 2002), nous pouvons réduire substantiellement l'ordre de ce correcteur ainsi que le structurer afin de nous rapprocher d'une architecture classique. Une méthode d'auto-séquencement de correcteurs, nous permet finalement de séquencer ce correcteur à travers toute l'enveloppe de vol. Deux voies différentes sont donc empruntées pour la résolution du même problème; chacune montre ses avantages et ses inconvénients.----------ABSTRACT Fulfilling handling qualities still remains a challenging problem during flight control design. These criteria of different nature are derived from a wide experience based upon flight tests and data analysis, and they have to be considered if one expects a good behavior of the aircraft. The goal of this thesis is to develop synthesis methods able to satisfy these criteria with fixed classical architectures imposed by the manufacturer or with a new flight control architecture. This is applied to the longitudinal flight model of a Bombardier Inc. business jet aircraft, namely the Challenger 604. A first step of our work consists in compiling the most commonly used handling qualities in order to compare them. A special attention is devoted to the dropback criterion for which theoretical analysis leads us to establish a practical formulation for synthesis purpose. Moreover, the comparison of the criteria through a reference model highlighted dominant criteria that, once satisfied, ensure that other ones are satisfied too.Consequently, we are able to consider the fulfillment of these criteria in the fixed control architecture framework. Guardian maps (Saydy et al., 1990) are then considered to handle the problem. Initially for robustness study, they are integrated in various algorithms for controller synthesis. Incidently, this fixed architecture problem is similar to the static output feedback stabilization problem and reduced-order controller synthesis. Algorithms performing stabilization and pole assignment in a specific region of the complex plane are then proposed. Afterwards, they are extended to handle the gain-scheduling problem. The controller is then scheduled through the entire flight envelope with respect to scheduling parameters. Thereafter, the fixed architecture is put aside while only conserving the same output signals. The main idea is to use H synthesis to obtain an initial controller satisfying handling qualities thanks to reference model pairing and robust versus mass and center of gravity variations. Using robust modal control (Magni, 2002), we are able to reduce substantially the controller order and to structure it in order to come close to a classical architecture. An auto-scheduling method finally allows us to schedule the controller with respect to scheduling parameters. Two different paths are used to solve the same problem; each one exhibits its own advantages and disadvantages

Multi particle swarm optimisation algorithm applied to supervisory power control systems

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University LondonPower quality problems come in numerous forms (commonly spikes, surges, sags, outages and harmonics) and their resolution can cost from a few hundred to millions of pounds, depending on the size and type of problem experienced by the power network. They are commonly experienced as burnt-out motors, corrupt data on hard drives, unnecessary downtime and increased maintenance costs. In order to minimise such events, the network can be monitored and controlled with a specific control regime to deal with particular faults. This study developed a control and Optimisation system and applied it to the stability of electrical power networks using artificial intelligence techniques. An intelligent controller was designed to control and optimise simulated models for electrical system power stability. Fuzzy logic controller controlled the power generation, while particle swarm Optimisation (PSO) techniques optimised the system’s power quality in normal operation conditions and after faults. Different types of PSO were tested, then a multi-swarm (M-PSO) system was developed to give better Optimisation results in terms of accuracy and convergence speed.. The developed Optimisation algorithm was tested on seven benchmarks and compared to the other types of single PSOs. The developed controller and Optimisation algorithm was applied to power system stability control. Two power electrical network models were used (with two and four generators), controlled by fuzzy logic controllers tuned using the Optimisation algorithm. The system selected the optimal controller parameters automatically for normal and fault conditions during the operation of the power network. Multi objective cost function was used based on minimising the recovery time, overshoot, and steady state error. A supervisory control layer was introduced to detect and diagnose faults then apply the correct controller parameters. Different fault scenarios were used to test the system performance. The results indicate the great potential of the proposed power system stabiliser as a superior tool compared to conventional control systems

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

State Omniscience for Cooperative Local Catalog Maintenance of Close Proximity Satellite Systems

Resiliency in multi-agent system navigation is reliant on the inherent ability of the system to withstand, overcome, or recover from adverse conditions and disturbances. In large part, resiliency is achieved through reducing the impact of critical failure points to the success and/or performance of the system. In this view, decentralized multi-agent architectures have become an attractive solution for multi-agent navigation, but decentralized architectures place the burden of information acquisition directly on the agents themselves. In fact, the design of distributed estimators has been a growing interest to enable complex multi-sensor/multi-agent tasks. In such scenarios, it is important that each local estimator converges to the true global system state - a quality known as state omniscience. Most previous related work has focused on the design of such systems under varying assumptions on the graph topology with simplified information fusion schemes. Contrarily, this work introduces characterizations of state omniscience under generalized graph topologies and generalized information fusion schemes. State omniscience is discussed analogously to observability from classical control theory; and a collection of necessary and sufficient conditions for a distributed estimator to be state omniscient are presented. This dissertation discusses this phenomena in terms of an on-orbit scenarios dubbed the local catalog maintenance problem and the cooperative local catalog maintenance problem. The goal of each agent is to maintain their catalog of all bodies (objects and agents) within this neighborhood through onboard angles-only measurements and cooperative communication with the other agents. A central supervisor selects the target body for each agent, a local controller tracks the selected target body for each agent, and a local estimator coalesces both an agent\u27s measurements and state estimates provided by neighboring agents within the communication graph. Numerical results are provided to demonstrate the supervisor\u27s ability to select an appropriate target subject to an uncertainty threshold, the controller\u27s ability to track the selected target, and the estimator\u27s ability to maintain an accurate and precise estimate of each of the bodies in the local environment