We present a motion control framework which allows a group of robots to work together to decide upon their motions by minimizing a collective cost without any central computing component or any one agent performing a large portion of the computation. When developing distributed control algorithms, care must be taken to respect the limited computational capacity of each agent as well as respect the information and communication constraints of the network. To address these issues, we develop a distributed, behavior-based model predictive control (MPC) framework which alleviates the computational difficulties present in many distributed MPC frameworks, while respecting the communication and information constraints of the network. In developing the multi-agent control framework, we make three contributions. First, we develop a distributed optimization technique which respects the dynamic communication restraints of the network, converges to a collective minimum of the cost, and has transients suitable for robot motion control. Second, we develop a behavior-based MPC framework to control the motion of a single-agent and apply the framework to robot navigation. The third contribution is to combine the concepts of distributed optimization and behavior-based MPC to develop the mentioned multi-agent behavior-based MPC algorithm suitable for multi-robot motion control.

This thesis develops efficient optimization methods for Model Predictive Control (MPC) to enable its application to constrained systems with fast and uncertain dynamics. The key contribution is an active set method which exploits the parametric nature of the sequential optimization problem and is obtained from a dynamic programming formulation of the MPC problem. This method is first applied to the nominal linear MPC problem and is successively extended to linear systems with additive uncertainty and input constraints or state/input constraints. The thesis discusses both offline (projection-based) and online (active set) methods for the solution of controllability problems for linear systems with additive uncertainty. The active set method uses first-order necessary conditions for optimality to construct parametric programming regions for a particular given active set locally along a line of search in the space of feasible initial conditions. Along this line of search the homotopy of optimal solutions is exploited: a known solution at some given plant state is continuously deformed into the solution at the actual measured current plant state by performing the required active set changes whenever a boundary of a parametric programming region is crossed during the line search operation. The sequence of solutions for the finite horizon optimal control problem is therefore obtained locally for the given plant state. This method overcomes the main limitation of parametric programming methods that have been applied in the MPC context which usually require the offline precomputation of all possible regions. In contrast to this the proposed approach is an online method with very low computational demands which efficiently exploits the parametric nature of the solution and returns exact local DP solutions. The final chapter of this thesis discusses an application of robust tube-based MPC to the nonlinear MPC problem based on successive linearization.

<div>Class 8 trucks on average drive the most miles and consume the most fuel of any major vehicle category annually. Indiana specifically is the fifth busiest state for commercial freight traffic and moves $750 billion dollars of freight annually, and this number is expected to grow by 60% by 2040. Reducing fuel consumption for class 8 trucks would have a significant benefit on business and the proportional decrease in CO₂ would be exceptionally beneficial for the environment.</div><div><br></div><div>Platooning is one of the most important strategies for increasing class 8 truck fuel savings. Platooning alone can help trucks save upwards of 7% platoon average fuel savings on flat ground. However, it can be difficult for a platooning controller to maintain a desired truck separation during uncoordinated shifting events. Using a high-fidelity simulation model, it is shown that simultaneous shifting–having the follow truck shift whenever the lead truck shifts (unless shifting would cause its engine to overspeed or underspeed)–decreases maximum truck separation by 24% on a moderately challenging grade route and 40% on a heavy grade route.</div><div><br></div><div>Model Predictive Control (MPC) of the follow truck is considered as a means to reduce the distance the follow truck falls behind during uncoordinated shifting events. The result in simulation is a reduction in maximum truck separation of 1% on a moderately challenging grade route and 19% on a heavy grade route. However, simultaneous shifting largely alleviates the need for MPC for the sake of tracking for the follow truck.</div><div><br></div><div>A different MPC formulation is considered to dynamically change the desired set point for truck separation for routes through a strategy called Route Optimized Gap Growth (ROGG). The result in simulation is 1% greater fuel savings on a moderately challenging grade route and 7% greater fuel savings on a route with heavy grade for the follow truck.</div>

Pour faciliter la transition énergétique vers la réduction de la consommation des énergies fossiles, la réduction des émissions de CO2 et l’intégration des sources d’énergie renouvelables, il convient d’étudier des stratégies permettant d’adapter en temps réel la gestion énergétique de manière optimale par rapport aux contraintes extérieures et intérieures du bâtiment. Des leviers d’action existent à l’échelle de l’îlot comme la mutualisation des productions et des consommations. Cette thèse présente l’application de techniques d’optimisation au développement de stratégies de gestion du chauffage électrique d’un bâtiment multizone comportant des logements et des bureaux. Pour réduire les temps de calcul par rapport à une approche de résolution globale d’un problème d’optimisation à grande échelle, les méthodes de décomposition-coordination ont été étudiées. Ces méthodes permettent de résoudre des sous-problèmes d’optimisation à l’échelle de chaque zone et de réintégrer les couplages entre zones (couplages thermiques et partage d’une ressource) avec une étape de coordination. Une méthode décomposée-coordonnée a été retenue pour chaque type de couplage permettant la mise en place d’une gestion en temps réel à l’échelle multizone. / To facilitate the energy transition towards the reduction of fossil fuels consumption, CO2 emissions and the integration of renewable energy sources, it is necessary to study realtime management strategies to adapt energy management in an optimal way according to external and internal perturbations and the evolution of the building. Solutions exist at the scale of blocks of buildings such as production and consumption pooling. This thesis presents the development of real-time management strategies, using optimisation techniques, for the electric heating of a multi-zone building mixing residential and tertiary uses. To decrease computation time compared to a global resolution approach of large-scale optimisation problems, decomposition-coordination methods were studied. These methods consist in solving sub-problems of optimisation in each zone and reintegrating the links between zones (thermal couplings and resource sharing) using a coordination step. One of these methods was chosen for each type of coupling allowing the implementation of real-time management at a multi-zone scale.

The UK domestic sector accounts for more than a quarter of total energy use. This energy use can be reduced through more efficient building operations. The energy efficiency can be improved through better control of heating in houses, which account for a large portion of total energy consumption. The energy consumption can be lowered by using renewable energy systems, which will also help the UK government to meet its targets towards reduction in carbon emissions and generation of clean energy. Building control has gained considerable interest from researchers and much improved ways of control strategies for heating and hot water systems have been investigated. This intensified research is because heating systems represent a significant share of our primary energy consumption to meet thermal comfort and indoor air quality criteria. Advances in computing control and research in advanced control theory have made it possible to implement advanced controllers in building control applications. Heating control system is a difficult problem because of the non-linearities in the system and the wide range of operating conditions under which the system must function. A model of a two zone building was developed in this research to assess the performance of different control strategies. Two conventional (On-Off and proportional integral controllers) and one advanced control strategies (model predictive controller) were applied to a solar heating system combined with a heat pump. The building was modelled by using a lumped approach and different methods were deployed to obtain a suitable model for an air source heat pump. The control objectives were to reduce electricity costs by optimizing the operation of the heat pump, integrating the available solar energy, shifting electricity consumption to the cheaper night-time tariff and providing better thermal comfort to the occupants. Different climatic conditions were simulated to test the mentioned controllers. Both on-off and PI controllers were able to maintain the tank and room temperatures to the desired set-point temperatures however they did not make use of night-time electricity. PI controller and Model Predictive Controller (MPC) based on thermal comfort are developed in this thesis. Predicted mean vote (PMV) was used for controlling purposes and it was modelled by using room air and radiant temperatures as the varying parameters while assuming other parameters as constants. The MPC dealt well with the disturbances and occupancy patterns. Heat energy was also stored into the fabric by using lower night-time electricity tariffs. This research also investigated the issue of model mismatch and its effect on the prediction results of MPC. MPC performed well when there was no mismatch in the MPC model and simulation model but it struggled when there was a mismatch. A genetic algorithm (GA) known as a non-dominated sorting genetic algorithm (NSGA II) was used to solve two different objective functions, and the mixed objective from the application domain led to slightly superior results. Overall results showed that the MPC performed best by providing better thermal comfort, consuming less electric energy and making better use of cheap night-time electricity by load shifting and storing heat energy in the heating tank. The energy cost was reduced after using the model predictive controller.

A identificação de modelos é usualmente a tarefa mais significativa e demorada no trabalho de implementação e manutenção de sistemas de controle que usam Controle Preditivo baseado em Modelos (MPC) tendo em vista a complexidade da tarefa e a importância que o modelo possui para um bom desempenho do controlador. Após a implementação, o controlador tende a permanecer com o modelo original mesmo que mudanças de processo tenham ocorrido levando a uma degradação das ações do controlador. Este trabalho apresenta uma aplicação industrial de re-identificação em malha fechada. A metodologia de excitação da planta utilizada foi apresentada em Sotomayor et al. (2009). Tal técnica permite obter o comportamento das variáveis de processo sem desligar o MPC e sem modificar sua estrutura, aumentando assim, o automatismo e a segurança do procedimento de re-identificação. O sistema re-identificado foi uma coluna debutanizadora de uma refinaria brasileira sendo que os modelos fazem parte do controle preditivo multivariável dessa coluna de destilação. A metodologia foi aplicada com sucesso podendo-se obter os seis novos modelos para atualizar o controlador em questão, o que resultou em uma melhoria de seu desempenho. / Model identification is usually the most significant and time-consuming task of implementing and maintaining control systems based on models (MPC) concerning the complexity of the task and the importance of the model for a good performance of the controller. After being implemented the MPC tends to remain with the original model even after process changes have occurred, leading to a degradation of the controller actions. The present work shows an industrial application of closed-loop re-identification. The plant excitation methodology used here was presented in Sotomayor et al. (2009). Such technique allows for obtaining the behavior of the process variables with the MPC still working and without modifying the MPC structure, increasing automation and safety of the re-identification procedure. The system re-identified was a debutanizer column of a Brazilian refinery being the models part of the multivariable predictive control of this distillation column. The methodology was applied with reasonable success managing to obtain 6 new models to update this MPC, and resulting in improved control performance.

In modern cyber-physical systems (CPSs) where the control signals are generally transmitted via shared communication networks, there is a desire to balance the closed-loop control performance with the communication cost necessary to achieve it. In this context, aperiodic real-time scheduling of control tasks comes into being and has received increasing attention recently. It is well known that model predictive control (MPC) is currently widely utilized in industrial control systems and has greatly increased profits in comparison with the proportional integral-derivative (PID) control. As communication and networks play more and more important roles in modern society, there is a great trend to upgrade and transform traditional industrial systems into CPSs, which naturally requires extending conventional MPC to communication-efficient MPC to save network resources. Motivated by this fact, we in this thesis propose robust MPC and scheduling co-design algorithms to networked CPSs possibly affected by both parameter uncertainties and additive disturbances. In Chapter 2, a dynamic event-triggered robust tube-based MPC for constrained linear systems with additive disturbances is developed, where a time-varying pre-stabilizing gain is obtained by interpolating multiple static state feedbacks and the interpolating coefficient is determined via optimization at the time instants when the MPC-based control is triggered. The original constraints are properly tightened to achieve robust constraint optimization and a sequence of dynamic sets used to test events are derived according to the optimized coefficient. We theoretically show that the proposed algorithm is recursively feasible and the closed-loop system is input-to-state stable (ISS) in the attraction region. Numerical results are presented to verify the design. In Chapter 3, a self-triggered min-max MPC strategy is developed for constrained nonlinear systems subject to both parametric uncertainties and additive disturbances, where the robust constraint satisfaction is achieved by considering the worst case of all possible uncertainty realizations. First, we propose a new cost function that relaxes the penalty on the system state in a time period where the controller will not be invoked. With this cost function, the next triggering time instant can be obtained at current time instant by solving a min-max optimization problem where the maximum triggering period becomes a decision variable. The proposed strategy is proved to be input-to-state practical stable (ISpS) in the attraction region at triggering time instants under some standard assumptions. Extensions are made to linear systems with additive disturbances, for which the conditions reduce to a linear matrix inequality (LMI). Comprehensive numerical experiments are performed to verify the correctness of the theoretical results. / Graduate

L’objectif de cette thèse est d’apporter des réponses à deux problèmes importants dans le domaine de l’automatique : l'estimation d'état et la commande prédictive robuste sous contraintes pour des systèmes incertains, en se basant sur des méthodes ensemblistes, plus précisément liées aux ensembles zonotopiques. Les incertitudes agissant sur le système sont modélisées de façon déterministe, elles sont donc inconnues mais bornées par des ensembles connus.Dans ce contexte, la première partie de la thèse développe une méthode d’estimation afin d’élaborer à chaque instant un ensemble zonotopique contenant l’état du système malgré la présence de perturbations, de bruits de mesure et d’incertitudes paramétriques définies par intervalle. Cette méthode est fondée sur la minimisation du P-rayon d’un zonotope, critère original permettant de caractériser la taille de l’ensemble zonotopique et réalisant un bon compromis entre la complexité et la précision de l’estimation. Cette approche est tout d’abord développée pour les systèmes mono-sortie, puis étendue au cas des systèmes multi-sorties, dans un premier temps par des extensions directes de la solution mono-sortie (le système multi-sorties est considéré comme plusieurs systèmes mono-sortie). Une autre solution est ensuite proposée, qui conduit à résoudre un problème d’optimisation de type Inégalités Matricielles Polynomiales en utilisant une méthode de relaxation. Les approches précédentes n’étant que des extensions de la solution à une seule sortie, et malgré leurs bons résultats obtenus en simulation, une démarche originale, dédiée aux systèmes multi-sorties, fondée sur l’intersection entre un polytope et un zonotope, est finalement développée et validée.La deuxième partie de la thèse aborde la problématique de la commande robuste par retour de sortie pour des systèmes incertains. La commande prédictive est retenue du fait de son utilisation dans de nombreux domaines, de sa facilité de mise en œuvre et de sa capacité à traiter des contraintes. Parmi les démarches issues de la littérature, l’implantation de techniques robustes fondées sur des tubes de trajectoire est développée plus spécifiquement. Le recours à un observateur ensembliste à base de zonotopes permet d’améliorer la qualité de l’estimation, ainsi que la performance de la commande, dans le cas de systèmes soumis à des perturbations et des bruits de mesure inconnus, mais bornés.Dans une dernière partie, cette combinaison de l’estimation ensembliste et de la commande prédictive robuste est testée en simulation sur un système de suspension magnétique. Les résultats de simulation traduisent un comportement tout à fait satisfaisant validant les structures théoriques élaborées. / The aim of this thesis is answering to two significant problems in the field of automatic control: the state estimation and the robust model predictive control for uncertain systems in the presence of input and state constraints, based on the set-membership approach, more precisely related to zonotopic sets. Uncertainties acting on the system are modeled via the deterministic approach, and thus they are unknown but bounded by a known set.In this context, the first part of the thesis proposes an estimation method to compute a zonotope containing the real states of the system, which are consistent with the disturbances, the measurement noise and the interval parametric uncertainties. This method is based on the minimization of the P-radius of a zonotope, which is an original criterion to characterize the size of the zonotope, in order to obtain a good trade-off between the complexity and the precision of the estimation. This approach is first developed for single-output systems, and then extended to the case of multi-output systems. The first solution for multi-output systems is a direct extension of the solution for single-output systems (the multi-output system being considered as several single-output systems). Another solution is then proposed, leading to solve a Polynomial Matrix Inequality optimization problem using a relaxation technique. Due to the fact that the previous approaches are just extensions of the solution for a single-output system, and despite their good performance results obtained in simulation, a novel approach dedicated to multi-output systems based on the intersection of a polytope and a zonotope is finally developed and validated.The second part of the thesis deals with the problem of robust output feedback control for uncertain systems. Model predictive control is chosen due to its use in many areas, its ability to deal with constraints and uncertainties. Among the approaches from the literature, the implementation of robust predictive techniques based on tubes of trajectories is developed. The use of a zonotopic set-membership estimation improves the quality of the estimation, as well as the performance of the control, for systems subject to unknown, but bounded disturbances and measurement noise.In the last part, the combination of zonotopic set-membership estimation and robust model predictive control is tested in simulation on a magnetic levitation system. The simulation results reflect a satisfactory behavior validating the developed theoretical techniques.

Durante a operação de um controlador MPC, a planta pode ir para outro ponto de operação principalmente pela decisão operacional ou pela presença de perturbações medidas/não-medidas. Assim, o modelo do controlador deve ser adaptado para a nova condição de operação favorecendo o controle sob as novas condições. Desta forma, as condições ótimas de controle podem ser alcançadas com a maior quantidade de modelos identificados e com um controlador adaptativo que seja capaz de selecionar o melhor modelo. Neste trabalho é apresentada uma metodologia de controle adaptativo com identificação on-line do melhor modelo o qual pertence a um conjunto previamente levantado. A metodologia proposta considera um controlador em duas camadas e a excitação do processo através de um sinal GBN na camada de otimização com o controlador em malha fechada. Está sendo considerada a validação deste controlador adaptativo através da comparação dos resultados com duas diferentes técnicas Controlador MMPC e Identificação ARX, para a comprovação dos bons resultados desta metodologia. / During the operation of a MPC, the plant can change the operation point mainly due to management decision or due to the presence of measured or unmeasured disturbances. Thus, the model of the controller must be adapted to improve the control in the new operation conditions. In such a way, a better control policy can be achieved if a large number of models are identified at the possible operation points and it is available an adaptive controller that is capable of selecting the best model. In this work is presented a methodology of adaptive control with on-line identification of the most adequate model which belongs to a set of models previously obtained. The proposed methodology considers a two-layer controller and process excitation by a GBN signal in the LP optimization layer with the controller in closed loop mode. It is also presented the adaptive controller validation by comparing the proposed approach with two different techniques - MMPC and ARX Identification, to confirm the good results with this new methodology to the adaptive controller.

Soft lightweight robots provide an inherently safe solution to using robots in unmodeled environments by maintaining safety without increasing cost through expensive sensors. Unfortunately, many practical problems still need to be addressed before soft robots can become useful in real world tasks. Unlike traditional robots, soft robot geometry is not constant but can change with deflation and reinflation. Small errors in a robot's kinematic model can result in large errors in pose estimation of the end effector. This error, coupled with the inherent compliance of soft robots and the difficulty of soft robot joint angle sensing, makes it very challenging to accurately control the end effector of a soft robot in task space. However, this inherent compliance means that soft robots lend themselves nicely to coordinated multi-arm manipulation tasks, as deviations in end effector pose do not result in large force buildup in the arms or in the object being manipulated. Coordinated, multi-arm manipulation with soft robots is the focus of this thesis. We first developed two tools enabling multi-arm manipulation with soft robots: (1) a hybrid servoing control scheme for task space control of soft robot arms, and (2) a general base placement optimization for the robot arms in a multi-arm manipulation task. Using these tools, we then developed and implemented a simple multi-arm control scheme. The hybrid servoing control scheme combines inverse kinematics, joint angle control, and task space servoing in order to reduce end effector pose error. We implemented this control scheme on two soft robots and demonstrated its effectiveness in task space control. Having developed a task space controller for soft robots, we then approached the problem of multi-arm manipulation. The placement of each arm for a multi-arm task is non-trivial. We developed an evolutionary optimization that finds the optimal arm base location for any number of user-defined arms in a user-defined task or workspace. We demonstrated the utility of this optimization in simulation, and then used it to determine the arm base locations for two arms in two real world coordinated multi-arm manipulation tasks. Finally, we developed a simple multi-arm control scheme for soft robots and demonstrated its effectiveness using one soft robot arm, and one rigid robot with low-impedance torque control. We placed each arm base in the pose determined by the base placement optimization, and then used the hybrid servoing controller in our multi-arm control scheme to manipulate an object through two desired trajectories.