Yes / A milk pasteurization process, a nonlinear process and multivariable interacting system, is difficult to control by the conventional on-off controllers since the on-off controller can handled the temperature profiles for milk and water oscillating over the plant requirements. The multi-variable control approach with model predictive control (MPC) is proposed in this study. The proposed algorithm was tested for control of a milk pasteurization process in three cases of simulation such as set point tracking, model mismatch, difference control and prediction horizons, and time sample. The results for the proposed algorithm show the well performance in keeping both the milk and water temperatures at the desired set points without any oscillation and overshoot and giving less drastic control action compared to the cascade generic model control (GMC) strategy.

Pathological tremor is a common neuromuscular disorder that significantly affects the quality of life for patients worldwide. With recent developments in robotics, rehabilitation exoskeletons serve as one of the solutions to alleviate these tremors. For improved performance of such devices, we need to solve a few problems, which include developing a model for pathological tremors, and a safe control system that can conveniently incorporate constraints on the wrist's range of motion and it's input force/torque. Accurate predictive modeling of tremor signals can be used to provide alleviation from these tremors via various currently available solutions like adaptive deep brain stimulation, electrical stimulation and rehabilitation orthoses. Existing methods are either too general or too simplistic to accurately predict these tremors in the long term, motivating us to explore better modeling of tremors for long-term predictions and analysis. We explore towards the prediction of tremors using artificial neural networks using EMG signals, leveraging the 20- 100 ms of Electromechanical Delay. The kinematics and EMG data of a publicly available Parkinson's tremor dataset is first analyzed, which confirms that the underlying EMGs have similar frequency composition as the actual tremor. 2 hybrid CNN-LSTM based deep learning architectures are then proposed to predict the tremor kinematics ahead of time using EMG signals and tremor kinematics history, and the results are compared with baseline models. This is then further extended by adding constraints-based losses in an attempt to further improve the predictions. Then, we explore the application of model-based predictive control (MPC) for the full wrist exoskeleton designed in our lab for the alleviation of tremors. The main motivation for using MPC here relies on its ability to incorporate state and input constraints, which are crucial for the user's safety. We employ a linear MPC methodology, in which the forearm-exoskeleton model is successively linearized at each time sample to obtain a linear state space model, which is then used to obtain the optimal input by minimizing a convex quadratic cost function. This is then integrated with the tremor model developed via BMFLC and neural networks to provide tremor suppression. Simulation studies are provided to demonstrate the effectiveness of the control schemes. The numerical simulations suggest that the MPC framework is capable of accurate trajectory tracking while providing better tremor suppression than a PD controller without using any tremor model, while the neural network model outperforms the frequency-based BMFLC model. The findings could set up for devising physics-based Neural networks for pathological tremor modeling and experimentally evaluate the performance of the developed framework. / Master of Science / Pathological tremors are involuntary, rhythmic, and oscillatory movements of the limbs that affect millions of people worldwide, and daily life activities like writing, eating, and object manipulation are challenging for them. In recent years, rehabilitation exoskeletons have been developed as non-invasive solutions to pathological tremor alleviation. The wrist is pivotal to human manipulation capabilities, and thus, a wrist exoskeleton (TAWE) has been developed in our lab to provide tremor alleviation. For improved performance of such devices, we need to solve a few problems, which include developing a model for pathological tremors, and a safe control system that can conveniently incorporate constraints on the wrist's range of motion and its input force/torque. We propose a deep-learning-based method for accurate modeling of tremors, along with a model predictive control framework for tremor suppression. Simulations and analyses are done to validate the tremor-modeling framework and the control framework of an exoskeleton for the tremor alleviation, and highlight shortcomings in the current methods that call for more research and advancements.

Spacecraft relative motion modeling and control promises to enable or augment a wide range of missions for scientific research, military applications, and space situational awareness. This dissertation focuses on the development of novel, optimization-based, control design for some representative relative-motion-enabled missions. Spacecraft relative motion refers to two (or more) satellites in nearly identical orbits. We examine control design for relative configurations on the scale of meters (for the purposes of proximity operations) as well as on the scale of tens of kilometers (representative of science gathering missions). Realistic control design for satellites is limited by accurate modeling of the relative orbital perturbations as well as the highly constrained nature of most space systems. We present solutions to several types of optimal orbital maneuvers using a variety of different, realistic assumptions based on the maneuver objectives. Initially, we assume a perfectly circular orbit with a perfectly spherical Earth and analytically solve the under-actuated, minimum-energy, optimal transfer using techniques from optimal control and linear operator theory. The resulting open-loop control law is guaranteed to be a global optimum. Then, recognizing that very few, if any, orbits are truly circular, the optimal transfer problem is generalized to the elliptical linear and nonlinear systems which describe the relative motion. Solution of the minimum energy transfer for both the linear and nonlinear systems reveals that the resulting trajectories are nearly identical, implying that the nonlinearity has little effect on the relative motion. A continuous-time, nonlinear, sliding mode controller which tracks the linear trajectory in the presence of a higher fidelity orbit model shows that the closed-loop system is both asymptotically stable and robust to disturbances and un-modeled dynamics. Next, a novel method of computing discrete-time, multi-revolution, finite-thrust, fuel-optimal, relative orbit transfers near an elliptical, perturbed orbit is presented. The optimal control problem is based on the classical, continuous-time, fuel-optimization problem from calculus of variations, and we present the discrete-time analogue of this problem using a transcription-based method. The resulting linear program guarantees a global optimum in terms of fuel consumption, and we validate the results using classical impulsive orbit transfer theory. The new method is shown to converge to classical impulsive orbit transfer theory in the limit that the duration of the zero-order hold discretization approaches zero and the time horizon extends to infinity. Then the fuel/time optimal control problem is solved using a hybrid approach which uses a linear program to solve the fuel optimization, and a genetic algorithm to find the minimizing time-of-flight. The method developed in this work allows mission planners to determine the feasibility for realistic spacecraft and motion models. Proximity operations for robotic inspection have the potential to aid manned and unmanned systems in space situational awareness and contingency planning in the event of emergency. A potential limiting factor is the large number of constraints imposed on the inspector vehicle due to collision avoidance constraints and limited power and computational resources. We examine this problem and present a solution to the coupled orbit and attitude control problem using model predictive control. This control technique allows state and control constraints to be encoded as a mathematical program which is solved on-line. We present a new thruster constraint which models the minimum-impulse bit as a semi-continuous variable, resulting in a mixed-integer program. The new model, while computationally more expensive, is shown to be more fuel-efficient than a sub-optimal approximation. The result is a fuel efficient, trajectory tracking, model predictive controller with a linear-quadratic attitude regulator which tracks along a pre-computed ``safe'' trajectory in the presence of un-modeled dynamics on a higher fidelity orbital and attitude model. / Ph. D.

This thesis aims at investigating numerical methods through which the accuracy in landing of a Mars entry-descent-landing (EDL) vehicle can be improved. The methods investigated include the collocation method and model predictive control (MPC). The primary control variable utilized in this study is the bank angle of the spacecraft, which is the angle between the lift vector and the vertical direction. Modulating this vector affects the equations of system of equations and the seven state variables, namely altitude, velocity, latitude, longitude, flight path angle, heading angle and total time taken. An optimizer is implemented which utilizes the collocation method, through which the optimal bank angle is found at every discretized state along the trajectory which are equally separated through a definite timestep, which is a function of the end time state. A 3-sigma wind disturbance model is introduced to the system, as a function of the altitude, which introduces uncertainties to the system, resulting in a final state deviating from the targeted location. The trajectory is split into two parts, for better control of the vehicle during the end stages of flight. The MPC aims at reducing the end state deviation, through the implementation of a predictor-corrector algorithm that propagates the trajectory for a certain number of timesteps, followed by running the optimizer from the current disturbed state to the desired target location. At the end of this analysis, a new set of optimal bank angle are found, which account for the wind disturbances and navigates the EDL vehicle to the desired location. / M.S. / Landing on Mars has always been a process of following a set of predetermined instructions by the spacecraft, in order to reach a calculated landing target. This work aims to take the first steps towards autonomy in maneuvering the spacecraft, and finding a method by which the vehicle navigates itself towards the target. This work determines the optimal control scheme a Mars reentry vehicle must have through the atmosphere to reach the target location, and employs method through which the uncertainty in the final landing location is mitigated. A model predictive controller is employed which corrects the disturbed trajectory of the vehicle at certain timesteps, through which the previously calculated optimal control is changed so as to account for the disturbances. The control is achieved by means of changing the bank angle of the spacecraft, which in turn affects the lift and drag experienced by the vehicle. Through this work, a method has been demonstrated which reduces the uncertainty in final landing location, even with wind disturbances present.

Networked control systems (NCSs) present many advantages such as easy installation and maintenance, flexible layouts and structures of components, and efficient allocation and distribution of resources. Consequently, they find potential applications in a variety of emerging industrial systems including multi-agent systems, power grids, tele-operations and cyber-physical systems. The study of NCSs with nonlinear dynamics (i.e., nonlinear NCSs) is a very significant yet challenging topic, and it not only widens application areas of NCSs in practice, but also extends the theoretical framework of NCSs with linear dynamics (i.e., linear NCSs). Numerous issues are required to be resolved towards a fully-fledged theory of industrial nonlinear NCS design. In this dissertation, three important problems of nonlinear NCSs are investigated: The robust filtering problem, the robust model predictive control (MPC) problem and the robust distributed MPC problem of large-scale nonlinear systems. In the robust filtering problem of nonlinear NCSs, the nonlinear system model is subject to uncertainties and external disturbances, and the measurements suffer from time delays governed by a Markov process. Utilizing the Lyapunov theory, the algebraic Hamilton-Jacobi inequality (HJI)-based sufficient conditions are established for designing the H_infty nonlinear filter. Moreover, the developed results are specialized for a special type of nonlinear systems, by presenting the HJI in terms of matrix inequalities. For the robust MPC problem of NCSs, three aspects are considered. Firstly, to reduce the computation and communication load, the networked MPC scheme with an efficient transmission and compensation strategy is proposed, for constrained nonlinear NCSs with disturbances and two-channel packet dropouts. A novel Lyapunov function is constructed to ensure the input-to-state practical stability (ISpS) of the closed-loop system. Secondly, to improve robustness, a networked min-max MPC scheme are developed, for constrained nonlinear NCSs subject to external disturbances, input and state constraints, and network-induced constraints. The ISpS of the resulting nonlinear NCS is established by constructing a new Lyapunov function. Finally, to deal with the issue of unavailability of system state, a robust output feedback MPC scheme is designed for constrained linear systems subject to periodical measurement losses and external disturbances. The rigorous feasibility and stability conditions are established. For the robust distributed MPC problem of large-scale nonlinear systems, three steps are taken to conduct the studies. In the first step, the issue of external disturbances is addressed. A robustness constraint is proposed to handle the external disturbances, based on which a novel robust distributed MPC algorithm is designed. The conditions for guaranteeing feasibility and stability are established, respectively. In the second step, the issue of communication delays are dealt with. By designing the waiting mechanism, a distributed MPC scheme is proposed, and the feasibility and stability conditions are established. In the third step, the robust distributed MPC problem for large-scale nonlinear systems subject to control input constraints, communication delays and external disturbances are studied. A dual-mode robust distributed MPC strategy is designed to deal with the communication delays and the external disturbances simultaneously, and the feasibility and the stability conditions are developed, accordingly. / Graduate / 0548 / 0544

Platooning is an interesting area which involve the possibility of decreasing the fuel consumption of heavy-duty vehicles. By reducing the inter-vehicle spacing in the platoon we can reduce air drag, which in turn reduces fuel consumption. Two fuel-efficient model predictive controllers for HDVs in a platoon has been formulated in this master thesis, both utilizing road grade preview information. The first controller is based on linear programming (LP) algorithms and the second on quadratic programming (QP). These two platooning controllers are compared with each other and with generic controllers from Scania. The LP controller proved to be more fuel-efficient than the QP controller, the Scania controllers are however more fuel-efficient than the LP controller.

The control and optimization of chemical plants is a major area of research as it has the potential to improve both economic output and plant safety. It is often prudent to separate control and optimization tasks of varying complexities and time scales, creating a hierarchical control structure. Within this structure, it is beneficial for one control layer to be able to account for the effects of other layers. A clear example of this, and the basis of this work, is closed-loop dynamic real-time optimization (CL-DRTO), in which an economic optimization method considers both the plant behavior and the effects of an underlying model predictive controller (MPC). This technique can be expanded on to allow its use and methods to be employed in a greater diversity of applications, particularly unstable and uncertain plant environments. First, this work seeks to improve on existing robust MPC techniques, which incorporate plant uncertainty via direct multi-scenario modelling, by also including future MPC behavior through the use of the CL modelling technique of CL-DRTO. This allows the CL robust MPC to account for how future MPC executions will be affected by uncertain plant behavior. Second, Lyapunov MPC (LMPC) is a generally nonconvex technique which focuses on effective control of plants which exhibit open-loop unstable behavior. A new convex LMPC formulation is presented here which can be readily embedded into a CL-DRTO scheme. Next, uncertainty handling is incorporated directly into a CL-DRTO via a robust multi-scenario method to allow for the economic optimization to take uncertain plant behavior into account while also modelling MPC behavior under plant uncertainty. Finally, the robust CL-DRTO method is computationally expensive, so a decomposition method which separates the robust CL-DRTO into its respective scenario subproblems is developed to improve computation time, especially for large optimization problems. / Thesis / Doctor of Philosophy (PhD) / It is common for control and optimization of chemical plants to be performed in a multi-layered hierarchy. The ability to predict the behavior of other layers or the future behavior of the same layer can improve overall plant performance. This thesis presents optimization and control frameworks which use this concept to more effectively control and economically optimize chemical plants which are subject to uncertain behavior or instability. The strategy is shown, in a series of simulated case studies, to effectively control chemical plants with uncertain behavior, control and optimize unstable plant systems, and economically optimize uncertain chemical plants. One of the drawbacks of these strategies is the relatively large computation time required to solve the optimization problems. Therefore, for uncertain systems, the problem is separated into smaller pieces which are then coordinated towards a single solution. This results in reduced computation time.

Cette thèse se développe sur deux fronts: nous nous concentrons sur les méthodes numériques des problèmes de contrôle optimal, en particulier sur le Principe de la Programmation Dynamique et sur le Model Predictive Control (MPC) et nous présentons des applications de techniques de contrôle en biologie. Dans la première partie, nous considérons l'approximation d'un problème de contrôle optimal avec horizon infini, qui combine une première étape, basée sur MPC permettant d'obtenir rapidement une bonne approximation de la trajectoire optimal, et une seconde étape, dans la quelle l¿équation de Bellman est résolue dans un voisinage de la trajectoire de référence. De cette façon, on peux réduire une grande partie de la taille du domaine dans lequel on résout l¿équation de Bellman et diminuer la complexité du calcul. Le deuxième sujet est le contrôle des méthodes Level Set: on considère un problème de contrôle optimal, dans lequel la dynamique est donnée par la propagation d'un graphe à une dimension, contrôlé par la vitesse normale. Un état finale est fixé, l'objectif étant de le rejoindre en minimisant une fonction coût appropriée. On utilise la programmation dynamique grâce à une réduction d'ordre de l'équation utilisant la Proper Orthogonal Decomposition. La deuxième partie est dédiée à l'application des méthodes de contrôle en biologie. On présente un modèle décrit par une équation aux dérivées partielles qui modélise l'évolution d'une population de cellules tumorales. On analyse les caractéristiques du modèle et on formule et résout numériquement un problème de contrôle optimal concernant ce modèle, où le contrôle représente la quantité du médicament administrée. / This thesis is divided in two parts: in the first part we focus on numerical methods for optimal control problems, in particular on the Dynamic Programming Principle and on Model Predictive Control (MPC), in the second part we present some applications of the control techniques in biology. In the first part of the thesis, we consider the approximation of an optimal control problem with an infinite horizon, which combines a first step based on MPC, to obtain a fast but rough approximation of the optimal trajectory and a second step where we solve the Bellman equation in a neighborhood of the reference trajectory. In this way, we can reduce the size of the domain in which the Bellman equation can be solved and so the computational complexity is reduced as well. The second topic of this thesis is the control of the Level Set methods: we consider an optimal control, in which the dynamics is given by the propagation of a one dimensional graph, which is controlled by the normal velocity. A final state is fixed and the aim is to reach the trajectory chosen as a target minimizing an appropriate cost functional. To apply the Dynamic Programming approach we firstly reduce the size of the system using the Proper Orthogonal Decomposition. The second part of the thesis is devoted to the application of control methods in biology. We present a model described by a partial differential equation that models the evolution of a population of tumor cells. We analyze the mathematical and biological features of the model. Then we formulate an optimal control problem for this model and we solve it numerically.

In this thesis, after a comprehensive literature review on different conventional and predictive torque control strategies for switched reluctance motor (SRM) drives, two online methods and one offline multi-objective optimization-based method are proposed to extend the operating speed range of finite control set model predictive torque control (FCS-MPTC) for SRM by adaptively controlling the commutation angles in the entire speed range. Furthermore, a method is proposed to minimize the steady state torque tracking error of FCS-MPTC for SRM drives. The incapability of the conventional FCS-MPTC in controlling the commutation angles, which is considered as one of the main drawbacks of the conventional FCS-MPTC, limits its application for high-speed torque control of SRM drives. The phase turn-off angle is always selected to be close to the aligned position with the conventional FCS-MPTC regardless of the operating speed. However, commutation angle advancement is required for high-speed torque control of SRM drives to limit the negative phase torque resulting from the current tail after the turn-off angle in the generating region. Excessive negative torque with the conventional FCS-MPTC at higher speeds can result in a degraded performance with high rms current, low average torque, high torque ripple, and reduced efficiency. The phase turn-off angle can be adaptively controlled as speed changes with the first online commutation angle control strategy proposed in this thesis. This method is based on predicting the free-wheeling phase current in an extended time interval which is much bigger than the prediction horizon of FCS-MPTC. The second online turn-off angle control method is also proposed by improving the optimality condition defined for determining the optimal turn-off angle. The optimality condition is determined by calculating the work done by the conducting phase after the phase is turned off. The weighting factor of the objective function of FCS-MPTC is kept constant with both proposed online methods. An offline multi-objective optimization-based strategy is proposed to determine the globally optimal turn-off angle and the weighting factor in the entire operating torque and speed ranges. The effectiveness of both proposed online methods and the offline commutation angle control strategy is verified using simulations and experimental results. The results are also compared to the conventional FCS-MPTC and the indirect average torque control with optimized conduction angles which is considered as one of the main conventional torque control strategies for SRM drives. In order to minimize the torque tracking error as a result of either parameter uncertainties or tracking multiple objectives with a single objective function with weighting factors, a method is proposed which is based on updating the reference torque at each sample time by calculating the average torque tracking error in the previous sample times. The validity of the proposed method is verified using simulations. / Thesis / Doctor of Philosophy (PhD)

In this thesis, we first use the reachability theory to develop algorithms for state predictionunder delayed state or output measurements. We next develop control strategies forcollision avoidance and trajectory tracking of UAVs based on the devised algorithms andthe model predictive control theory. Finally, simulations results for collision avoidanceand trajectory tracking problems are presented, for different communication delays,using a UAV model with 6 degrees of freedom. / I denna avhandling använder vi först tillgänglighetsteorin för att utveckla algoritmerför tillståndsförutsägelse under fördröjda tillstånds- eller utgångsmätningar. Därefterutvecklar kontrollstrategier för undvikande av kollision och spårning av UAV: er baseradepå de planerade algoritmerna och modellen förutsägbar kontrollteori. Slutligenpresenteras simuleringsresultat för att undvika kollision och problem med spårningav banan, för olika kommunikationsförseningar, med en UAV-modell med 6 frihetsgrader.