This thesis develops Lyapunov-based control techniques for nonlinear process systems subject to input constraints and stochastic uncertainty. The problems considered include those which focus on the null-controllable region (NCR) for unstable systems. The NCR is the set of states in the state-space from where controllability to desired equilibrium point is possible. For unstable systems, the presence of input constraints induces bounds on the NCR and thereby limits the ability of any controller to steer the system at will. Common approaches for applying control to such systems utilize Control Lyapunov Functions (CLFs) . Such functions can be used for both designing controllers and also preforming closed--loop stability analysis. Existing CLF-based controllers result in closed--loop stability regions that are subsets of the NCR and do not guarantee closed--loop stability from the entire NCR. In effort to mitigate this shortcoming, we introduce a special type of CLF known as a Constrained Control Lyapunov Function (CCLF) which accounts for the presence of input constraints in its definition. CCLFs result in closed--loop stability regions which correspond to the NCR. We demonstrate how CCLFs can be constructed using a function defined by the NCR boundary trajectories for varying values of the available control capacity. We first consider linear systems and utilize available explicit characterization of the NCR to construct CCLFs. We then develop a Model Predictive Control (MPC) design which utilizes this CCLF to achieve stability from the entire NCR for linear anti-stable systems. We then consider the problem of nonlinear systems where explicit characterizations of the NCR boundary are not available. To do so, the problem of boundary construction is considered and an algorithm which is computationally tractable is developed and results in the construction of the boundary trajectories. This algorithm utilizes properties of the boundary pertaining to control equilibrium points to initialize the controllability minimum principle. We then turn to the problem of closed--loop stabilization from the entire NCR for nonlinear systems. Following a similar development as the CCLF construction for linear systems, we establish the validity of the use of the NCR as a CCLF for nonlinear systems. This development involves relaxing the conditions which define a classical CLF and results in CCLF-based control achieving stability to an to an equilibrium manifold. To achieve stabilization from the entire NCR, the CCLF-based control design is coupled with a classical CLF-based controller in a hybrid control framework. In the final part of this thesis, we consider nonlinear systems subject to stochastic uncertainty. Here we design a Lyapunov-based model predictive controller (LMPC) which provides an explicitly characterized region from where stability can be probabilistically obtained. The design exploits the constraint-handling ability of model predictive controllers in order to inherent the stabilization in probability characterization of a Lyapunov-based feedback controller. All the proposed control designs along with the NCR boundary computation are illustrated using simulation results. / Thesis / Doctor of Philosophy (PhD)

<p> This thesis considers the problem of control of nonlinear process systems subject to input constraints and faults in the control actuators and process equipments. Faults are considered that preclude the possibility of continued operating at the nominal equilibrium point and a framework (which we call the safe-parking framework) is developed to enable efficient resumption of nominal operation upon fault-recovery. First, Lyapunov-based model predictive controllers, that allow for an explicit characterization of the stability region subject to constraints on the manipulated input, are designed. The stability region characterization is utilized in selecting 'safe-park' points from the safe-park candidates (equilibrium points subject to failed actuators). This safe-park point is chosen as a temporary operating point where process is to be operated during fault rectification. This ensures that process can be safely operated during fault rectification and the nominal operation can be resumed upon fault recovery. When multiple candidate safe-park points are available, performance considerations, such as ease of transition from and to the safe-park point and cost of running the process at the safe-park point, are quantified and utilized in choosing the optimal safe-park point. </p> <p> Next, we extend the safe-parking framework to handle practical issues such as plant-model mismatch, disturbances and unavailability of all process state measurements. \i\Te first consider the presence of constraints and uncertainty and develop a robust Lyapunov-based model predictive controller. This controller is utilized to characterize robust stability region which, subsequently, is utilized to select 'safepark' points. Then we consider the problem of availability of limited measurements. An output feedback Lyapunov-based model predictive controller, with high-gain observer to estimate unmeasured states, is formulated and its stability region explicitly characterized. An algorithm is then presented that accounts for the estimation errors in the implementation of the safe-parking framework. </p> <p> We then further extend the framework to handle faults in large scale chemical plants where multiple process units are connected via material, energy and information streams. In plant-wide setting, the safe-park point for the faulty unit is chosen such that the safe-parking has no or minimum effect on downstream units, and hence, the nominal operation in the downstream units can be continued. Next we consider the scenario where no viable safe-park point for the faulty unit exists such that its effect can be completely absorbed in the subsequent unit. A methodology is developed that allows simultaneous safe-parking of the consecutive units. The efficacy of the proposed framework is illustrated using a chemical reactor example, a styrene polymerization process and two CSTRs in series example. </p> <p> Finally, we demonstrate the efficacy of proposed Lyapunov based Model Predictive Controller and Safe-Parking framework on a polymerization reactor model to control the polymerization reactor and to handle faults that dont allow continuation of the nominal operation in the reactor. </p> / Thesis / Doctor of Philosophy (PhD)

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Dans cette thèse, une méthode de résolution de problèmes de commande optimale non linéaires sous contraintes d'état et de commande. Cette méthode repose sur l'adaptation des méthodes de points intérieurs, utilisées en optimisation de dimension finie, à la commande optimale. Un choix constructif de fonctions de pénalisation intérieure est fourni dans cette thèse. On montre que ce choix permet d'approcher la solution d'un problème de commande optimale sous contraintes en résolvant une suite de problèmes de commande optimale sans contraintes dont les solutions sont simplement caractérisées par les conditions de stationnarité du calcul des variations.Deux études dans le domaine de la gestion de l'énergie dans les bâtiments sont ensuite conduites. La première consiste à quantifier la durée maximale d'effacement quotidien du chauffage permettant de maintenir la température intérieure dans une certaine bande de confort, et ce pour différents types de bâtiments classés de mal à bien isolés. La seconde étude se concentre sur les bâtiments BBC et consiste à quantifier la capacité de ces bâtiments à réaliser des effacements électriques complets du chauffage de 6h00 à 22h00 tout en maintenant, là encore, la température intérieure dans une bande de confort. Cette étude est réalisée sur l'ensemble de la saison de chauffe. / This thesis exposes a methodology to solve constrained optimal controlof non linear systems by interior penalty methods. A constructivechoice for the penalty functions used to implement the interior methodis exhibited in this thesis. It is shown that itallows us to approach the solution of the non linear optimal controlproblem using a sequence of unconstrained problems, whose solutionsare readily characterized by the simple calculus of variations.Two representatives study of energy management in buildings are conducted using the provided algorithm. The first study consists in quantifying the maximal duration of daily complete load shiftings achievable by several buildings ranging from poorly to well insulated. The second study focuses on low consumption buildings and aim at quantifying the ability of these buildings to perform complete load shiftings of the heating electrical consumption from the day (6 a.m. to 10 p.m.) to the night period over the whole heating season.