Boundary control of parabolic PDE using adaptive dynamic programming

In this dissertation, novel adaptive/approximate dynamic programming (ADP) based state and output feedback control methods are presented for distributed parameter systems (DPS) which are expressed as uncertain parabolic partial differential equations (PDEs) in one and two dimensional domains. In the first step, the output feedback control design using an early lumping method is introduced after model reduction. Subsequently controllers were developed in four stages; Unlike current approaches in the literature, state and output feedback approaches were designed without utilizing model reduction for uncertain linear, coupled nonlinear and two-dimensional parabolic PDEs, respectively. In all of these techniques, the infinite horizon cost function was considered and controller design was obtained in a forward-in-time and online manner without solving the algebraic Riccati equation (ARE) or using value and policy iterations techniques. Providing the stability analysis in the original infinite dimensional domain was a major challenge. Using Lyapunov criterion, the ultimate boundedness (UB) result was demonstrated for the regulation of closed-loop system using all the techniques developed herein. Moreover, due to distributed and large scale nature of state space, pure state feedback control design for DPS has proven to be practically obsolete. Therefore, output feedback design using limited point sensors in the domain or at boundaries are introduced. In the final two papers, the developed state feedback ADP control method was extended to regulate multi-dimensional and more complicated nonlinear parabolic PDE dynamics --Abstract, page iv

Experimental Implementation of Adaptive-Critic Based Infinite Time Optimal Neurocontrol for a Heat Diffusion System

Recently the synthesis methodology for the infinite time optimal neuro-controllers for PDE systems in the framework of adaptive-critic design has been developed. In this paper, first we model an experimental setup representing one dimensional heat diffusion problems. Then we synthesize and implement an adaptive-critic based neuro-controller for online temperature profile control of the experimental setup

Optimization based control design techniques for distributed parameter systems

The study presents optimization based control design techniques for the systems that are governed by partial differential equations. A control technique is developed for systems that are actuated at the boundary. The principles of dynamic inversion and constrained optimization theory are used to formulate a feedback controller. This control technique is demonstrated for heat equations and thermal convection loops. This technique is extended to address a practical issue of parameter uncertainty in a class of systems. An estimator is defined for unknown parameters in the system. The Lyapunov stability theory is used to derive an update law of these parameters. The estimator is used to design an adaptive controller for the system. A second control technique is presented for a class of second order systems that are actuated in-domain. The technique of proper orthogonal decomposition is used first to develop an approximate model. This model is then used to design optimal feedback controller. Approximate dynamic programming based neural network architecture is used to synthesize a sub-optimal controller. This control technique is demonstrated to stabilize the heave dynamics of a flexible aircraft wings. The third technique is focused on the optimal control of stationary thermally convected fluid flows from the numerical point of view. To overcome the computational requirement, optimization is carried out using reduced order model. The technique of proper orthogonal decomposition is used to develop reduced order model. An example of chemical vapor deposition reactor is considered to examine this control technique --Abstract, page iii

Planning And Control Of Swarm Motion As Continua

In this thesis, new algorithms for formation control of multi agent systems (MAS) based on continuum mechanics principles will be investigated. For this purpose agents of the MAS are treated as particles in a continuum, evolving in an n-D space, whose desired configuration is required to satisfy an admissible deformation function. Considered is a specific class of mappings that is called homogenous where the Jacobian of the mapping is only a function of time and is not spatially varying. The primary objectives of this thesis are to develop the necessary theory and its validation via simulation on a mobile-agent based swarm test bed that includes two primary tasks: 1) homogenous transformation of MAS and 2) deployment of a random distribution of agents on to a desired configuration. Developed will be a framework based on homogenous transformations for the evolution of a MAS in an n-D space (n=1, 2, and 3), under two scenarios: 1) no inter-agent communication (predefined motion plan); and 2) local inter-agent communication. Additionally, homogenous transformations based on communication protocols will be used to deploy an arbitrary distribution of a MAS on to a desired curve. Homogenous transformation with no communication: A homogenous transformation of a MAS, evolving in an space, under zero inter agent communication is first considered. Here the homogenous mapping, is characterized by an n x n Jacobian matrix ( ) and an n x 1 rigid body displacement vector ( ), that are based on positions of n+1 agents of the MAS, called leader agents. The designed Jacobian ( ) and rigid body displacement vector ( ) are passed onto rest of the agents of the MAS, called followers, who will then use that information to update their positions under a pre- iv defined motion plan. Consequently, the motion of MAS will evolve as a homogenous transformation of the initial configuration without explicit communication among agents. Homogenous Transformation under Local Communication: We develop a framework for homogenous transformation of MAS, evolving in , under a local inter agent communication topology. Here we assume that some agents are the leaders, that are transformed homogenously in an n-D space. In addition, every follower agent of the MAS communicates with some local agents to update its position, in order to grasp the homogenous mapping that is prescribed by the leader agents. We show that some distance ratios that are assigned based on initial formation, if preserved, lead to asymptotic convergence of the initial formation to a final formation under a homogenous mapping. Deployment of a Random Distribution on a Desired Manifold: Deployment of agents of a MAS, moving in a plane, on to a desired curve, is a task that is considered as an application of the proposed approach. In particular, a 2-D MAS evolution problem is considered as two 1-D MAS evolution problems, where x or y coordinates of the position of all agents are modeled as points confined to move on a straight line. Then, for every coordinate of MAS evolution, bulk motion is controlled by two agents considered leaders that move independently, with rest of the follower agents motions evolving through each follower agent communicating with two adjacent agents

Model based fault diagnosis and prognosis of class of linear and nonlinear distributed parameter systems modeled by partial differential equations

With the rapid development of modern control systems, a significant number of industrial systems may suffer from component failures. An accurate yet faster fault prognosis and resilience can improve system availability and reduce unscheduled downtime. Therefore, in this dissertation, model-based prognosis and resilience control schemes have been developed for online prediction and accommodation of faults for distributed parameter systems (DPS). First, a novel fault detection, estimation and prediction framework is introduced utilizing a novel observer for a class of linear DPS with bounded disturbance by modeling the DPS as a set of partial differential equations. To relax the state measurability in DPS, filters are introduced to redesign the detection observer. Upon detecting a fault, an adaptive term is activated to estimate the multiplicative fault and a tuning law is derived to tune the fault parameter magnitude. Then based on this estimated fault parameter together with its failure limit, time-to-failure (TTF) is derived for prognosis. A novel fault accommodation scheme is developed to handle actuator and sensor faults with boundary measurements. Next, a fault isolation scheme is presented to differentiate actuator, sensor and state faults with a limited number of measurements for a class of linear and nonlinear DPS. Subsequently, actuator and sensor fault detection and prediction for a class of nonlinear DPS are considered with bounded disturbance by using a Luenberger observer. Finally, a novel resilient control scheme is proposed for nonlinear DPS once an actuator fault is detected by using an additional boundary measurement. In all the above methods, Lyapunov analysis is utilized to show the boundedness of the closed-loop signals during fault detection, prediction and resilience under mild assumptions --Abstract, page iv

Robust Adaptive Control of an Offshore Ocean Thermal Energy Conversion System

IEEE Boundary control strategy is developed to analyze the vibration problem of the offshore ocean thermal energy conversion (OTEC) system as well as to constrain the bottom tension and top motion. To provide an accurate dynamic behavior for the OTEC system, this distributed parameter system is modeled and formulated with a governing equation and boundary conditions (PDE-ODEs model). Two robust adaptive boundary controllers are designed and disposed at the endpoints of the system, and the stability of the controlled system under unknown disturbances is achieved. After selecting the relevant parameters appropriately, the offset of the offshore OTEC system can be suppressed to equilibrium position. Finally, the effectiveness of the proposed control is illustrated by simulation