Robust/Optimal Temperature Profile Control of a High-Speed Aerospace Vehicle using Neural Networks

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. a 1-D distributed parameter model of a fin is developed from basic thermal physics principles. ldquoSnapshotrdquo solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the ldquoproper orthogonal decompositionrdquo (POD) technique and the snapshot solutions. a low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. an ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with a single-network-adaptive-critic (SNAC) controller for this approximate nonlinear model. Actual control in the original domain is calculated with the same POD basis functions through a reverse mapping. Further contribution of this paper includes development of an online robust neurocontroller to account for unmodeled dynamics and parametric uncertainties inherent in such a complex dynamic system. a neural network (NN) weight update rule that guarantees boundedness of the weights and relaxes the need for persistence of excitation (PE) condition is presented. Simulation studies show that in a fairly extensive but compact domain, any desired temperature profile can be achieved starting from any initial temperature profile. Therefore, the ADP and NN-based controllers appear to have the potential to become controller synthesis tools for nonlinear distributed parameter systems

Issues on Stability of ADP Feedback Controllers for Dynamical Systems

This paper traces the development of neural-network (NN)-based feedback controllers that are derived from the principle of adaptive/approximate dynamic programming (ADP) and discusses their closed-loop stability. Different versions of NN structures in the literature, which embed mathematical mappings related to solutions of the ADP-formulated problems called “adaptive critics” or “action-critic” networks, are discussed. Distinction between the two classes of ADP applications is pointed out. Furthermore, papers in “model-free” development and model-based neurocontrollers are reviewed in terms of their contributions to stability issues. Recent literature suggests that work in ADP-based feedback controllers with assured stability is growing in diverse forms

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

Formation control of car-like mobile robots

A traditional tracking and control design approach already available in literature is derived and discussed for a car-like mobile robot. It involves a decoupled design involving two separate algorithms, one for velocity control design and another for torque control design. Weak interactions among the algorithms and separate designs make the robot performance optimization and the formation stability difficult to achieve. So, a new tracking and control architecture wherein the conventional elements are replaced by a single component that performs all the functions and hence called the integrated tracking and control scheme is used --Abstract, page iii

Robust/Optimal Temperature Profile Control of a High-Speed Aerospace Vehicle Using Neural Networks

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. A I-D distributed parameter model of a fin is developed from basic thermal physics principles. "Snapshot" solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the "proper orthogonal decomposition" (POD) technique and the snapshot solutions. A low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. An ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with a single-network-adaptive-critic (SNAC) controller for this approximate nonlinear model. Actual control in the original domain is calculated with the same POD basis functions through a reverse mapping. Further contribution of this paper includes development of an online robust neurocontroller to account for unmodeled dynamics and parametric uncertainties inherent in such a complex dynamic system. A neural network (NN) weight update rule that guarantees boundedness of the weights and relaxes the need for persistence of excitation (PE) condition is presented. Simulation studies show that in a fairly extensive but compact domain, any desired temperature profile can be achieved starting from any initial temperature profile. Therefore, the ADP and NN-based controllers appear to have the potential to become controller synthesis tools for nonlinear distributed parameter systems

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