In this thesis, energy optimal route of an unmanned solar powered air vehicle is obtained for the given mission constraints in order to sustain the maximum energy balance. The mission scenario and the constraints of the solar powered UAV are defined. Equations of motion are obtained for the UAV with respect to the chosen structural properties and aerodynamic parameters to achieve the given mission. Energy income and loss equations that state the energy balance, up to the position of the UAV inside the atmosphere are defined. The mathematical model and the cost function are defined according to the mission constraints, flight mechanics and energy balance equations to obtain the energy optimal path of the UAV. An available optimal control technique is chosen up to the mathematical model and the cost function in order to make the optimization. Energy optimal path of the UAV is presented with the other useful results. Optimal route and the other results are criticized by checking them with the critical positions of the sun rays.

Control of the transition of laminar flow to turbulence would result in lower drag and reduced energy consumption in many engineering applications. A spectral state-space model of linearised plane Poiseuille flow with wall transpiration ac¬tuation and wall shear measurements is developed from the Navier-Stokes and continuity equations, and optimal controllers are synthesized and assessed in sim¬ulations of the flow. The polynomial-form collocation model with control by rate of change of wall-normal velocity is shown to be consistent with previous interpo¬lating models with control by wall-normal velocity. Previous methods of applying the Dirichlet and Neumann boundary conditions to Chebyshev series are shown to be not strictly valid. A partly novel method provides the best numerical behaviour after preconditioning. Two test cases representing the earliest stages of the transition are consid¬ered, and linear quadratic regulators (LQR) and estimators (LQE) are synthesized. Finer discretisation is required for convergence of estimators. A novel estimator covariance weighting improves estimator transient convergence. Initial conditions which generate the highest subsequent transient energy are calculated. Non-linear open- and closed-loop simulations, using an independently derived finite-volume Navier-Stokes solver modified to work in terms of perturbations, agree with linear simulations for small perturbations. Although the transpiration considered is zero net mass flow, large amounts of fluid are required locally. At larger perturbations the flow saturates. State feedback controllers continue to stabilise the flow, but estimators may overshoot and occasionally output feedback destabilises the flow. Actuation by simultaneous wall-normal and tangential transpiration is derived. There are indications that control via tangential actuation produces lower highest transient energy, although requiring larger control effort. State feedback controllers are also synthesized which minimise upper bounds on the highest transient energy and control effort. The performance of these controllers is similar to that of the optimal controllers.

Positive systems, which carry the well known property of confining the state, output, and/or input variables to the nonnegative orphant, are of great practical importance, as the nonnegative property occurs quite frequently in numerous applications and in nature. These type of systems frequently occur in hydrology where they are used to model natural and artificial networks of reservoirs; in biology where they are used to describe the transportation, accumulation, and drainage processes of elements and compounds like hormones, glucose, insulin, and metals; and in stocking, industrial, and engineering systems where chemical reactions, heat exchanges, and distillation processes take place. The interest of this dissertation is in two key problems: positive stabilization and the positive servomechanism problem. In particular, this thesis outlines the necessary and sufficient conditions for the stabilization of positive linear time-invariant (LTI) systems using state feedback control, along with providing an algorithm for constructing such a stabilizing regulator. Moreover, the results on stabilization also encompass the two problems of the positive separation principle and stabilization via observer design. The second, and most emphasized, problem of this dissertation considers the positive servomechanism problem for both single-input single-output (SISO) and multi-input multi-output (MIMO) stable positive LTI systems. The study of the positive servomechanism problem focuses on the tracking problem of nonnegative constant reference signals for unknown/known stable SISO/MIMO positive LTI systems with nonnegative unmeasurable/measurable constant disturbances via switching tuning clamping regulators (TcR), linear quadratic clamping regulators (LTQcR), and ending with MPC control. Finally, all theoretical results on the positive servomechanism problem are justified via numerous experimental results on a waterworks system.

The goal of this thesis is to synthesize believable motions of a character interacting with its surroundings and manipulating objects through physical contacts and forces. Human-like autonomous avatars are in increasing demand in areas such as entertainment, education, and health care. Yet modeling the basic human motor skills of locomotion and manipulation remains a long-standing challenge in animation research. The seemingly simple tasks of navigating an uneven terrain or grasping cups of different shapes involve planning with complex kinematic and physical constraints as well as adaptation to unexpected perturbations. Moreover, natural movements exhibit unique personal characteristics that are complex to model. Although motion capture technologies allow virtual actors to use recorded human motions in many applications, the recorded motions are not directly applicable to tasks involving interactions for two reasons. First, the acquired data cannot be easily adapted to new environments or different tasks goals. Second, acquisition of accurate data is still a challenge for fine scale object manipulations. In this work, we utilize data to create natural looking animations, and mitigate data deficiency with physics-based simulations and numerical optimizations. We develop algorithms based on a single reference motion for three types of control problems. The first problem focuses on motions without contact constraints. We use joint torque patterns identified from the captured motion to simulate responses and recovery of the same style under unexpected pushes. The second problem focuses on locomotion with foot contacts. We use contact forces to control an abstract dynamic model of the center of mass, which sufficiently describes the locomotion task in the input motion. Simulation of the abstract model under unexpected pushes or anticipated changes of the environment results in responses consistent with both the laws of physics and the style of the input. The third problem focuses on fine scale object manipulation tasks, in which accurate finger motions and contact information are not available. We propose a sampling method to discover contact relations between the hand and the object from only the gross motion of the wrists and the object. We then use the abundant contact constraints to synthesize detailed finger motions. The algorithm creates finger motions of various styles for a diverse set of object shapes and tasks, including ones that are not present at capture time. The three algorithms together control an autonomous character with dexterous hands to interact naturally with a virtual world. Our methods are general and robust across character structures and motion contents when testing on a wide variety of motion capture sequences and environments. The work in this thesis brings closer the motor skills of a virtual character to its human counterpart. It provides computational tools for the analysis of human biomechanics, and can potentially inspire the design of novel control algorithms for humanoid robots.

In this paper we examine the stabilization of LTI discrete-time systems with control input constraints in the form of saturation nonlinearities. This kind of constraint is usually introduced to simulate the effect of actuator limitations. Since global controllability can not be assumed in the presence of constrained control, the controllable regions and their characterizations are analyzed first. We present an efficient algorithm for finding controllable regions in terms of their boundary hyperplanes (inequality constraints). A previously open question about the exact number of irredundant boundary hyperplanes is also resolved here. The main result of this research is a time-optimal nonlinear controller which stabilizes the system on its controllable region. We give analgorithm for on-line computation of control which is also implementable for high-order systems. Simulation results show superior response even in the presence of disturbances.

This report presents optimal control methods integrated with hierarchical control framework to realize real-time collision-free optimal trajectories for motion control in kinematic chain manipulator (KCM) robot systems under dynamic environments. Recently, they have been increasingly used in applications where manipulators are required to interact with random objects and humans. As a result, more complex trajectory planning schemes are required. The main objective of this research is to develop new motion control strategies that can enable such robots to operate efficiently and optimally in such unknown and dynamic environments. Two direct optimal control methods: The direct collocation method and discrete mechanics for optimal control methods are investigated for solving the related constrained optimal control problem and the results are compared. Using the receding horizon control structure, open-loop sub-optimal trajectories are generated as real-time input to the controller as opposed to the predefined trajectory over the entire time duration. This, in essence, captures the dynamic nature of the obstacles. The closed-loop position controller is then engaged to span the robot end-effector along this desired optimal path by computing appropriate torque commands for the joint actuators. Employing a two-degree of freedom technique, collision-free trajectories and robot environment information are transmitted in real-time by the aid of a bidirectional connectionless datagram transfer. A hierarchical network control platform is designed to condition triggering of precedent activities between a dedicated machine computing the optimal trajectory and the real-time computer running a low-level controller. Experimental results on a 2-link planar robot are presented to validate the main ideas. Real-time implementation of collision-free workspace trajectory control is achieved for cases where obstacles are arbitrarily changing in the robot workspace.

In this paper we examine the stabilization of LTI discrete-time systems with control input constraints in the form of saturation nonlinearities. This kind of constraint is usually introduced to simulate the effect of actuator limitations. Since global controllability can not be assumed in the presence of constrained control, the controllable regions and their characterizations are analyzed first. We present an efficient algorithm for finding controllable regions in terms of their boundary hyperplanes (inequality constraints). A previously open question about the exact number of irredundant boundary hyperplanes is also resolved here. The main result of this research is a time-optimal nonlinear controller which stabilizes the system on its controllable region. We give analgorithm for on-line computation of control which is also implementable for high-order systems. Simulation results show superior response even in the presence of disturbances.

In recent years, Unmanned Aerial Vehicles (UAVs) have been used extensively in military conflict situations to execute intelligence, surveillance and reconnaissance missions. However, most of the current UAV platforms have limited collaborative capabilities, and consequently they must be controlled individually by operators on the ground. The purpose of the research presented in this thesis is to derive algorithms that can enable multiple UAVs to reason about the movements of multiple ground targets and autonomously coordinate their efforts in real-time to ensure that the targets do not escape. By improving the autonomy of multivehicle systems, the workload placed on the command and control operators is reduced significantly. To derive effective adversarial control algorithms, the adversarial scenario is modeled as a multiplayer differential game. However, due to the inherent computational complexity of multiplayer differential games, three less computationally demanding differential pursuit-evasion game-based algorithms are presented. The purpose of the algorithms is to quickly derive interception strategies for a team of autonomous vehicles. The algorithms are applicable to scenarios with different base assumptions, that is, the three algorithms are meant to complement one another by addressing different types of adversarial problems.

Modern power systems operate much closer to their stability limits than before. With the introduction of highly sensitive industrial and residential loads, the loss of system stability becomes increasingly costly. Reinforcing the power grid by installing additional transmission lines, creating more complicated meshed networks and increasing the voltage level are among the effective, yet expensive solutions. An alternative approach is to improve the performance of the existing power system components by incorporating more intelligent control techniques. This can be achieved in two ways: introducing intelligent local controllers for the existing components in the power network in order to employ their utmost capabilities, and implementing global intelligent schemes for optimizing the performance of multiple local controllers based on an objective function associated with the overall performance of the power system. Both these aspects are investigated in this thesis. In the first section, artificial neural networks are adopted for designing an optimal nonlinear controller for a static compensator (STATCOM) connected to a multimachine power system. The neurocontroller implementation is based on the adaptive critic designs (ACD) technique and provides an optimal control policy over the infinite horizon time of the problem. The ACD based neurocontroller outperforms a conventional controller both in terms of improving the power system dynamic stability and reducing the control effort required. The second section investigates the further improvement of the power system behavior by introducing an ACD based neurocontroller for hierarchical control of a multimachine power system. The proposed wide area controller improves the power system dynamic stability by generating optimal control signals as auxiliary reference signals for the synchronous generators automatic voltage regulators and the STATCOM line voltage controller. This multilevel hierarchical control scheme forces the different controllers throughout the power system to optimally respond to any fault or disturbance by reducing a predefined cost function associated with the power system performance.

This dissertation addresses design and analysis aspects of stochastic dynamical systems using Fokker-Planck equation (FPE). A new numerical methodology based on the partition of unity meshless paradigm is developed to tackle the greatest hurdle in successful numerical solution of FPE, namely the curse of dimensionality. A local variational form of the Fokker-Planck operator is developed with provision for h- and p- refinement. The resulting high dimensional weak form integrals are evaluated using quasi Monte-Carlo techniques. Spectral analysis of the discretized Fokker- Planck operator, followed by spurious mode rejection is employed to construct a new semi-analytical algorithm to obtain near real-time approximations of transient FPE response of high dimensional nonlinear dynamical systems in terms of a reduced subset of admissible modes. Numerical evidence is provided showing that the curse of dimensionality associated with FPE is broken by the proposed technique, while providing problem size reduction of several orders of magnitude. In addition, a simple modification of norm in the variational formulation is shown to improve quality of approximation significantly while keeping the problem size fixed. Norm modification is also employed as part of a recursive methodology for tracking the optimal finite domain to solve FPE numerically. The basic tools developed to solve FPE are applied to solving problems in nonlinear stochastic optimal control and nonlinear filtering. A policy iteration algorithm for stochastic dynamical systems is implemented in which successive approximations of a forced backward Kolmogorov equation (BKE) is shown to converge to the solution of the corresponding Hamilton Jacobi Bellman (HJB) equation. Several examples, including a four-state missile autopilot design for pitch control, are considered. Application of the FPE solver to nonlinear filtering is considered with special emphasis on situations involving long durations of propagation in between measurement updates, which is implemented as a weak form of the Bayes rule. A nonlinear filter is formulated that provides complete probabilistic state information conditioned on measurements. Examples with long propagation times are considered to demonstrate benefits of using the FPE based approach to filtering.