Sub-optimal boundary control of semilinear pdes using a dyadic perturbation observer

In this paper, we present a sub-optimal controller for semilinear partial differential equations, with partially known nonlinearities, in the dyadic perturbation observer (DPO) framework. The dyadic perturbation observer uses a two-stage perturbation observer to isolate the control input from the nonlinearities, and to predict the unknown parameters of the nonlinearities. This allows us to apply well established tools from linear optimal control theory to the controlled stage of the DPO. The small gain theorem is used to derive a condition for the robustness of the closed loop system

Robust Adaptive Boundary Control of Semilinear PDE Systems Using a Dyadic Controller

In this paper, we describe a dyadic adaptive control (DAC) framework for output tracking in a class of semilinear systems of partial differential equations with boundary actuation and unknown distributed nonlinearities. The DAC framework uses the linear terms in the system to split the plant into two virtual sub-systems, one of which contains the nonlinearities, while the other contains the control input. Full-plant-state feedback is used to estimate the unmeasured, individual states of the two subsystems as well as the nonlinearities. The control signal is designed to ensure that the controlled sub-system tracks a suitably modified reference signal. We prove well-posedness of the closed-loop system rigorously, and derive conditions for closed-loop stability and robustness using finite-gain L stability theory

Sub-Optimality of a Dyadic Adaptive Control Architecture

The dyadic adaptive control architecture evolved as a solution to the problem of designing control laws for nonlinear systems with unmatched nonlinearities, disturbances and uncertainties. A salient feature of this framework is its ability to work with infinite as well as finite dimensional systems, and with a wide range of control and adaptive laws. In this paper, we consider the case where a control law based on the linear quadratic regulator theory is employed for designing the control law. We benchmark the closed-loop system against standard linear quadratic control laws as well as those based on the state-dependent Riccati equation. We pose the problem of designing a part of the control law as a Nehari problem. We obtain analytical expressions for the bounds on the sub-optimality of the control law

Robust Adaptive Boundary Control of Semilinear PDE Systems Using a Dyadic Controller

In this paper, we describe a dyadic adaptive control (DAC) framework for output tracking in a class of semilinear systems of partial differential equations with boundary actuation and unknown distributed nonlinearities. The DAC framework uses the linear terms in the system to split the plant into two virtual sub-systems, one of which contains the nonlinearities, while the other contains the control input. Full-plant-state feedback is used to estimate the unmeasured, individual states of the two subsystems as well as the nonlinearities. The control signal is designed to ensure that the controlled sub-system tracks a suitably modified reference signal. We prove well-posedness of the closed-loop system rigorously, and derive conditions for closed-loop stability and robustness using finite-gain L stability theory

Controlled transitory or sustained gliding flight with dihedral angle and trailing flaps

A micro aerial vehicle capable of controlled transitory or sustained gliding flight. The vehicle includes a fuselage. A pair of articulated wings are forward of a center of gravity of the vehicle, the wings being articulated and having trailing edge flaps, and having actuators for controlling the dihedral angles of the wings and the flaps for effective yaw control across the flight envelope. The dihedral angles can be varied symmetrically on both wings to control the aircraft speed independently of the angle of attack and flight-path angle, while an asymmetric dihedral setting can be used to control yaw and the actuators control the dihedral settings of each wing independently. The aircraft lacks a vertical tail or other vertical stabilizer

Controlled transitory or sustained gliding flight with dihedral angle and trailing flaps

A micro aerial vehicle capable of controlled transitory or sustained gliding flight. The vehicle includes a fuselage. A pair of articulated wings are forward of a center of gravity of the vehicle, the wings being articulated and having trailing edge flaps, and having actuators for controlling the dihedral angles of the wings and the flaps for effective yaw control across the flight envelope. The dihedral angles can be varied symmetrically on both wings to control the aircraft speed independently of the angle of attack and flight-path angle, while an asymmetric dihedral setting can be used to control yaw and the actuators control the dihedral settings of each wing independently. The aircraft lacks a vertical tail or other vertical stabilizer

Flight Mechanics of a Tail-less Articulated Wing Aircraft

This paper explores the flight mechanics of a Micro Aerial Vehicle (MAV) without a vertical tail. The key to stability and control of such an aircraft lies in the ability to control the twist and dihedral angles of both wings independently. Specifically, asymmetric dihedral can be used to control yaw whereas antisymmetric twist can be used to control roll. It has been demonstrated that wing dihedral angles can regulate sideslip and speed during a turn maneuver. The role of wing dihedral in the aircraft's longitudinal performance has been explored. It has been shown that dihedral angle can be varied symmetrically to achieve limited control over aircraft speed even as the angle of attack and flight path angle are varied. A rapid descent and perching maneuver has been used to illustrate the longitudinal agility of the aircraft. This paper lays part of the foundation for the design and stability analysis of an agile flapping wing aircraft capable of performing rapid maneuvers while gliding in a constrained environment

Output feedback stabilization of linear PDEs with finite dimensional input-output maps and Kelvin-Voigt damping

In this paper, we consider systems of partial differential equations with a finite relative degree between the input and the output. In such systems, an output feedback controller can be constructed to regulate the output with the desired convergence properties. Although the zero dynamics are infinite dimensional, we show that the controller alters the boundary conditions in such a way that it leads to a predictable expansion in the stable operating envelope of the system. Moreover, the expansion of the stable envelope depends only on the boundary conditions and the structure of the PDE, and is independent of the system parameters. The methodology is extended to output tracking and time-varying forcing functions as well. The phenomenon investigated in the paper is quite unique to partial differential equations and without any parallel in systems of ODEs

Output feedback stabilization of linear PDEs with finite dimensional input-output maps and Kelvin-Voigt damping

In this paper, we consider systems of partial differential equations with a finite relative degree between the input and the output. In such systems, an output feedback controller can be constructed to regulate the output with the desired convergence properties. Although the zero dynamics are infinite dimensional, we show that the controller alters the boundary conditions in such a way that it leads to a predictable expansion in the stable operating envelope of the system. Moreover, the expansion of the stable envelope depends only on the boundary conditions and the structure of the PDE, and is independent of the system parameters. The methodology is extended to output tracking and time-varying forcing functions as well. The phenomenon investigated in the paper is quite unique to partial differential equations and without any parallel in systems of ODEs