Alexander Leonessa

Nonlinear system stabilization via hierarchical switching control

A nonlinear control system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear control strategy is developed that stabilizes a given nonlinear system by stabilizing a collection of nonlinear controlled subsystems. The switching nonlinear controller architecture is designed based on a generalized lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized system equilibria. The proposed framework provides a rigorous alternative to designing gain-scheduled feedback controllers and guarantees local and global closed-loop system stability for general nonlinear systems.

A Lyapunov-based adaptive control framework for discrete-time non-linear systems with exogenous disturbances

A direct adaptive non-linear control framework for discrete-time multivariable non-linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non-linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the plant. In the case of bounded energy ℓ 2 disturbances the proposed approach guarantees a non-expansivity constraint on the closed-loop input–output map. Finally, three illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.

Direct Adaptive Tracking Control of Quadrotor Aerial Vehicles

This paper presents a novel adaptive control algorithm solving the trajectory tracking problem for quadrotor aerial vehicles. A model reference approach is used, such that the vehicle tracks the trajectory of a reference system, which itself tracks a specified desired trajectory. The control law is derived using a backstepping procedure. A technique derived from dynamic surface control is used to simplify the expression of the obtained control algorithm, with no significant loss in terms of performance. Proof of stability is obtained using Lyapunov theory. Results from numerical simulations illustrate the performance of the obtained controller.Copyright

Solution of aircraft inverse problems by local optimization

A feedforward control technique is presented for the determination of the input/output map associated to the inverse problem of the simulated motion of an aircraft. The procedure is particularly suitable in the redundant cases, which are reduced to nominal ones by imposing physically reasonable constraints on the state variables through a local optimization algorithm. Comparisons with already available solutions are shown together with some significant applications.

Globally stabilizing controllers for multi-mode axial flow compressors via equilibria-dependent Lyapunov functions

Compressor aerodynamic instabilities can have adverse effects on compression system performance. In this paper we develop a multimode model for rotating stall and surge in axial flow compression systems that lends itself to the application of nonlinear control design. Using Lyapunov stability theory, a novel nonlinear globally stabilizing control law based on equilibria-dependent Lyapunov functions with converging domains of attraction is developed. The multimode model is used to show that the second and higher-order disturbance velocity potential harmonics in the flow equations strongly interact with the first harmonic during stall inception and must be accounted for in the control-system design processes.

Design of a small, multi-purpose, autonomous surface vessel

The continued development of unmanned underwater vehicles (UUVs) has also brought about new complex missions that the vehicles must perform. Such missions include mine counter measures (MCM), underwater system inspection, route surveying, and oceanographic sampling. More recently, a growing need for missions to be performed by multiple vehicles has emerged. An important task in being able to perform such a multi-vehicle operation is for each vehicles position and orientation to be precisely known and updated to onboard sensors, in real-time, maximizing the surreptitious capabilities and quality of the data. Without this high quality navigation data, the mission performance is poor and little confidence can be given to the results. Currently, UUVs can use inertial navigation systems, coupled with Doppler velocity loggers (DVLs), for navigation. However, inertial navigation systems are large, high-power, and expensive, while DVLs have limited bottom-tracking range. Some UUVs are equipped with global positioning systems (GPS), however the vehicle must surface to establish either a RF or satellite communication link. A solution, to increase the accuracy of a vehicles position is the use of a surface vessel, notably an autonomous surface vessel (ASV). One such vehicle is currently under development by the Department of Ocean Engineering at Florida Atlantic University. The ASV is being built upon an existing surface vessel navigation and control package, a vertical communication and US BL navigation system derived from the FAU-Dual Purpose Acoustic Modem and 3D motion compensation algorithm that utilizes a low cost GPS/IMU/COMPASS/ADCP system. The accurate positioning system onboard the ASV uses an acoustic uplink system between the ASV and UUVs below, to provide the UUVs with the navigation information needed for a successful mission. The development of the ASV presents several problems such as controlling the vehicle, so that it can operate autonomously, gathering the sensor information, and passing the information to the UUVs below, in real-time. The control of the ASV can be divided into software and hardware components. On the software side, Simulink, part of Matlab, allows a user to develop a controller for the ASV by using a friendly graphical user interface (GUI). Matlab also allows for a host to target communication, either through RS-232 or TCP/IP, by using a toolbox called xPC Target. This setup allows the controller to be developed and compiled on a personal computer, the host, and then downloaded to a PC-104 stack inside the ASV, the target. Simulink blocks can also be created to control the flow of information from the sensors to the PC-104 stack, whether the sensors are connected via an AD/DA board or through serial ports using RS-232 communication. While the ASV is designed to give UUVs a more accurate position without installing expensive equipment on each of the UUVs, it can also be used so that a user can monitor the progress of a mission. The communication from the user to the ASV is also accomplished using xPC Targets host to target communication using a wireless link, and from the ASV to the UUVs using an acoustic modem. By using a surface vehicle, the mission performance of a group of UUVs can be improved by providing accurate and up-to-date positioning as well as by allowing a user to change the mission on the fly, without having to recover the UUVs.

Neural Network Model Reference Adaptive Control of Marine Vehicles

A neural network model reference adaptive controller for trajectory tracking of nonlinear systems is developed. The proposed control algorithm uses a single layer neural network that bypasses the need for information about the system’s dynamic structure and characteristics and provides portability. Numerical simulations are performed using nonlinear dynamic models of marine vehicles. Results are presented for two separate vehicle models, an autonomous surface vehicle and an autonomous underwater vehicle, to demonstrate the controller performance in terms of tuning, robustness, and tracking.

Adaptive tracking for nonlinear systems with control constraints

A direct adaptive nonlinear tracking control framework for multivariable nonlinear uncertain systems with actuator amplitude and rate saturation constraints is developed. To guarantee asymptotic stability of the closed-loop tracking error dynamics in the face of amplitude and rate saturation constraints, the adaptive control signal to a given reference system is modified to effectively robustify the error dynamics to the saturation constraints. An illustrative numerical example is provided to demonstrate the efficacy of the propose approach.

Nonlinear system stabilization via stability-based switching

A nonlinear control-system design framework predicated on a stability-based switching controller architecture parameterized over a set of system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions a hierarchical nonlinear control strategy is developed that stabilizes a given nonlinear system by stabilizing a collection of nonlinear controlled subsystems. The switching nonlinear controller architecture is designed based on a generalized lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized system equilibria. The proposed framework provides a rigorous alternative to designing gain scheduled feedback controllers and guarantees local and global closed-loop system stability for general nonlinear systems.

Adaptive nonlinear tracking control of an underactuated nonminimum phase model of a marine vehicle using ultimate boundedness

In this paper, an adaptive nonlinear tracking controller for an underactuated nonminimum phase model of a marine vehicle is derived. The result is kept flexible enough, throughout its derivation, to be applicable to a large variety of marine vehicles. The characteristics of the dynamic model are such that solving the tracking problem is non-trivial. Specifically, we consider a propulsion system composed of either a thruster and a rudder, or a vectored thruster, which provides two independent control commands and three degrees of freedom, with an overall unstable zero-dynamics. The tracking problem dealt with in this paper is solved using a backstepping approach, as well as a technique derived from dynamic surface control theory and the notion of ultimate boundedness. The tracking problem is first solved assuming full knowledge of the geometric and hydrodynamic coefficients appearing in the vehicles model. The control law is then modified into an adaptive one. Computer simulations are presented to illustrate the performances of the final control algorithm.