A Vector Matroid-Theoretic Approach in the Study of Structural Controllability Over F(z)

In this paper, the structural controllability of the systems over F(z) is studied using a new mathematical method-matroids. Firstly, a vector matroid is defined over F(z). Secondly, the full rank conditions of [sI-A|B] are derived in terms of the concept related to matroid theory, such as rank, base and union. Then the sufficient condition for the linear system and composite system over F(z) to be structurally controllable is obtained. Finally, this paper gives several examples to demonstrate that the married-theoretic approach is simpler than other existing approaches

Feedback Control Goes Wireless: Guaranteed Stability over Low-power Multi-hop Networks

Closing feedback loops fast and over long distances is key to emerging applications; for example, robot motion control and swarm coordination require update intervals of tens of milliseconds. Low-power wireless technology is preferred for its low cost, small form factor, and flexibility, especially if the devices support multi-hop communication. So far, however, feedback control over wireless multi-hop networks has only been shown for update intervals on the order of seconds. This paper presents a wireless embedded system that tames imperfections impairing control performance (e.g., jitter and message loss), and a control design that exploits the essential properties of this system to provably guarantee closed-loop stability for physical processes with linear time-invariant dynamics. Using experiments on a cyber-physical testbed with 20 wireless nodes and multiple cart-pole systems, we are the first to demonstrate and evaluate feedback control and coordination over wireless multi-hop networks for update intervals of 20 to 50 milliseconds.Comment: Accepted final version to appear in: 10th ACM/IEEE International Conference on Cyber-Physical Systems (with CPS-IoT Week 2019) (ICCPS '19), April 16--18, 2019, Montreal, QC, Canad

A vector matroid-theoretic approach in the study of structural controllability over F(z)

In this paper, the structural controllability of the systems over F(z) is studied using a new mathematical method-matroids. First, a vector matroid is de ned over F(z). Second, the full rank conditions of [sI AB](s 2 ) are derived in terms of the concept related to matroid theory, such as rank, base, and union. Then, the suf cient condition for the linear system and composite system over F(z) to be structurally controllable is obtained. Finally, this paper gives several examples to demonstrate that the married-theoretic approach is simpler than other existing approaches.This work was supported in part by the National Natural Science Fund under Grant 51307047 and Grant 51505475, in part by the Self-Determined and Innovative Research Funds of Wuhan University of Technology under Grant 2010-YB-12, in part by the Yingcai Project of CUMT, and in part by the National Research Foundation, South Africa under Grant RDYR160404161474.http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639am2017Electrical, Electronic and Computer Engineerin

Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (leaves 308-316).This thesis is devoted to nonlinear control, reduction, and classification of underactuated mechanical systems. Underactuated systems are mechanical control systems with fewer controls than the number of configuration variables. Control of underactuated systems is currently an active field of research due to their broad applications in Robotics, Aerospace Vehicles, and Marine Vehicles. The examples of underactuated systems include flexible-link robots, nobile robots, walking robots, robots on mobile platforms, cars, locomotive systems, snake-type and swimming robots, acrobatic robots, aircraft, spacecraft, helicopters, satellites, surface vessels, and underwater vehicles. Based on recent surveys, control of general underactuated systems is a major open problem. Almost all real-life mechanical systems possess kinetic symmetry properties, i.e. their kinetic energy does not depend on a subset of configuration variables called external variables. In this work, I exploit such symmetry properties as a means of reducing the complexity of control design for underactuated systems. As a result, reduction and nonlinear control of high-order underactuated systems with kinetic symmetry is the main focus of this thesis. By "reduction", we mean a procedure to reduce control design for the original underactuated system to control of a lowerorder nonlinear or mechanical system. One way to achieve such a reduction is by transforming an underactuated system to a cascade nonlinear system with structural properties. If all underactuated systems in a class can be transformed into a specific class of nonlinear systems, we refer to the transformed systems as the "normal form" of the corresponding class of underactuated systems. Our main contribution is to find explicit change of coordinates and control that transform several classes of underactuated systems, which appear in robotics and aerospace applications, into cascade nonlinear systems with structural properties that are convenient for control design purposes. The obtained cascade normal forms are three classes of nonlinear systems, namely, systems in strict feedback form, feedforward form, and nontriangular linear-quadratic form. The names of these three classes are due to the particular lower-triangular, upper-triangular, and nontriangular structure in which the state variables appear in the dynamics of the corresponding nonlinear systems. The triangular normal forms of underactuated systems can be controlled using existing backstepping and feedforwarding procedures. However, control of the nontriangular normal forms is a major open problem. We address this problem for important classes of nontriangular systems of interest by introducing a new stabilization method based on the solutions of fixed-point equations as stabilizing nonlinear state feedback laws. This controller is obtained via a simple recursive method that is convenient for implementation. For special classes of nontriangular nonlinear systems, such fixed-point equations can be solved explicitly ...by Reza Olfati-Saber.Ph.D

Nonlinear optimal control and its application to a two-wheeled robot

This research studies two advanced nonlinear optimal control techniques, i.e., the freezing control and the iteration scheme, and their associated applications, such as a single inverted pendulum (IP) on a cart system and a two-wheeled robot (TWR) system. These techniques are applied to stabilise the highly unstable nonlinear systems in the vertical upright position when facing different initial pitch angles. Different linear optimal controllers (linear quadratic regulator and linear quadratic Gaussian) and nonlinear optimal controllers are designed and applied to the models for concurrent control of all state variables. The controlled systems are tested in simulation and the best performing control design is eventually implemented on a robot prototype built with an educational kit – the LEGO EV3, after practical factors such as motor voltage limitation, gyro sensor drift and model uncertainties have been considered, analysed and dealt with. Simulations and experiments on the TWR robot prototype demonstrate the superiority of the nonlinear freezing optimal control technique, showing larger operation ranges of the robot pitch angle and better response performances (i.e., shorter rise time, less overshoot and reduced settling time) than the linear optimal control methods. In particular, a novel mixing method to create a new nonlinear model (Model AB) from two different models on the same physical prototype with an increased controllable region of the TWR system is introduced, for the first time, for the calculations of optimal feedback gains for the system. Significantly, the utilisation of this mixed model, combined with the nonlinear freezing controller, achieves true global control of the TWR, even from an initial pitch angle of 90° (i.e., the horizontal position), when a motor with a saturated voltage of 48V and nominal torque of 298 mNm is adopted in simulation tests. This is wider than the angle achievable from the primary model (Model A) and any other single feedback control method on TWR reported in the literature. Robustness tests when introducing model uncertainties by adding mass and height on the TWR also illustrate excellent control performances from the nonlinear optimal control in both simulations and hardware implementations

System analysis, modelling and control with polytopic linear models

This research investigates the suitability of Polytopic Linear Models (PLMs) for the analysis, modelling and control of a class of nonlinear dynamical systems. The PLM structure is introduced as an approximate and alternative description of nonlinear dynamical systems for the benefit of system analysis and controller design. The model structure possesses three properties that we would like to exploit. Firstly, a PLM is build upon a number of linear models, each one of which describes the system locally within a so-called operating regime. If these models are combined in an appropriate way, that is by taking operating point dependent convex combinations of parameter values that belong to the different linear models, then a PLM will result. Consequently, the parameter values of a PLM vary within a polytope, and the vertices of this polytope are the parameter values that belong to the different linear models. A PLM owes its name to this feature. Accordingly, a PLM can be interpreted on the basis of a regime decomposition. Secondly, since a PLM is based on several linear models, it is possible to describe the nonlinear system more globally compared to only a single linear model. Thirdly, it is demonstrated that, under the appropriate conditions, nonlinear systems can be approximated arbitrary close by a PLM, parametrized with a finite number of parameters. There will be given an upper bound for the number of required parameters, that is sufficient to achieve the prescribed desired accuracy of the approximation. An important motivation for considering PLMs rests on its structural similarities with linear models. Linear systems are well understood, and the accompanying system and control theory is well developed. Whether or not the control related system properties such as stability, controllability etcetera, are fulfilled, can be demonstrated by means of (often relatively simple) mathematical manipulations on the linear system’s parameterization. Controller design can often be automated and founded on the parameterization and the control objective. Think of control laws based on stability, optimality and so on. For nonlinear systems this is only partly the case, and therefore further development of system and control theory is of major importance. In view of the similarities between a linear model and a PLM, the expectation exists that one can benefit from (results and concepts of) the well developed linear system and control theory. This hypothesis is partly confirmed by the results of this study. Under the appropriate conditions, and through a simple analysis of the parametrization of a PLM, it is possible to establish from a control perspective relevant system properties. One of these properties is stability. Under the appropriate conditions stability of the PLM implies stability of the system. Moreover, a few easy to check conditions are derived concerning the notion of controllability and observability. It has to be noticed however, that these conditions apply to a class of PLMs of which the structure is further restricted. The determination of system properties from a PLM is done with the intention to derive a suitable model, and in particular to design a model based controller. This study describes several constructive methods that aim at building a PLM representation of the real system. On the basis of a PLM several control laws are formulated. The main objective of these control laws is to stabilize the system in a desired operating point. A few computerized stabilizing control designs, that additionally aim at optimality or robustness, are the outcome of this research. The entire route of representing a system with an approximate PLM, subsequently analyzing the PLM, and finally controlling the system by a PLM based control design is illustrated by means of several examples. These examples include experimental as well as simulation studies, and nonlinear dynamic (mechanical) systems are the subject of research

Observer-based robust fault estimation for fault-tolerant control

A control system is fault-tolerant if it possesses the capability of optimizing the system stability and admissible performance subject to bounded faults, complexity and modeling uncertainty. Based on this definition this thesis is concerned with the theoretical developments of the combination of robust fault estimation (FE) and robust active fault tolerant control (AFTC) for systems with both faults and uncertainties.This thesis develops robust strategies for AFTC involving a joint problem of on-line robust FE and robust adaptive control. The disturbances and modeling uncertainty affect the FE and FTC performance. Hence, the proposed robust observer-based fault estimator schemes are combined with several control methods to achieve the desired system performance and robust active fault tolerance. The controller approaches involve concepts of output feedback control, adaptive control, robust observer-based state feedback control. A new robust FE method has been developed initially to take into account the joint effect of both fault and disturbance signals, thereby rejecting the disturbances and enhancing the accuracy of the fault estimation. This is then extended to encompass the robustness with respect to modeling uncertainty.As an extension to the robust FE and FTC scheme a further development is made for direct application to smooth non-linear systems via the use of linear parameter-varying systems (LPV) modeling.The main contributions of the research are thus:- The development of a robust observer-based FE method and integration design for the FE and AFTC systems with the bounded time derivative fault magnitudes, providing the solution based on linear matrix inequality (LMI) methodology. A stability proof for the integrated design of the robust FE within the FTC system.- An improvement is given to the proposed robust observer-based FE method and integrated design for FE and AFTC systems under the existence of different disturbance structures.- New guidance for the choice of learning rate of the robust FE algorithm.- Some improvement compared with the recent literature by considering the FTC problem in a more general way, for example by using LPV modeling

On-line estimation approaches to fault-tolerant control of uncertain systems

This thesis is concerned with fault estimation in Fault-Tolerant Control (FTC) and as such involves the joint problem of on-line estimation within an adaptive control system. The faults that are considered are significant uncertainties affecting the control variables of the process and their estimates are used in an adaptive control compensation mechanism. The approach taken involves the active FTC, as the faults can be considered as uncertainties affecting the control system. The engineering (application domain) challenges that are addressed are: (1) On-line model-based fault estimation and compensation as an FTC problem, for systems with large but bounded fault magnitudes and for which the faults can be considered as a special form of dynamic uncertainty. (2) Fault-tolerance in the distributed control of uncertain inter-connected systems The thesis also describes how challenge (1) can be used in the distributed control problem of challenge (2). The basic principle adopted throughout the work is that the controller has two components, one involving the nominal control action and the second acting as an adaptive compensation for significant uncertainties and fault effects. The fault effects are a form of uncertainty which is considered too large for the application of passive FTC methods. The thesis considers several approaches to robust control and estimation: augmented state observer (ASO); sliding mode control (SMC); sliding mode fault estimation via Sliding Mode Observer (SMO); linear parameter-varying (LPV) control; two-level distributed control with learning coordination

Identification and control of dynamic systems using neural networks.

The aim of this thesis is to contribute in solving problems related to the on-line identification and control of unknown dynamic systems using feedforward neural networks. In this sense, this thesis presents new on-line learning algorithms for feedforward neural networks based upon the theory of variable structure system design, along with mathematical proofs regarding the convergence of solutions given by the algorithms; the boundedness of these solutions; and robustness features of the algorithms with respect to external perturbations affecting the neural networks' signals. In the thesis, the problems of on-line identification of the forward transfer operator, and the inverse transfer operator of unknown dynamic systems are also analysed, and neural networks-based identification schemes are proposed. These identification schemes are tested by computer simulations on linear and nonlinear unknown plants using both continuous-time and discrete-time versions of the proposed learning algorithms. The thesis reports about the direct inverse dynamics control problems using neural networks, and contributes towards solving these problems by proposing a direct inverse dynamics neural network-based control scheme with on-line learning capabilities of the inverse dynamics of the plant, and the addition of a feedback path that enables the resulting control scheme to exhibit robustness characteristics with respect to external disturbances affecting the output of the system. Computer simulation results on the performance of the mentioned control scheme in controlling linear and nonlinear plants are also included. The thesis also formulates a neural network-based internal model control scheme with on-line estimation capabilities of the forward transfer operator and the inverse transfer operator of unknown dynamic systems. The performance of this internal model control scheme is tested by computer simulations using a stable open-loop unknown plant with output signal corrupted by white noise. Finally, the thesis proposes a neural network-based adaptive control scheme where identification and control are simultaneously carried out