Dissertation (Ph.D.)--Worcester Polytechnic Institute. / Keywords: Parametric optimization; nonlinear dynamics; functional equations; chemical reaction system dynamics; time scale multiplicity; robust control; nonlinear observers; invariant manifold; process monitoring; Lyapunov stability. Includes bibliographical references (leaves 92-98).

In this thesis we study the problem of stabilizing smooth embedded submanifolds in the state space of smooth, nonlinear, autonomous, deterministic control-affine systems. Our motivation stems from a realization that important applications, such as path following and synchronization, are best understood in the set stabilization framework. Instead of directly attacking the above set stabilization problem, we seek feedback equivalence of the given control system to a normal form that facilitates control design. The process of putting a control system into the normal form of this thesis is called transverse feedback linearization. When feasible, transverse feedback linearization allows for a decomposition of the nonlinear system into a “transverse” and a “tangential” subsystem relative to the goal submanifold. The dynamics of the transverse subsystem determine whether or not the system’s state approaches the submanifold. To ease controller design, we ask that the transverse subsystem be linear time-invariant and controllable. The dynamics of the tangential subsystem determine the motion on the submanifold. The main problem considered in this work, the local transverse feedback linearization problem (LTFLP), asks: when is such a decomposition possible near a point of the goal submanifold? This problem can equivalently be viewed as that of finding a system output with a well-defined relative degree, whose zero dynamics manifold coincides with the goal submanifold. As such, LTFLP can be thought of as the inverse problem to input-output feedback linearization. We present checkable, necessary and sufficient conditions for the existence of a local coordinate and feedback transformation that puts the given system into the desired normal form. A key ingredient used in the analysis is the new notion of transverse controllability indices of a control system with respect to a set. When the goal submanifold is diffeomorphic to Euclidean space, we present sufficient conditions for feedback equivalence in a tubular neighbourhood of it. These results are used to develop a technique for solving the path following problem. When applied to this problem, transverse feedback linearization decomposes controller design into two separate stages: transversal control design and tangential control design. The transversal control inputs are used to stabilize the path, and effectively generate virtual constraints forcing the system’s output to move along the path. The tangential inputs are used to control the motion along the path. A useful feature of this twostage approach is that the motion on the set can be controlled independently of the set stabilizing control law. The effectiveness of the proposed approach is demonstrated experimentally on a magnetically levitated positioning system. Furthermore, the first satisfactory solution to a problem of longstanding interest, path following for the planar/vertical take-off and landing aircraft model to the unit circle, is presented. This solution, developed in collaboration with Luca Consolini and Mario Tosques at the University of Parma, is made possible by taking a set stabilization point of view.

In this thesis we study the problem of stabilizing smooth embedded submanifolds in the state space of smooth, nonlinear, autonomous, deterministic control-affine systems. Our motivation stems from a realization that important applications, such as path following and synchronization, are best understood in the set stabilization framework. Instead of directly attacking the above set stabilization problem, we seek feedback equivalence of the given control system to a normal form that facilitates control design. The process of putting a control system into the normal form of this thesis is called transverse feedback linearization. When feasible, transverse feedback linearization allows for a decomposition of the nonlinear system into a “transverse” and a “tangential” subsystem relative to the goal submanifold. The dynamics of the transverse subsystem determine whether or not the system’s state approaches the submanifold. To ease controller design, we ask that the transverse subsystem be linear time-invariant and controllable. The dynamics of the tangential subsystem determine the motion on the submanifold. The main problem considered in this work, the local transverse feedback linearization problem (LTFLP), asks: when is such a decomposition possible near a point of the goal submanifold? This problem can equivalently be viewed as that of finding a system output with a well-defined relative degree, whose zero dynamics manifold coincides with the goal submanifold. As such, LTFLP can be thought of as the inverse problem to input-output feedback linearization. We present checkable, necessary and sufficient conditions for the existence of a local coordinate and feedback transformation that puts the given system into the desired normal form. A key ingredient used in the analysis is the new notion of transverse controllability indices of a control system with respect to a set. When the goal submanifold is diffeomorphic to Euclidean space, we present sufficient conditions for feedback equivalence in a tubular neighbourhood of it. These results are used to develop a technique for solving the path following problem. When applied to this problem, transverse feedback linearization decomposes controller design into two separate stages: transversal control design and tangential control design. The transversal control inputs are used to stabilize the path, and effectively generate virtual constraints forcing the system’s output to move along the path. The tangential inputs are used to control the motion along the path. A useful feature of this twostage approach is that the motion on the set can be controlled independently of the set stabilizing control law. The effectiveness of the proposed approach is demonstrated experimentally on a magnetically levitated positioning system. Furthermore, the first satisfactory solution to a problem of longstanding interest, path following for the planar/vertical take-off and landing aircraft model to the unit circle, is presented. This solution, developed in collaboration with Luca Consolini and Mario Tosques at the University of Parma, is made possible by taking a set stabilization point of view.

No description available.

The complexity of large industrial engineering systems such as chemical plants has continued to increase over the years. As a result, flexible control systems are required to handle variation in the operating conditions. In the classical approach, first the plant model should be linearized at the nominal operating point and then, a robust controller should be designed for the resulting linear system. However, the performance of a controller designed by this method deteriorates when operation deviates from the nominal point. When the distance between the operating region and the nominal operating point increases, this performance degradation may lead to instability. In the context of traditional linear control, one method to solve this problem is to consider the impact of nonlinearity as “uncertainty” around the nominal model and design a controller such that the desired performance is satisfied for all possible systems in the uncertainty set. As the size of uncertainty increases, conservatism occurs and at some point, it becomes impossible to design a controller that can provide satisfactory performance. One of the methods proposed to overcome the aforementioned shortcomings is the so-called Multiple Model approach. Using Multi-Models, local designs are performed for various operating regions and membership functions or a supervisory switching scheme is used to interpolate or switch among the controllers as the operating point moves among local regions. Since the Multiple Model method is a natural extension of the linear control method, it inherits some benefits of linear control such as simplicity of analysis and implementation. However, all these benefits are valid locally. For example, the multiple model method may be vulnerable when global stability is taken into account. The core objective of this thesis is to develop new tools to study stability of closed-loop nonlinear systems controlled by local controllers in order to improve design of multiple model control systems. For example, one of the aims of this work is to investigate how to determine the region where closed loop system is stable. A secondary objective is to study the effects of the exogenous signals on stability of such systems. / Controls

In this thesis we study the stabilization of closed sets for passive nonlinear control systems, developing necessary and sufficient conditions under which a passivity-based feedback stabilizes a given goal set. The development of this result takes us to a journey through the so-called reduction problem: given two nested invariant sets G1 subset of G2, and assuming that G1 enjoys certain stability properties relative to G2, under what conditions does G1 enjoy the same stability properties with respect to the whole state space? We develop reduction principles for stability, asymptotic stability, and attractivity which are applicable to arbitrary closed sets. When applied to the passivity-based set stabilization problem, the reduction theory suggests a new definition of detectability which is geometrically appealing and captures precisely the property that the control system must possess in order for the stabilization problem to be solvable. The reduction theory and set stabilization results developed in this thesis are used to solve a distributed coordination problem for a group of unicycles, whereby the vehicles are required to converge to a circular formation of desired radius, with a specific ordering and spacing on the circle.

In this thesis we study the stabilization of closed sets for passive nonlinear control systems, developing necessary and sufficient conditions under which a passivity-based feedback stabilizes a given goal set. The development of this result takes us to a journey through the so-called reduction problem: given two nested invariant sets G1 subset of G2, and assuming that G1 enjoys certain stability properties relative to G2, under what conditions does G1 enjoy the same stability properties with respect to the whole state space? We develop reduction principles for stability, asymptotic stability, and attractivity which are applicable to arbitrary closed sets. When applied to the passivity-based set stabilization problem, the reduction theory suggests a new definition of detectability which is geometrically appealing and captures precisely the property that the control system must possess in order for the stabilization problem to be solvable. The reduction theory and set stabilization results developed in this thesis are used to solve a distributed coordination problem for a group of unicycles, whereby the vehicles are required to converge to a circular formation of desired radius, with a specific ordering and spacing on the circle.

No description available.

Networked predictive control is a new research method for Networked Control Systems (NCS), which is able to handle network-induced problems such as time-delay, data dropouts, packets disorders, etc. while stabilizing the closed-loop system. This work is an extension and complement of networked predictive control methodology. There is always present model uncertainties or physical nonlinearity in the process of NCS. Therefore, it makes the study of the robust control of NCS and that of networked nonlinear control system (NNCS) considerably important. This work studied the following three problems: the robust control of networked predictive linear control systems, the control scheme for networked nonlinear control systems (NNCS) and the robust control of NNCS. The emphasis is on stability analysis and the design of robust control. This work adapted the two control schemes, namely, the time-driven and the event driven predictive controller for the implementation of NCS. It studied networked linear control systems and networked nonlinear control systems. Firstly, time-driven predictive controller is used to compensate for the networked-induced problems of a class of networked linear control systems while robustly stabilizing the closed-loop system. Secondly, event-driven predictive controller is applied to networked linear control system and NNCS and the work goes on to solve the robust control problem. The event-driven predictive controller brings great benefits to NCS implementation: it makes the synchronization of the clocks of the process and the controller unnecessary and it avoids measuring the exact values of the individual components of the network induced time-delay. This work developed the theory of stability analysis and robust synthesis of NCS and NNCS. The robust stability analysis and robust synthesis of a range of different system configurations have been thoroughly studied. A series of methods have been developed to handle the stability analysis and controller design for NCS and NNCS. The stability of the closed-loop of NCS has been studied by transforming it into that of a corresponding augmented system. It has been proved that if some equality conditions are satisfied then the closed-loop of NCS is stable for an upper-bounded random time delay and data dropouts. The equality conditions can be incorporated into a sub-optimal problem. Solving the sub-optimal problem gives the controller parameters and thus enables the synthesis of NCS. To simplify the calculation of solving the controller parameters, this thesis developed the relationship between networked nonlinear control system and a class of uncertain linear feedback control system. It proves that the controller parameters of some types of networked control system can be equivalently derived from the robust control of a class of uncertain linear feedback control system. The methods developed in this thesis for control design and robustness analysis have been validated by simulations or experiments.

No / An adaptive iterative learning control approach is proposed for a class of single-input single-output uncertain nonlinear systems with completely unknown control gain. Unlike the ordinary iterative learning controls that require some preconditions on the learning gain to stabilize the dynamic systems, the adaptive iterative learning control achieves the convergence through a learning gain in a Nussbaum-type function for the unknown control gain estimation. This paper shows that all tracking errors along a desired trajectory in a finite time interval can converge into any given precision through repetitive tracking. Simulations are carried out to show the validity of the proposed control method.