On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

A Passivity-based Nonlinear Observer and a Semi-global Separation Principle

The main topics of this dissertation are the observer problem and its applications to the output feedback stabilization for nonlinear systems. The observer problem refers to the general problem of reconstructing the state of a system only with the input and output information of the system. While the problem has been solved in depth for linear systems, the nonlinear counterpart has not yet been wholly solved in the general sense. Motivated by this fact, we pursue the general method of observer construction in order to provide much larger classes of systems with the design method. In particular, we propose a new approach to the observer problem via the passivity, which is therefore named the passivity framework for state observer. It begins by considering the observer problem as the static output feedback stabilization for a suitably defined error dynamics. We then make use of the output feedback passification which is the recent issue in the literature, to the design of observer as a tool for static output feedback stabilization. The proposed framework includes the precise definition of passivity-based state observer (PSO), the design scheme of it, and the redesign technique for a given PSO to have the robust property to the measurement disturbances in the sense of input-to-state stability. Moreover, it is also shown that the framework of PSO provides the unified viewpoint to the earlier works on the nonlinear observer and generalizes them much more. As well as the new notion of PSO, two other methods of observer design are proposed for the special classes of nonlinear systems. They are, in fact, a part of or an extension of the design scheme of PSO. However, compared to the general design scheme of PSO, these methods specifically utilize the particular structure of the system, which therefore lead to more explicit techniques for the observer design. The first one we present for the special cases is the semi-global observer, which extends with much flexibility the earlier designs of Gauthiers high-gain observer. By introducing the saturation function into the observer design, several difficulties to construct the high-gain observer (e.g. peaking phenomenon, etc.) are effectively eliminated. As the second result, we propose a novel design method for the nonlinear observer, which may be regarded as the observer backstepping since the design is recursively carried out similarly to the well-known backstepping control design. It enlarges the class of systems, for which the observer can be designed, to the systems that have the non-uniformly observable modes and detectable modes as well as uniformly observable modes. The other topic of the dissertation is the output feedback stabilization of nonlinear systems. Our approach to the problem is the state feedback control law plus the state observer, therefore, in view of the so-called separation principle. The benefits of the approach via separation principle is that the designs of state feedback law and observer are completely separated so that any state feedback and any observer can be combined to yield the output feedback controller, which is well-known for linear systems. Unfortunately, it has been pointed out that the separation principle for nonlinear systems does not hold in the global sense, and thus the alternative semiglobal separation principle (i.e., the separation principle on a bounded region rather than on the global region) has been studied so far. In this dissertation, we continue that direction of research and establish the semi-global separation principle that shares the more common properties with the linear one than the earlier works do. In particular, it is shown that, for general nonlinear systems, when a state feedback control stabilizes an equilibrium point with a certain bounded region of attraction, it is also stabilized by an output feedback controller with arbitrarily small loss of the region, under uniform observability. The proposed output feedback controller has the dynamic order n which is the same as the order of the plant, which is the essential difference from the earlier works. As a consequence, the nonlinear separation principle enables the state observer of the dissertation to be used in conjunction with any state feedback for the output feedback stabilization, although the observer problem in itself is worthwhile in several practical situations

Output-feedback IDA stabilisation of an SMIB system using a TCSC

Interconnection and damping assignment (IDA) passivity-based control (PBC) is currently a well-known viable alternative for solving regulation control problems of a wide class of nonlinear systems. However, a distinctive feature that, in spite of its appearance under several applications, has not been exhaustively exploited, is the flexibility that this technique exhibits for designing output-feedback controllers (OFCs). The purpose of this article is to illustrate this attractive characteristic by approaching the (practically important) case study given by the improvement of the transient stability properties of power systems. The particular system composed by a synchronous generator connected to an infinite bus via a thyristor controlled series capacitor is considered. Two OFCs are presented, one that does not involve the unmeasurable state and another that, although including this state, presents some input-to-state stability properties that allow for establishing a sort of separation principle concerning an observer-based structure for the closed-loop system. The advantages of both controllers are illustrated by numerical simulations when a three-phase short circuit at the generator bus is induced.Postprint (published version

Reinforcement Learning Based Output-Feedback Control of Nonlinear Nonstrict Feedback Discrete-Time Systems with Application to Engines

A novel reinforcement-learning based output-adaptive neural network (NN) controller, also referred as the adaptive-critic NN controller, is developed to track a desired trajectory for a class of complex nonlinear discrete-time systems in the presence of bounded and unknown disturbances. The controller includes an observer for estimating states and the outputs, critic, and two action NNs for generating virtual, and actual control inputs. The critic approximates certain strategic utility function and the action NNs are used to minimize both the strategic utility function and their outputs. All NN weights adapt online towards minimization of a performance index, utilizing gradient-descent based rule. A Lyapunov function proves the uniformly ultimate boundedness (UUB) of the closed-loop tracking error, weight, and observer estimation. Separation principle and certainty equivalence principles are relaxed; persistency of excitation condition and linear in the unknown parameter assumption is not needed. The performance of this adaptive critic NN controller is evaluated through simulation with the Daw engine model in lean mode. The objective is to reduce the cyclic dispersion in heat release by using the controller

Near Optimal Output-Feedback Control of Nonlinear Discrete-Time Systems in Nonstrict Feedback Form with Application to Engines

A novel reinforcement-learning based output-adaptive neural network (NN) controller, also referred as the adaptive-critic NN controller, is developed to track a desired trajectory for a class of complex nonlinear discrete-time systems in the presence of bounded and unknown disturbances. The controller includes an observer for estimating states and the outputs, critic, and two action NNs for generating virtual, and actual control inputs. The critic approximates certain strategic utility function and the action NNs are used to minimize both the strategic utility function and their outputs. All NN weights adapt online towards minimization of a performance index, utilizing gradient-descent based rule. A Lyapunov function proves the uniformly ultimate boundedness (UUB) of the closed-loop tracking error, weight, and observer estimation. Separation principle and certainty equivalence principles are relaxed; persistency of excitation condition and linear in the unknown parameter assumption is not needed. The performance of this controller is evaluated on a spark ignition (SI) engine operating with high exhaust gas recirculation (EGR) levels and experimental results are demonstrated

Estimation and control of some classes of dynamical systems with application to biological wastewater treatment

It is well-known that there are no general approaches for observer and controller design for nonlinear systems. Instead, focus is placed upon design for classes of systems. On the other hand, a wide variety of dynamical systems belong to the class of state-affine systems. Amongst these are biological wastewater treatment processes, which are essential in order to prevent pollution in the environment and prevent disease in the consumption of recycled water. An interesting aspect found in biological wastewater treatment systems, and many typical industrial processes, are time-delays. In almost all systems there are time-delays and nonlinearities and it is not surprising that time-delay and nonlinear systems have received a great deal of attention in mathematics and control engineering. This project introduces new methodologies for the design of controllers and observers for a class of state-affine systems and a class of linear time-delay systems. Firstly, new observable and controllable canonical forms are introduced. These are then used to establish new controller and observer design methodologies for a class of state¬affine systems. In particular, an adaptive observer design is established. The methodologies are simple since they are based upon linear techniques. Secondly, a full-state controller and a separation principle are established for a class of single-input single-output linear time-delay systems. The designs are based on a new stability criterion and are derived from first principles. Finally, the new observer design methodology for the class of state-affine systems is used to produce observers for the estimation of biomass concentration in a biological wastewater treatment bioreactor. The observers are applied in theory and in simulation, where a full and a partial knowledge of the kinetic rate of reaction of biomass are considered. In addition, the performances are shown both in the absence and in the presence of measurement noise for a variety of influent flow characteristics.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Estimation and control of some classes of dynamical systems with application to biological wastewater treatment

It is well-known that there are no general approaches for observer and controller design for nonlinear systems. Instead, focus is placed upon design for classes of systems. On the other hand, a wide variety of dynamical systems belong to the class of state-affine systems. Amongst these are biological wastewater treatment processes, which are essential in order to prevent pollution in the environment and prevent disease in the consumption of recycled water. An interesting aspect found in biological wastewater treatment systems, and many typical industrial processes, are time-delays. In almost all systems there are time-delays and nonlinearities and it is not surprising that time-delay and nonlinear systems have received a great deal of attention in mathematics and control engineering. This project introduces new methodologies for the design of controllers and observers for a class of state-affine systems and a class of linear time-delay systems. Firstly, new observable and controllable canonical forms are introduced. These are then used to establish new controller and observer design methodologies for a class of state¬affine systems. In particular, an adaptive observer design is established. The methodologies are simple since they are based upon linear techniques. Secondly, a full-state controller and a separation principle are established for a class of single-input single-output linear time-delay systems. The designs are based on a new stability criterion and are derived from first principles. Finally, the new observer design methodology for the class of state-affine systems is used to produce observers for the estimation of biomass concentration in a biological wastewater treatment bioreactor. The observers are applied in theory and in simulation, where a full and a partial knowledge of the kinetic rate of reaction of biomass are considered. In addition, the performances are shown both in the absence and in the presence of measurement noise for a variety of influent flow characteristics.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

The Separation Principle in Stochastic Control, Redux

Over the last 50 years a steady stream of accounts have been written on the separation principle of stochastic control. Even in the context of the linear-quadratic regulator in continuous time with Gaussian white noise, subtle difficulties arise, unexpected by many, that are often overlooked. In this paper we propose a new framework for establishing the separation principle. This approach takes the viewpoint that stochastic systems are well-defined maps between sample paths rather than stochastic processes per se and allows us to extend the separation principle to systems driven by martingales with possible jumps. While the approach is more in line with "real-life" engineering thinking where signals travel around the feedback loop, it is unconventional from a probabilistic point of view in that control laws for which the feedback equations are satisfied almost surely, and not deterministically for every sample path, are excluded.Comment: 23 pages, 6 figures, 2nd revision: added references, correction

A State-Space Approach to Parametrization of Stabilizing Controllers for Nonlinear Systems

A state-space approach to Youla-parametrization of stabilizing controllers for linear and nonlinear systems is suggested. The stabilizing controllers (or a class of stabilizing controllers for nonlinear systems) are characterized as (linear/nonlinear) fractional transformations of stable parameters. The main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems. The parametrized output feedback controllers have separation structures. A separation principle follows from the construction. This machinery allows the parametrization of stabilizing controllers to be conducted directly in state space without using coprime-factorization