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

On stochastic stabilization in sample-and-hold sense

Sample-and-hold refers to implementation of control policies in a digital mode, in which the dynamical system is treated continuous, whereas the control actions are held constant in predefined time steps. In such a setup, special attention should be paid to the sample-to-sample behavior of the involved Lyapunov function. This paper extends on the stochastic stability results specifically to address for the sample-and-hold mode. We show that if a Markov policy stabilizes the system in a suitable sense, then it also practically stabilizes it in the sample-and-hold sense. This establishes a bridge from an idealized continuous application of the policy to its digital implementation. The central result applies to dynamical systems described by stochastic differential equations driven by the standard Brownian motion. Generalizations are discussed, including the case of non-smooth Lyapunov functions for systems driven by bounded noise. A brief overview of bounded noise models is given. An experimental study of mobile robot parking under influence of different noise levels and sampling times is provided

LTV stochastic systems stabilization with large and variable input delay

In this paper we propose a solution to the state-feedback and output-feedback stabilization problem for linear time-varying stochastic systems affected by arbitrarily large and variable input delay. It is proved that under the proposed controller the underlying stochastic process is exponentially centered and mean square bounded. The solution is given through a set of delay differential equations with cardinality proportional to the delay bound. The predictor is based on the semigroup generated by the closed-loop system in absence of delay, and its computation is described by a numerically reliable and robust method. In the deterministic case this method generates the same optimal trajectories as in the delay-less case

Robust finite-time fault estimation for stochastic nonlinear systems with Brownian motions

Motivated by real-time monitoring and fault diagnosis for complex systems, the presented paper aims to develop effective fault estimation techniques for stochastic nonlinear systems subject to partially decoupled unknown input disturbances and Brownian motions. The challenge of the research is how to ensure the robustness of the proposed fault estimation techniques against stochastic Brownian perturbations and additive process disturbances, and provide a rigorous mathematical proof of the finite-time input-to-stabilization of the estimation error dynamics. In this paper, stochastic input-to-state stability and finite-time stochastic input-to-state stability of stochastic nonlinear systems are firstly investigated based on Lyapunov theory, leading to simple and straightforward criteria. By integrating augmented system approach, unknown input observer technique, and finite-time stochastic input-to-state stability theory, a highly-novel fault estimation technique is proposed. The convergence of the estimation error with respect to un-decoupled unknown inputs and Brownian perturbations is proven by using the derived stochastic input-to-state stability and finite-time stochastic input-to-state stability theorems. Based on linear matrix inequality technique, the robust observer gains can be obtained in order to achieve both stability and robustness of the error dynamic. Finally, the effectiveness of the proposed fault estimation techniques is demonstrated by the detailed simulation studies using a robotic system and a numerical example