Nonlinear Control and Estimation with General Performance Criteria

This dissertation is concerned with nonlinear systems control and estimation with general performance criteria. The purpose of this work is to propose general design methods to provide systematic and effective design frameworks for nonlinear system control and estimation problems. First, novel State Dependent Linear Matrix Inequality control approach is proposed, which is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. By solving a state dependent linear matrix inequality at each time step, the sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this dissertation unify existing results on nonlinear quadratic regulator, Hinfinity and positive real control. Secondly, an H2-Hinfinity State Dependent Riccati Equation controller is proposed in this dissertation. By solving the generalized State Dependent Riccati Equation, the optimal control solution not only achieves the optimal quadratic regulation performance, but also has the capability of external disturbance reduction. Numerically efficient algorithms are developed to facilitate effective computation. Thirdly, a robust multi-criteria optimal fuzzy control of nonlinear systems is proposed. To improve the optimality and robustness, optimal fuzzy control is proposed for nonlinear systems with general performance criteria. The Takagi-Sugeno fuzzy model is used as an effective tool to control nonlinear systems through fuzzy rule models. General performance criteria have been used to design the controller and the relative weighting matrices of these criteria can be achieved by choosing different coefficient matrices. The optimal control can be achieved by solving the LMI at each time step. Lastly, since any type of controller and observer is subject to actuator failures and sensors failures respectively, novel robust and resilient controllers and estimators are also proposed for nonlinear stochastic systems to address these failure problems. The effectiveness of the proposed control and estimation techniques are demonstrated by simulations of nonlinear systems: the inverted pendulum on a cart and the Lorenz chaotic system, respectively

Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control

Repetitive Control Systems: Stability and Periodic Tracking beyond the Linear Case

Periodic output regulation studies the problem of steering the output of a dynamical system along a periodic reference. This is a fundamental control problem which has a great interest from a practical point of view, since most industrial activities oriented to production are based on tasks with a cyclic nature. Nevertheless this interest extends rapidly to a theoretical framework once the problem is formalized. Mathematical tools coming from different fields can be used to provide an insight to the output regulation problem in different ways. An important control technique that is classically used to achieve periodic out- put regulation si called Repetitive Control (RC) and this thesis focuses on (but is not limited to) the development and the analysis with novel tools of RC schemes. Periodic output regulation for nonlinear dynamical systems is a challenging topic. This thesis, besides of providing consistent and practically useful results in the linear case, introduces promising tools dealing with the nonlinear periodic output regulation problem, whose solution is presented for particular classes of systems. The contribution of this research is mainly theoretical and relies on the use of mathematical tools like infinite-dimensional port-Hamiltonian systems and autonomous discrete-time systems to study stability and tracking properties in RC schemes and periodic regulation in general. Differently from the classical continuous-time formulation of RC, internal model arguments are not directly used is this work to study asymptotic tracking. In this way the linear case can be reinterpreted under a new light and novel strategies to consistently attack the nonlinear case are presented. Furthermore an application-oriented chapter with experimental results is present which describes the possibility of implementing a discrete-time RC scheme involving trajectory generation and non-minimum phase systems

Distributed resilient filtering of large-scale systems with channel scheduling

summary:This paper addresses the distributed resilient filtering for discrete-time large-scale systems (LSSs) with energy constraints, where their information are collected by sensor networks with a same topology structure. As a typical model of information physics systems, LSSs have an inherent merit of modeling wide area power systems, automation processes and so forth. In this paper, two kinds of channels are employed to implement the information transmission in order to extend the service time of sensor nodes powered by energy-limited batteries. Specifically, the one has the merit of high reliability by sacrificing energy cost and the other reduces the energy cost but could result in packet loss. Furthermore, a communication scheduling matrix is introduced to govern the information transmission in these two kind of channels. In this scenario, a novel distributed filter is designed by fusing the compensated neighboring estimation. Then, two matrix-valued functions are derived to obtain the bounds of the covariance matrices of one-step prediction errors and the filtering errors. In what follows, the desired gain matrices are analytically designed to minimize the provided bounds with the help of the gradient-based approach and the mathematical induction. Furthermore, the effect on filtering performance from packet loss is profoundly discussed and it is claimed that the filtering performance becomes better when the probability of packet loss decreases. Finally, a simulation example on wide area power systems is exploited to check the usefulness of the designed distributed filter

Unconventional Signals Oscillators

Dizertační práce se zabývá elektronicky nastavitelnými oscilátory, studiem nelineárních vlastností spojených s použitými aktivními prvky a posouzením možnosti vzniku chaotického signálu v harmonických oscilátorech. Jednotlivé příklady vzniku podivných atraktorů jsou detailně diskutovány. V doktorské práci je dále prezentováno modelování reálných fyzikálních a biologických systémů vykazujících chaotické chování pomocí analogových elektronických obvodů a moderních aktivních prvků (OTA, MO-OTA, CCII ±, DVCC ±, atd.), včetně experimentálního ověření navržených struktur. Další část práce se zabývá možnostmi v oblasti analogově – digitální syntézy nelineárních dynamických systémů, studiem změny matematických modelů a odpovídajícím řešením. Na závěr je uvedena analýza vlivu a dopadu parazitních vlastností aktivních prvků z hlediska kvalitativních změn v globálním dynamickém chování jednotlivých systémů s možností zániku chaosu v důsledku parazitních vlastností použitých aktivních prvků.The doctoral thesis deals with electronically adjustable oscillators suitable for signal generation, study of the nonlinear properties associated with the active elements used and, considering these, its capability to convert harmonic signal into chaotic waveform. Individual platforms for evolution of the strange attractors are discussed in detail. In the doctoral thesis, modeling of the real physical and biological systems exhibiting chaotic behavior by using analog electronic building blocks and modern functional devices (OTA, MO-OTA, CCII±, DVCC±, etc.) with experimental verification of proposed structures is presented. One part of theses deals with possibilities in the area of analog–digital synthesis of the nonlinear dynamical systems, the study of changes in the mathematical models and corresponding solutions. At the end is presented detailed analysis of the impact and influences of active elements parasitics in terms of qualitative changes in the global dynamic behavior of the individual systems and possibility of chaos destruction via parasitic properties of the used active devices.