Event-based global stabilization of linear systems via a saturated linear controller

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Event-triggered synchronization of saturated lur’e type systems

This dissertation addresses the problem of master-slave synchronization of nonlinear discrete-time Lur’e systems subject to input saturation via event-triggered control (ETC) techniques. Synchronization, which is considered a remarkable property in the physics literature specially when chaotic systems are under investigation, is achieved through the stabilization of the error between the states of the master and the slave system. Regarding the Lur’e type nonlinearity, two different cases are studied along this work: generic slope-restricted state-dependent nonlinearity and piecewise-affine function. In the ETC paradigm, the control signal is updated aperiodically only after the occurrence of an event, which is generated according to a triggering criterion that depends on the evaluation of a triggering function. In the emulation-based design, a synchronization error feedback controller is given a priori and the task is to compute the event generator parameters ensuring performance and closed-loop stability. On the other hand, in the co-design approach the event generator and the control law are simultaneously designed. Theoretical results are obtained for three types of event-triggered mechanism (ETM), namely: static, dynamic and relaxed. In the last case, practical synchronization conditions are derived as form of ultimately boundedness stability. In order to tune the parameters of the event-based strategy, optimization problems are formulated aiming to reduce the number of control signal updates (number of events) with respect to a time-triggered implementation. Numerical simulations are presented to illustrate the application of the proposed methods.Esta dissertação aborda o problema de sincronização mestre-escravo de sistemas Lur’e não lineares de tempo discreto sujeitos à saturação de entrada via técnicas de controle baseado em eventos. A sincronização, que é considerada uma propriedade importante na literatura de Física especialmente quando sistemas caóticos são investigados, é alcançada através da estabilização do erro entre os estados do mestre e do sistema escravo. Em relação à não linearidade do tipo Lur’e, dois casos diferentes são estudados ao longo do trabalho: não linearidade genérica dependente do estado e restrita em inclinação e função afim por partes. No paradigma de controle baseado em eventos (ETC), o sinal de controle é atualizado aperiodicamente apenas após a ocorrência de um evento, que é gerado de acordo com um critério de disparo que depende da avaliação de uma função de disparo. No projeto baseado em emulação, um controlador por realimentação do erro de sincronização é dado a priori e a tarefa é calcular os parâmetros do gerador de eventos garantindo desempenho e estabilidade em malha fechada. Na abordagem de co-design, o gerador de eventos e a lei de controle são projetados simultaneamente. Resultados teóricos são obtidos para três tipos de mecanismo de geração de eventos (ETM), nomeadamente: estático, dinâmico e relaxado. Neste último caso, condições de sincronização prática são derivadas como uma forma de estabilidade ultimamente limitada. Para sintonizar os parâmetros da estratégia baseada em eventos, problemas de otimização são formulados visando reduzir o número de atualizações do sinal de controle (número de eventos) em relação a uma implementação time-triggered. Simulações numéricas são apresentadas para ilustrar a aplicação dos métodos propostos

Stabilizing solution and parameter dependence of modified Algebraic Riccati Equation with application to discrete-time input-saturated network synchronization

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Adaptive Control of Systems with Quantization and Time Delays

This thesis addresses problems relating to tracking control of nonlinear systems in the presence of quantization and time delays. Motivated by the importance in areas such as networked control systems (NCSs) and digital systems, where the use of a communication network in NCS introduces several constraints to the control system, such as the occurrence of quantization and time delays. Quantization and time delays are of both practical and theoretical importance, and the study of systems where these issues arises is thus of great importance. If the system also has parameters that vary or are uncertain, this will make the control problem more complicated. Adaptive control is one tool to handle such system uncertainty. In this thesis, adaptive backstepping control schemes are proposed to handle uncertainties in the system, and to reduce the effects of quantization. Different control problems are considered where quantization is introduced in the control loop, either at the input, the state or both the input and the state. The quantization introduces difficulties in the controller design and stability analysis due to the limited information and nonlinear characteristics, such as discontinuous phenomena. In the thesis, it is analytically shown how the choice of quantization level affects the tracking performance, and how the stability of the closed-loop system equilibrium can be achieved by choosing proper design parameters. In addition, a predictor feedback control scheme is proposed to compensate for a time delay in the system, where the inputs are quantized at the same time. Experiments on a 2-degrees of freedom (DOF) helicopter system demonstrate the different developed control schemes.publishedVersio

Event-based Global Stabilization of Linear Systems via a Saturated Linear Controller

SUMMARY This paper investigates the problem of event-based linear control of systems subject to input saturation. First, for discrete-time systems with neutrally stable or double-integrator dynamics, novel event-triggered control algorithms with non-quadratic event-triggering conditions are proposed to achieve global stabilization. Compared with the quadratic event-triggering conditions, the non-quadratic ones can further reduce unnecessary control updates for the input-saturated systems. Furthermore, for continuous-time systems with neutrally stable or double-integrator dynamics, since that an inherent lower bound of the inter-event time does not exist for systems subject to input saturation, novel event-triggered control algorithms with an appropriately selected minimum inter-event time are proposed to achieve global stabilization. Finally, numerical examples are provided to illustrate the theoretical results

Event-triggered Control For Semi-global Stabilisation Of Systems With Actuator Saturation

This paper investigates the problem of event-triggered control for semi-global stabilisation of null controllable systems subject to actuator saturation. First, for a continuous-time system, novel event-triggered low-gain control algorithms based on Riccati equations are proposed to achieve semi-global stabilisation. The algebraic Riccati equation with a low-gain parameter is utilised to design both the event-triggering condition and the linear controller; a minimum inter-event time based on the Riccati ordinary differential equation is set a priori to exclude the Zeno behaviour. In addition, the high-low-gain techniques are utilised to extend the semi-global results to event-based global stabilisation. Furthermore, for a discrete-time system, novel low-gain and high–low-gain control algorithms are proposed to achieve event-triggered stabilisation. Numerical examples are provided to illustrate the theoretical results.postprin

Coordination of multi-agent systems: stability via nonlinear Perron-Frobenius theory and consensus for desynchronization and dynamic estimation.

This thesis addresses a variety of problems that arise in the study of complex networks composed by multiple interacting agents, usually called multi-agent systems (MASs). Each agent is modeled as a dynamical system whose dynamics is fully described by a state-space representation. In the first part the focus is on the application to MASs of recent results that deal with the extensions of Perron-Frobenius theory to nonlinear maps. In the shift from the linear to the nonlinear framework, Perron-Frobenius theory considers maps being order-preserving instead of matrices being nonnegative. The main contribution is threefold. First of all, a convergence analysis of the iterative behavior of two novel classes of order-preserving nonlinear maps is carried out, thus establishing sufficient conditions which guarantee convergence toward a fixed point of the map: nonnegative row-stochastic matrices turns out to be a special case. Secondly, these results are applied to MASs, both in discrete and continuous-time: local properties of the agents' dynamics have been identified so that the global interconnected system falls into one of the above mentioned classes, thus guaranteeing its global stability. Lastly, a sufficient condition on the connectivity of the communication network is provided to restrict the set of equilibrium points of the system to the consensus points, thus ensuring the agents to achieve consensus. These results do not rely on standard tools (e.g., Lyapunov theory) and thus they constitute a novel approach to the analysis and control of multi-agent dynamical systems. In the second part the focus is on the design of dynamic estimation algorithms in large networks which enable to solve specific problems. The first problem consists in breaking synchronization in networks of diffusively coupled harmonic oscillators. The design of a local state feedback that achieves desynchronization in connected networks with arbitrary undirected interactions is provided. The proposed control law is obtained via a novel protocol for the distributed estimation of the Fiedler vector of the Laplacian matrix. The second problem consists in the estimation of the number of active agents in networks wherein agents are allowed to join or leave. The adopted strategy consists in the distributed and dynamic estimation of the maximum among numbers locally generated by the active agents and the subsequent inference of the number of the agents that took part in the experiment. Two protocols are proposed and characterized to solve the consensus problem on the time-varying max value. The third problem consists in the average state estimation of a large network of agents where only a few agents' states are accessible to a centralized observer. The proposed strategy projects the dynamics of the original system into a lower dimensional state space, which is useful when dealing with large-scale systems. Necessary and sufficient conditions for the existence of a linear and a sliding mode observers are derived, along with a characterization of their design and convergence properties

Robust and Cooperative Formation Control of Nonlinear Multi-Agent Systems

Compared with the conventional approach of controlling autonomous systems individually, building up a cooperative multi-agent structure is more robust and efficient for both research and industrial purposes. Among the many subbranches of multiagent systems, formation control has been a popular research direction due to its close connection with complex missions such as spacecraft clustering and intelligent transportation. Hence, this thesis focuses on providing new robust formation control algorithms for first-order, second-order and mixed-order nonlinear multi-agent systems to construct and maintain stable system structure in practical scenarios. System uncertainties and external disturbances are commonly seen factors that could negatively affect the formation tracking precision. Among the many popular tools of uncertainty estimation, the implementation of approaches including neural network adaptive estimation and observer-based approximation are discussed in this thesis. Regarding the neural-based approximation process, different neural network structures including Chebyshev neural network, radial basis function neural network, twolayer artificial neural network and three-layer artificial neural network are tested and implemented. The merits and drawbacks of each network design in the field of control is then analysed. Apart from that, this thesis also offers detailed comparison between the cooperative tuning approach and the observer-based tuning approach regarding the neural network structure to find their corresponding applicable scenarios. To ensure the safety of the formation control algorithms, the issues of obstacle avoidance and inter-agent collision avoidance are both considered. Although the method of constructing artificial potential fields is a popular approach in both the field of path planning and motion control, few have discussed the effect of the inter-agent communication on the collision avoidance scheme. For the obstacle avoiding scenarios, the passive correcting behaviour of individual agent is defined and investigated. A new algorithm is then introduced to modify the reference of individual agents to act as the mitigation. The issue of insufficient information accessibility is then discussed for multi-agent systems with a static and uncompleted communication topology. A distance-based communication topology is proposed to create necessary information exchange channel for unconnected agent pairs that are close enough. The actuator saturation issue is also considered for both first-order multi-agent systems and second-order multi-agent systems to increase the practicality of the formation control schemes. Apart from restricting the amplitudes of the control input, the effect of the input coupling phenomenon is investigated. The oscillation of states brought by the coupled and saturated control input is then summarised as the reverse effect. To attenuate the state oscillation, the methods of developing control input regulation algorithms and employing auxiliary compensator are discussed and validated. The last technical problem to discuss is the hierarchical control scheme. The issue of how to decouple the inter-agent communication and the motion dynamics is discussed for both unified-order and mixed-order multi-agent systems. By using a hierarchical formation control structure, the inter-agent communication process is considered based on a group of virtual agents with ideal characteristics, which can significantly reduce the complexity of the system design. Adaptive hierarchical control schemes are then proposed and validated for both unified-order and mixed-order multi-agent systems through the examples of a multi-drone system and a multiple omni-directional robot system, respectively.Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 202